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Publications of Lawrence N. Virgin    :chronological  alphabetical  combined listing:

%% Books   
@book{fds282326,
   Author = {Wagg, D and Virgin, L},
   Title = {Exploiting Nonlinear Behavior in Structural
             Dynamics},
   Pages = {280 pages},
   Publisher = {SPRINGER},
   Year = {2012},
   Month = {April},
   ISBN = {3709111862},
   Abstract = {- Control and exploitation of nonlinearity in smart
             structures. The articles in this volume give an overview and
             introduction to nonlinear phenomena in structural
             dynamics.},
   Key = {fds282326}
}

@book{fds346276,
   Author = {Virgin, L and Wagg, D},
   Title = {Preface},
   Volume = {536},
   Year = {2012},
   Month = {January},
   Key = {fds346276}
}

@book{fds282328,
   Author = {Virgin, LN},
   Title = {Vibration of axially loaded structures},
   Pages = {1-359},
   Publisher = {Cambridge University Press},
   Year = {2007},
   Month = {January},
   ISBN = {9780521880428},
   url = {http://dx.doi.org/10.1017/CBO9780511619236},
   Abstract = {© Lawrence N. Virgin 2007 and Cambridge University Press,
             2010. This book concerns the vibration and the stability of
             slender structural components. The loss of stability of
             structures is an important aspect of structural mechanics
             and is presented here in terms of dynamic behavior. A
             variety of structural components are analyzed with a view to
             predict their response to various (primarily axial) loading
             conditions. A number of different techniques are presented,
             with experimental verification from the laboratory. The book
             presents methods by which the combined effects of vibration
             and buckling on various structures can be
             assessed.},
   Doi = {10.1017/CBO9780511619236},
   Key = {fds282328}
}

@book{fds282327,
   Author = {Virgin, LN},
   Title = {Introduction to Experimental Nonlinear Dynamics A Case Study
             in Mechanical Vibration},
   Pages = {272 pages},
   Publisher = {Cambridge University Press},
   Year = {2000},
   Month = {March},
   ISBN = {0521662869},
   Abstract = {This work uses an extended case study--an experiment in
             mechanical vibration--to introduce and explore the subject
             of nonlinear behavior and chaos from an engineering
             perspective.},
   Key = {fds282327}
}

@book{fds71110,
   Author = {L.N. Virgin},
   Title = {Introduction to Experimental Nonlinear Dynamics},
   Publisher = {Cambridge University Press},
   Year = {2000},
   Key = {fds71110}
}


%% Papers Published   
@article{fds341418,
   Author = {Virgin, LN and Susan Guan and Y and Plaut, RH},
   Title = {Curved structures that can elastically snap-through},
   Journal = {Conference Proceedings of the Society for Experimental
             Mechanics Series},
   Volume = {1},
   Pages = {275-277},
   Year = {2019},
   Month = {January},
   ISBN = {9783319742793},
   url = {http://dx.doi.org/10.1007/978-3-319-74280-9_28},
   Abstract = {© The Society for Experimental Mechanics, Inc. 2019. Curved
             structures, such as beams, arches and panels are capable of
             exhibiting snap-through buckling behavior when loaded
             laterally. However, the propensity to maintain a stable
             snapped-through equilibrium position (in addition to the
             nominally unloaded equilibrium configuration) after the load
             is removed depends on certain geometric properties. A number
             of clamped arches are used to illustrate the relation
             between geometry (thickness, span, initial deflection) and
             the corresponding equilibrium configuration(s). The finite
             element method and an elastica analysis compare well with a
             number of specifically-shaped arches produced using a 3D
             printer.},
   Doi = {10.1007/978-3-319-74280-9_28},
   Key = {fds341418}
}

@article{fds321792,
   Author = {Knight, JD and Virgin, LN and Plaut, RH},
   Title = {Predicting Critical Speeds in Rotordynamics: A New
             Method},
   Journal = {Journal of Physics: Conference Series},
   Volume = {744},
   Number = {1},
   Pages = {012155-012155},
   Publisher = {IOP Publishing},
   Year = {2016},
   Month = {October},
   url = {http://dx.doi.org/10.1088/1742-6596/744/1/012155},
   Abstract = {© Published under licence by IOP Publishing Ltd. In
             rotordynamics, it is often important to be able to predict
             critical speeds. The passage through resonance is generally
             difficult to model. Rotating shafts with a disk are analyzed
             in this study, and experiments are conducted with one and
             two disks on a shaft. The approach presented here involves
             the use of a relatively simple prediction technique, and
             since it is a black-box data-based approach, it is suitable
             for in-situ applications.},
   Doi = {10.1088/1742-6596/744/1/012155},
   Key = {fds321792}
}

@article{fds321793,
   Author = {Virgin, LN and Wiebe, R and Spottswood, SM and Beberniss,
             T},
   Title = {Inferring unstable equilibrium configurations from
             experimental data},
   Journal = {Journal of Physics: Conference Series},
   Volume = {744},
   Number = {1},
   Pages = {012090-012090},
   Publisher = {IOP Publishing},
   Year = {2016},
   Month = {October},
   url = {http://dx.doi.org/10.1088/1742-6596/744/1/012090},
   Abstract = {© Published under licence by IOP Publishing Ltd. This
             research considers the structural behavior of slender,
             mechanically buckled beams and panels of the type commonly
             found in aerospace structures. The specimens were deflected
             and then clamped in a rigid frame in order to exhibit
             snap-through. That is, the initial equilibrium and the
             buckled (snapped-through) equilibrium configurations both
             co-existed for the given clamped conditions. In order to
             transit between these two stable equilibrium configurations
             (for example, under the action of an externally applied
             load), it is necessary for the structural component to pass
             through an intermediate unstable equilibrium configuration.
             A sequence of sudden impacts was imparted to the system, of
             various strengths and at various locations. The goal of this
             impact force was to induce relatively intermediate-sized
             transients that effectively slowed-down in the vicinity of
             the unstable equilibrium configuration. Thus, monitoring the
             velocity of the motion, and specifically its slowing down,
             should give an indication of the presence of an equilibrium
             configuration, even though it is unstable and not amenable
             to direct experimental observation. A digital image
             correlation (DIC) system was used in conjunction with an
             instrumented impact hammer to track trajectories and
             statistical methods used to infer the presence of unstable
             equilibria in both a beam and a panel.},
   Doi = {10.1088/1742-6596/744/1/012090},
   Key = {fds321793}
}

@article{fds321796,
   Author = {Virgin, LN and Plaut, RH and Cartee, EV},
   Title = {The effect of gravity on a slender loop structure},
   Journal = {Conference Proceedings of the Society for Experimental
             Mechanics Series},
   Volume = {1},
   Pages = {185-190},
   Publisher = {Springer International Publishing},
   Year = {2016},
   Month = {January},
   ISBN = {9783319152202},
   url = {http://dx.doi.org/10.1007/978-3-319-15221-9_16},
   Abstract = {© The Society for Experimental Mechanics, Inc. 2016. The
             deformation and vibration of vertical, highly flexible loops
             are investigated primarily from an experimental perspective.
             Both upright and hanging loops are considered with a small
             clamped length. The effects of self-weight on the loop
             static deformation and lowest frequency for in-plane
             symmetric vibrations are determined. Good agreement is
             attained between some theoretical results (based on an
             inextensible elastica model) and the experimental data. An
             interesting phenomenon of adjacent, co-existing solutions is
             also described.},
   Doi = {10.1007/978-3-319-15221-9_16},
   Key = {fds321796}
}

@article{fds321797,
   Author = {Detroux, T and Noël, JP and Kerschen, G and Virgin,
             LN},
   Title = {Experimental study of isolated response curves in a
             two-degree-of-freedom nonlinear system},
   Journal = {Conference Proceedings of the Society for Experimental
             Mechanics Series},
   Volume = {1},
   Pages = {229-235},
   Publisher = {Springer International Publishing},
   Year = {2016},
   Month = {January},
   ISBN = {9783319297385},
   url = {http://dx.doi.org/10.1007/978-3-319-29739-2_21},
   Abstract = {© The Society for Experimental Mechanics, Inc. 2016. In the
             present paper, the observation and characterization of
             isolated response curves (IRCs) are experimentally reported
             in the case of a nonlinear system consisting of two masses
             sliding on an horizontal guide. Transverse springs are
             attached to one mass to provide the nonlinear restoring
             force, and a harmonic motion of the complete system is
             imposed by prescribing the displacement of their supports.
             The existence of an IRC is related to a 3:1 internal
             resonance between the two modes of the system. The observed
             IRC is studied in detached and merged conditions using
             swept-sine excitations and system perturbations.},
   Doi = {10.1007/978-3-319-29739-2_21},
   Key = {fds321797}
}

@article{fds321798,
   Author = {Nöel, JP and Detroux, T and Masset, L and Kerschen, G and Virgin,
             LN},
   Title = {Isolated response curves in a base-excited,
             two-degree-of-freedom, nonlinear system},
   Journal = {Proceedings of the Asme Design Engineering Technical
             Conference},
   Volume = {6},
   Publisher = {ASME},
   Year = {2015},
   Month = {January},
   ISBN = {9780791857168},
   url = {http://dx.doi.org/10.1115/DETC2015-46106},
   Abstract = {© Copyright 2015 by ASME. In the present paper, isolated
             response curves in a nonlinear system consisting of two
             masses sliding on a horizontal guide are examined.
             Transverse springs are attached to one mass to provide the
             nonlinear restoring force, and a harmonic motion of the
             complete system is imposed by prescribing the displacement
             of their supports. Numerical simulations are carried out to
             study the conditions of existence of isolated solutions,
             their bifurcations, their merging with the main response
             branch and their basins of attraction. This is achieved
             using tools including nonlinear normal modes, energy
             balance, harmonic balance-based continuation and bifurcation
             tracking, and global analysis.},
   Doi = {10.1115/DETC2015-46106},
   Key = {fds321798}
}

@article{fds282340,
   Author = {Virgin, LN and Waite, JJ and Wiebe, R},
   Title = {Co-existing responses in a harmonically-excited nonlinear
             structural system},
   Journal = {Conference Proceedings of the Society for Experimental
             Mechanics Series},
   Volume = {2},
   Pages = {1-9},
   Publisher = {Springer International Publishing},
   Year = {2014},
   Month = {January},
   ISBN = {9783319045214},
   ISSN = {2191-5644},
   url = {http://dx.doi.org/10.1007/978-3-319-04522-1_1},
   Abstract = {A key feature of many nonlinear dynamical systems is the
             presence of co-existing solutions, i.e, nonlinear systems
             are often sensitive to initial conditions. While there have
             been many studies to explore this behavior from a numerical
             perspective, in which case it is trivial to prescribe
             initial conditions (for example using a regular grid), this
             is more challenging from an experimental perspective. This
             paper will discuss the basins of attraction in a simple
             mechanical experiment. By applying both small and large
             stochastic perturbations to steady-state behavior, it is
             possible to interrogate the initial condition space and
             map-out basins of attraction as system parameters are
             changed. This tends to provide a more complete picture of
             possible behavior than conventional bifurcation diagrams
             with their focus on local steady-state behavior. © The
             Society for Experimental Mechanics, Inc.
             2014.},
   Doi = {10.1007/978-3-319-04522-1_1},
   Key = {fds282340}
}

@article{fds282368,
   Author = {Virgin, LN and Plaut, RH},
   Title = {Some non-smooth dynamical systems in offshore
             mechanics},
   Journal = {Lecture Notes in Applied and Computational
             Mechanics},
   Volume = {44},
   Pages = {259-268},
   Publisher = {Springer Berlin Heidelberg},
   Year = {2009},
   Month = {December},
   ISBN = {9783642006289},
   ISSN = {1613-7736},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000267756000026&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Doi = {10.1007/978-3-642-00629-6_26},
   Key = {fds282368}
}

@article{fds321799,
   Author = {Santillan, ST and Virgin, LN and Plaut, RH},
   Title = {Nonlinear two-dimensional elastica analysis of subsea
             risers},
   Journal = {7th European Conference on Structural Dynamics, Eurodyn
             2008},
   Year = {2008},
   Month = {January},
   ISBN = {9780854328826},
   Abstract = {This paper models two configurations of flexible risers and
             pipelines as slender elastica structures. The theoretical
             formulation leads to a type of nonlinear boundary value
             problem that can be solved numerically given appropriate
             boundary conditions. The offsetting effects of gravity and
             buoyancy are included in the analysis. These forces can
             provide considerable axial loading (as can thermal changes)
             and hence stability (buckling) is a major concern. Initial
             studies are based on the planar problem. A free-vibration
             analysis is also conducted for small-amplitude oscillations
             about various deflected equilibrium configurations in terms
             of natural frequencies and corresponding mode shapes [1].
             Energy dissipation and fluid forces are a key issue in the
             forced problem, especially when large deformations are
             involved [2, 3]. Knowledge of free vibration behavior is a
             vital prerequisite in understanding the response of these
             types of structures in practice [4].},
   Key = {fds321799}
}

@article{fds282331,
   Author = {Nichols, JM and Moniz, L and Todd, MD and Trickey, ST and Seaver, M and Nichols, CJ and Virgin, LN},
   Title = {Detection of fastener preload loss in a hybrid
             composite-to-metal bolted joint},
   Journal = {Structural Health Monitoring 2003: From Diagnostics and
             Prognostics to Structural Health Management Proceedings of
             the 4th International Workshop on Structural Health
             Monitoring, Iwshm 2003},
   Pages = {623-633},
   Year = {2003},
   Month = {January},
   ISBN = {1932078207},
   Abstract = {Copyright © 2003 by DEStech Publications, Inc. All right
             reserved. In this work we present two novel nonlinear time
             series analysis techniques-nonlinear cross prediction error
             and chaotic amplification of attractor distortion-for
             detecting preload loss in a hybrid metal-to-composite bolted
             joint. The two techniques involve imposing a chaotic
             steady-state on the structure and analyzing features from
             the resulting reconstructed attractors. The joint preload is
             controlled from a "fully tight" 10200 Ibf preload condition
             to complete failure (no preload), and numerous vibration
             tests are performed at discrete increments in that range.
             The two nonlinear techniques are compared to a linear
             autoregressive model fit for detection capability.},
   Key = {fds282331}
}

@article{fds282355,
   Author = {VIRGIN, LAWRENCE and TRICKEY, STEPHEN and DOWELL,
             EARL},
   Title = {STABILITY TRANSITIONS IN A NONLINEAR AIRFOIL},
   Journal = {Proceedings of the 5th Experimental Chaos
             Conference},
   Pages = {335-344},
   Publisher = {World Scientific},
   Year = {2001},
   Month = {April},
   ISBN = {9789810245610},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000172293200033&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Doi = {10.1142/9789812811516_0033},
   Key = {fds282355}
}

@article{fds343777,
   Author = {Slade, KN and Virgin, LN and Tinker, ML},
   Title = {Mode splitting in an inflated polyimide cylinder with
             circumferential asymmetry},
   Journal = {19th Aiaa Applied Aerodynamics Conference},
   Year = {2001},
   Month = {January},
   url = {http://dx.doi.org/10.2514/6.2001-1411},
   Abstract = {In the past, a good deal of the research on the feasibility
             of inflatable structures for space applications has focused
             on the behavior of inflated cylinders. In many cases,
             especially in theoretical and numerical studies, the
             cylinder has been assumed to be uniform across its
             circumference. In the case of many thin-film structures,
             this assumption does not hold. These structures often
             contain at least one seam that produces localized changes in
             film thickness and stiffness. Experimental evidence of the
             effect of this seam in the form of mode splitting and the
             accompanying divergence of repeated eigenvalues was seen
             during modal testing of a polyimide cylinder at NASA
             Marshall Space Flight Center (MSFC). This paper will examine
             the effect of asymmetry through the inspection of
             experimental data and the use of finite element methods. ©
             2001 by the American Institute of Aeronautics and
             Astronautics, Inc.},
   Doi = {10.2514/6.2001-1411},
   Key = {fds343777}
}

@article{fds282364,
   Author = {Virgin, LN and Begley, CJ},
   Title = {Nonlinear features in the dynamics of an impact-friction
             oscillator},
   Journal = {Aip Conference Proceedings},
   Volume = {502},
   Pages = {469-475},
   Publisher = {AMER INST PHYSICS},
   Editor = {Broomhead, DS and Luchinskaya, EA and McClintock, PVE and Mullin,
             T},
   Year = {2000},
   Month = {January},
   ISBN = {1-56396-915-7},
   ISSN = {0094-243X},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000086079200065&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Key = {fds282364}
}

@article{fds321800,
   Author = {Conner, MD and Tang, DM and Dowell, EH and Virgin,
             LN},
   Title = {Nonlinear aeroelasticity of an airfoil with control surface
             freeplay},
   Journal = {35th Aerospace Sciences Meeting and Exhibit},
   Year = {1997},
   Month = {January},
   ISBN = {9780000000002},
   Abstract = {© 1997, American Institute of Aeronautics and Astronautics,
             Inc.This paper presents a correlation study between
             numerical and experimental results for the response of a
             typical section airfoil with freeplay in the control
             surface. Since this is an inherently nonlinear system the
             equations of motion are integrated numerically. The typical
             response of this three-degree-of-freedom system, is either
             stationary or limit cycle prior to the onset of divergent
             flutter. The equations of motion are solved in state-space
             with the aerodynamic modeling based on Theodorsen’s
             theory. The freeplay condition is modeled as piecewise
             linear and a special procedure is developed to account
             accurately for this effect numerically. The physical
             experiments were conducted in the Duke University wind
             runnel. The paper describes how the response of the system
             changes with freestream velocity, and how these responses
             exhibit characteristic nonlinear behavior, in both the
             experimental and numerical results.},
   Key = {fds321800}
}

@article{fds330071,
   Author = {Conner, MD and Tang, DM and Dowell, EH and Virgin,
             LN},
   Title = {Nonlinear aeroelasticity of an airfoil with control surface
             freeplay},
   Journal = {35th Aerospace Sciences Meeting and Exhibit},
   Year = {1997},
   Month = {January},
   Abstract = {© 1997, American Institute of Aeronautics and Astronautics,
             Inc. This paper presents a correlation study between
             numerical and experimental results for the response of a
             typical section airfoil with freeplay in the control
             surface. Since this is an inherently nonlinear system the
             equations of motion are integrated numerically. The typical
             response of this three-degree-of-freedom system, is either
             stationary or limit cycle prior to the onset of divergent
             flutter. The equations of motion are solved in state-space
             with the aerodynamic modeling based on Theodorsen’s
             theory. The freeplay condition is modeled as piecewise
             linear and a special procedure is developed to account
             accurately for this effect numerically. The physical
             experiments were conducted in the Duke University wind
             runnel. The paper describes how the response of the system
             changes with freestream velocity, and how these responses
             exhibit characteristic nonlinear behavior, in both the
             experimental and numerical results.},
   Key = {fds330071}
}

@article{fds282365,
   Author = {MURPHY, KD and VIRGIN, LN and RIZZI, SA},
   Title = {FREE VIBRATION OF THERMALLY LOADED PANELS INCLUDING INITIAL
             IMPERFECTIONS AND POST-BUCKLING EFFECTS},
   Journal = {Structural Dynamics: Recent Advances Proceedings of the 5th
             International Conference, Vols I and Ii},
   Pages = {401-411},
   Publisher = {INST SOUND VIBRATION RESEARCH},
   Editor = {Ferguson, NS and Wolfe, HF and Mei, C},
   Year = {1994},
   Month = {January},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1994BC39K00036&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Key = {fds282365}
}

@article{fds282369,
   Author = {BAYLY, PV and VIRGIN, LN and GOTTWALD, JA and DOWELL,
             EH},
   Title = {STABILITY MEASUREMENTS IN NONLINEAR MECHANICAL EXPERIMENTS
             GUIDED BY DYNAMICAL SYSTEMS THEORY},
   Journal = {Nonlinearity and Chaos in Engineering Dynamics},
   Pages = {59-70},
   Publisher = {JOHN WILEY & SONS LTD},
   Editor = {Thompson, JMT and Bishop, SR},
   Year = {1994},
   Month = {January},
   ISBN = {0-471-94458-0},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1994BC33S00004&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Key = {fds282369}
}


%% Papers Published   
@article{fds338076,
   Author = {Maki, A and Virgin, LN and Umeda, N and Ueta, T and Miino, Y and Sakai, M and Kawakami, H},
   Title = {On the loss of stability of periodic oscillations and its
             relevance to ship capsize},
   Journal = {Journal of Marine Science and Technology
             (Japan)},
   Volume = {24},
   Number = {3},
   Pages = {846-854},
   Publisher = {Springer Nature America, Inc},
   Year = {2019},
   Month = {September},
   url = {http://dx.doi.org/10.1007/s00773-018-0591-x},
   Abstract = {© 2018, JASNAOE. This research revisits the analysis of
             roll motion and the possible capsize of floating vessels in
             beam seas. Many analytical investigations of this topic have
             adopted the softening Duffing equation, which is similar to
             the ship roll equation of motion. Here we focus on the loss
             of stability of periodic oscillations and its relevance to
             ship capsize. Previous researchers have found the thresholds
             of the saddle-node, flip, and heteroclinic bifurcations.
             They derived the flip condition from the negative stiffness
             condition in a Mathieu type variational equation. In our
             revisited analysis, we show that this threshold is identical
             to a pitchfork bifurcation. On the other hand, we
             simultaneously find that the generated asymmetry solution is
             unstable due to the limitation of the first order
             analysis.},
   Doi = {10.1007/s00773-018-0591-x},
   Key = {fds338076}
}

@article{fds343384,
   Author = {Xu, Y and Virgin, LN and Ross, SD},
   Title = {On experimentally locating saddle-points on a potential
             energy surface from observed dynamics},
   Journal = {Mechanical Systems and Signal Processing},
   Volume = {130},
   Pages = {152-163},
   Year = {2019},
   Month = {September},
   url = {http://dx.doi.org/10.1016/j.ymssp.2019.05.002},
   Abstract = {© 2019 Elsevier Ltd This paper details a new method to
             estimate the location of unstable equilibria, specifically
             saddle-points, based on transient trajectories from
             experiments. We describe a system in which saddle-points
             (not easily observed in a direct sense)influence the
             behavior of trajectories that pass ’close-by’ them. This
             influence is used to construct a model and thus identify a
             more accurate estimate of the location using a number of
             refinements associated with linearization and regression.
             Both simulations and experiments were conducted to verify
             the method. The experiment consists of a small ball rolling
             on a relatively shallow curved surface under the influence
             of gravity: a potential energy surface in two dimensions.
             Tracking the motion of the ball with a digital camera
             provides data that compares closely with the output of
             numerical simulation. The experimental results suggest that
             this method can effectively locate the saddle equilibria in
             a system, and the robustness of the approach is assessed
             relative to the effect of noise, size of the local
             neighborhood, etc., in addition to providing information on
             the local dynamics. Given the relative simplicity of the
             experiment system used and a priori knowledge of the
             saddle-points, it is a useful testing environment for system
             identification in a nonlinear context.},
   Doi = {10.1016/j.ymssp.2019.05.002},
   Key = {fds343384}
}

@article{fds345483,
   Author = {Harvey, PS and Virgin, LN and Tehrani, MH},
   Title = {Buckling of elastic columns with second-mode
             imperfections},
   Journal = {Meccanica},
   Volume = {54},
   Number = {8},
   Pages = {1245-1255},
   Year = {2019},
   Month = {June},
   url = {http://dx.doi.org/10.1007/s11012-019-01025-z},
   Abstract = {© 2019, Springer Nature B.V. The pin-ended, slender, Euler
             strut has been used as the archetypal buckling problem for
             many years (Euler in Additamentum I de curvis elasticis,
             methodus inveniendi lineas curvas maximi minimivi
             proprietate gaudentes, Bousquet, Lausanne, 1744). Even
             though it is not conventionally imperfection-sensitive
             (i.e., in which the magnitude of the buckling load is
             compromised by the presence of imperfections), initial
             geometric imperfections are still important, and 3D-printing
             now allows a versatility in geometric prescription and
             accuracy previously unavailable. This paper focuses
             attention on Euler struts, primarily from an experimental
             viewpoint, in which a second mode (full sine wave) initial
             shape, with varying magnitude, is used to produce specimens,
             test them, and compare with the elementary
             theory.},
   Doi = {10.1007/s11012-019-01025-z},
   Key = {fds345483}
}

@article{fds339325,
   Author = {Ehrhardt, DA and Virgin, LN},
   Title = {Experiments on the thermal post-buckling of panels,
             including localized heating},
   Journal = {Journal of Sound and Vibration},
   Volume = {439},
   Pages = {300-309},
   Publisher = {Elsevier BV},
   Year = {2019},
   Month = {January},
   url = {http://dx.doi.org/10.1016/j.jsv.2018.08.043},
   Abstract = {© 2018 Elsevier Ltd The suppression of expansion in thin
             clamped panels subjected to elevated thermal loading often
             results in buckling. However, a number of possible
             post-buckled equilibrium configurations typically exist, and
             which shape ensues depends on a number of factors including
             the role of symmetry, boundary conditions, aspect ratio, and
             the effect of small geometric imperfections associated with
             the initial shape. It is possible to force the panel to go
             between different buckled shapes, given a sufficiently large
             perturbation. Sometimes the panel will spontaneously jump,
             or snap, when the temperature is gradually increased or
             decreased (mode jumping). The extent to which these features
             occur when the thermal loading is applied locally is also
             investigated. This paper describes some interesting
             nonlinear (essentially buckling) behavior in
             thermally-loaded panels from a primarily experimental
             perspective, with an additional focus on non-uniform
             heating. The full force of stereo 3D digital image
             correlation and forward-looking infrared cameras are
             exploited to provide a relatively complete picture of this
             behavior.},
   Doi = {10.1016/j.jsv.2018.08.043},
   Key = {fds339325}
}

@article{fds337708,
   Author = {Guan, Y and Virgin, LN and Helm, D},
   Title = {Structural behavior of shallow geodesic lattice
             domes},
   Journal = {International Journal of Solids and Structures},
   Volume = {155},
   Pages = {225-239},
   Publisher = {Elsevier BV},
   Year = {2018},
   Month = {December},
   url = {http://dx.doi.org/10.1016/j.ijsolstr.2018.07.022},
   Abstract = {© 2018 Elsevier Ltd This paper describes experiments and
             analysis of the complete post-buckling behavior of shallow
             geodesic lattice domes. Although individual members are
             straight, their geometric arrangement approximates a curved
             surface and typical behavior is highly nonlinear, including
             the possibility of sudden jumps in which there may be
             multiple discontinuous pops from one equilibrium
             configuration to another. A number of shallow domes were
             produced using a 3D printer and tested using a load cell and
             proximity laser sensor. In contrast to most previous
             studies, rather than pinned or semi-rigid joints, the
             lattices studied here incorporate moment-transmitting joints
             and clamped boundary conditions at the perimeter. Thus,
             flexure is the dominant mode of deformation under lateral
             loading and coupled instability behaviors are possible in
             practice. The complete load-displacement relationship and
             multiple equilibrium configurations are exhibited both in
             experiment and in simulation. The experimental data shows a
             close correlation with nonlinear finite element analysis
             using path-following techniques. A typical member (coupled)
             buckling behavior and its influence on the critical load are
             presented. Conclusions are drawn with respect to symmetry
             and geometric sensitivity.},
   Doi = {10.1016/j.ijsolstr.2018.07.022},
   Key = {fds337708}
}

@article{fds331449,
   Author = {Zhong, J and Virgin, LN and Ross, SD},
   Title = {A tube dynamics perspective governing stability transitions:
             An example based on snap-through buckling},
   Journal = {International Journal of Mechanical Sciences},
   Volume = {149},
   Pages = {413-428},
   Publisher = {Elsevier BV},
   Year = {2018},
   Month = {December},
   url = {http://dx.doi.org/10.1016/j.ijmecsci.2017.10.040},
   Abstract = {© 2017 Elsevier Ltd The equilibrium configuration of an
             engineering structure, able to withstand a certain loading
             condition, is usually associated with a local minimum of the
             underlying potential energy. However, in the nonlinear
             context, there may be other equilibria present, and this
             brings with it the possibility of a transition to an
             alternative (remote) minimum. That is, given a sufficient
             disturbance, the structure might buckle, perhaps suddenly,
             to another shape. This paper considers the dynamic
             mechanisms under which such transitions (typically via
             saddle points) occur. A two-mode Hamiltonian is developed
             for a shallow arch/buckled beam. The resulting form of the
             potential energy—two stable wells connected by rank-1
             saddle points—shows an analogy with resonance transitions
             in celestial mechanics or molecular reconfigurations in
             chemistry, whereas here the transition corresponds to
             switching between two stable structural configurations.
             Then, from Hamilton's equations, the equilibria are
             determined and linearization of the equations of motion
             about the saddle is obtained. After computing the
             eigenvalues and eigenvectors of the coefficient matrix
             associated with the linearization, a symplectic
             transformation is given which puts the Hamiltonian into
             normal form and simplifies the equations, allowing us to use
             the conceptual framework known as tube dynamics. The flow in
             the equilibrium region of phase space as well as the
             invariant manifold tubes in position space are discussed.
             Also, we account for the addition of damping in the tube
             dynamics framework, which leads to a richer set of behaviors
             in transition dynamics than previously explored.},
   Doi = {10.1016/j.ijmecsci.2017.10.040},
   Key = {fds331449}
}

@article{fds339930,
   Author = {Ross, SD and Bozorgmagham, AE and Naik, S and Virgin,
             LN},
   Title = {Experimental validation of phase space conduits of
             transition between potential wells},
   Journal = {Physical Review. E},
   Volume = {98},
   Number = {5},
   Year = {2018},
   Month = {November},
   url = {http://dx.doi.org/10.1103/PhysRevE.98.052214},
   Abstract = {© 2018 American Physical Society. A phase space boundary
             between transition and nontransition trajectories, similar
             to those observed in Hamiltonian systems with rank-1
             saddles, is verified experimentally in a macroscopic system.
             We present a validation of the phase space flux across
             rank-1 saddles connecting adjacent potential wells, and we
             confirm the underlying phase space conduits that mediate the
             transition. Experimental regions of transition are found to
             agree with the theory to within 1%, suggesting the
             robustness of phase space conduits of transition in a broad
             array of two or more degrees of freedom experimental
             systems, despite the presence of small dissipation.},
   Doi = {10.1103/PhysRevE.98.052214},
   Key = {fds339930}
}

@article{fds337118,
   Author = {Virgin, LN},
   Title = {Enhancing the teaching of elastic buckling using additive
             manufacturing},
   Journal = {Engineering Structures},
   Volume = {174},
   Pages = {338-345},
   Publisher = {Elsevier BV},
   Year = {2018},
   Month = {November},
   url = {http://dx.doi.org/10.1016/j.engstruct.2018.07.059},
   Abstract = {© 2018 Elsevier Ltd This is the third part in a trilogy of
             papers examining ways in which additive manufacturing can be
             used to facilitate the introduction of basic principles in
             structural analysis. Each paper uses 3D-printing and simple,
             but non-trivial, slender geometric forms, to provide a
             hands-on aspect to structural behavior in which flexure
             plays a dominant role. The first part dealt with linear
             structural analysis (Virgin, 2017), extended to dynamics and
             vibration in the second part (Virgin, 2017). The current
             paper focuses on slender structures in which compressive
             axial loading is the new ingredient and hence buckling
             becomes a central issue. This has similarities and
             differences with the two previous papers, but in all
             instances the role played by relatively high-precision
             3D-printing opens the door to versatile and effective
             illustration, and the development of a deeper appreciation
             of structural phenomena.},
   Doi = {10.1016/j.engstruct.2018.07.059},
   Key = {fds337118}
}

@article{fds337748,
   Author = {Virgin, L},
   Title = {Tailored Buckling Constrained by Adjacent
             Members},
   Journal = {Structures},
   Volume = {16},
   Pages = {20-26},
   Publisher = {Elsevier BV},
   Year = {2018},
   Month = {November},
   url = {http://dx.doi.org/10.1016/j.istruc.2018.08.005},
   Abstract = {© 2018 Institution of Structural Engineers This paper
             exploits the accuracy and versatility of additive
             manufacturing to display interesting buckling behavior in
             slender elastic columns. A set of parallel columns were
             printed to relatively high precision, and then subjected to
             axial loading. The load-deflection behavior is influenced by
             the post-buckled mutual contact between adjacent columns.
             Given the capability of incorporating prescribed (but small)
             initial geometric imperfections using additive manufacturing
             it is feasible to seed post-bucking behavior, effectively
             tailoring stiffness.},
   Doi = {10.1016/j.istruc.2018.08.005},
   Key = {fds337748}
}

@article{fds337749,
   Author = {Virgin, LN and Giliberto, JV and Plaut, RH},
   Title = {Deformation and vibration of compressed, nested, elastic
             rings on rigid base},
   Journal = {Thin Walled Structures},
   Volume = {132},
   Pages = {167-175},
   Publisher = {Elsevier BV},
   Year = {2018},
   Month = {November},
   url = {http://dx.doi.org/10.1016/j.tws.2018.08.015},
   Abstract = {© 2018 Elsevier Ltd Vertical circular rings and a system of
             three nested rings are tested and analyzed. The rings are
             clamped to a flat rigid base and are loaded vertically at
             the top by either a concentrated load or a rigid plate. The
             tests involve rings made by 3D printing. In the analysis,
             each ring is modeled as an inextensible elastica. For
             downward quasi-static loading, point contact at the base
             becomes line contact under sufficiently high loads.
             Deformations are determined, and small vibrations about
             equilibrium are examined. Good agreement is found between
             experiments and theory. The topic is motivated by the
             application of short nested tubes for energy
             absorption.},
   Doi = {10.1016/j.tws.2018.08.015},
   Key = {fds337749}
}

@article{fds339683,
   Author = {Virgin, LN and Thompson, JMT},
   Title = {Applications of Bifurcation: Nonautonomous
             Periodically-Excited Systems},
   Journal = {International Journal of Bifurcation and
             Chaos},
   Volume = {28},
   Number = {11},
   Pages = {1830035-1830035},
   Publisher = {World Scientific Pub Co Pte Lt},
   Year = {2018},
   Month = {October},
   url = {http://dx.doi.org/10.1142/S0218127418300355},
   Abstract = {© 2018 World Scientific Publishing Company. This paper
             reviews some examples of bifurcation in low-order,
             periodically driven dynamical systems. The generic loss of
             stability is a key component in dynamical systems theory,
             and provides a central pillar in assessing qualitative
             changes in system dynamics. Although bifurcation tends to be
             thought of in rather abstract, theoretical terms, we show
             that it also provides a compelling framework to guide
             laboratory-based experiments. Both local and global
             stability transitions and their connection are illustrated
             in this accessible, review-like pictorial overview of simple
             mechanical/structural systems driven toward
             instability.},
   Doi = {10.1142/S0218127418300355},
   Key = {fds339683}
}

@article{fds333685,
   Author = {Brzeski, P and Virgin, LN},
   Title = {System identification of energy dissipation in a mechanical
             model undergoing high velocities: An indirect use of
             perpetual points},
   Journal = {Mechanical Systems and Signal Processing},
   Volume = {108},
   Pages = {115-125},
   Publisher = {Elsevier BV},
   Year = {2018},
   Month = {August},
   url = {http://dx.doi.org/10.1016/j.ymssp.2018.02.010},
   Abstract = {© 2018 Elsevier Ltd Energy dissipation is often the most
             challenging component of system identification in the
             modeling of dynamical behavior in mechanical systems. Even
             for a relatively simple single-degree-of-freedom system such
             as the rigid-arm pendulum, it can be difficult to choose the
             form of the best damping model, as well as the subsequent
             challenge of estimating the appropriate parameters,
             especially for a model that accurately captures the nature
             of energy dissipation over a wide range of operational
             conditions. This paper specifically focuses on a mechanical
             system in which subtle changes can be made to the system
             with a view to isolating and modeling energy dissipation.
             The approach described in this paper was developed as a
             by-product of experimentally investigating perpetual points.
             It is shown that certain features of high-velocity, spinning
             motion lends itself to greater fidelity in the data-fitting
             process and thus added confidence in choosing the most
             accurate energy dissipation model with the most appropriate
             parameters.},
   Doi = {10.1016/j.ymssp.2018.02.010},
   Key = {fds333685}
}

@article{fds336173,
   Author = {Virgin, LN},
   Title = {Sympathetic resonance},
   Journal = {American Journal of Physics},
   Volume = {86},
   Number = {6},
   Pages = {439-442},
   Year = {2018},
   Month = {June},
   url = {http://dx.doi.org/10.1119/1.5025037},
   Abstract = {© 2018 American Association of Physics Teachers. This short
             paper describes a useful teaching tool, ideal for
             demonstration purposes within the classroom or lab setting.
             It is based on the simple dynamic response of flexible
             cantilevers and evolves naturally from the underlying
             principles of a vibrating reed tachometer. Utilizing a
             3D-printer, these ideas conveniently encompass the
             phenomenon of resonance in which all the cantilevers of a
             similar length respond in harmony when just one of their
             number is plucked.},
   Doi = {10.1119/1.5025037},
   Key = {fds336173}
}

@article{fds331448,
   Author = {Harvey, PS and Virgin, LN},
   Title = {Effect of stiffener geometry on the response of
             grid-stiffened panels},
   Journal = {Journal of Engineering Mechanics},
   Volume = {144},
   Number = {2},
   Pages = {06017021-06017021},
   Publisher = {American Society of Civil Engineers (ASCE)},
   Year = {2018},
   Month = {February},
   url = {http://dx.doi.org/10.1061/(ASCE)EM.1943-7889.0001415},
   Abstract = {© 2017 American Society of Civil Engineers. It is well
             established that the lateral bending stiffness of thin
             panels is considerably enhanced by judicious use of ribs or
             stiffeners. This increase in stiffness is primarily due to a
             disproportionate increase in the second moment of area, and
             because relatively little mass is added, stiffened panels
             are especially appealing in an aerospace engineering
             context. In experiments it is relatively straightforward to
             measure bending deflections (especially in a cantilever
             configuration) and natural frequencies using laser
             vibrometry and associated signal-processing tools. This
             paper reports on a parametric study in which bending
             stiffness and natural frequencies are measured for a set of
             rectangular panels, conveniently manufactured using a
             three-dimensional (3D) printer. Both isogrid (stiffeners in
             a triangular configuration) and orthogrid (stiffeners in a
             rectangular configuration) structures were made and tested,
             with certain nondimensional parameters held constant (for
             example, total mass and length-to-width ratio) to facilitate
             easier comparison. The boundary condition considered was one
             edge clamped and the other edges free (simple cantilever)
             with a consistent plan area aspect ratio, and with the
             height and arrangement of stiffening ribs providing the
             major parametric variation.},
   Doi = {10.1061/(ASCE)EM.1943-7889.0001415},
   Key = {fds331448}
}

@article{fds333792,
   Author = {Detroux, T and Noël, J-P and Virgin, LN and Kerschen,
             G},
   Title = {Experimental study of isolas in nonlinear systems featuring
             modal interactions.},
   Journal = {Plos One},
   Volume = {13},
   Number = {3},
   Pages = {e0194452},
   Year = {2018},
   Month = {January},
   url = {http://dx.doi.org/10.1371/journal.pone.0194452},
   Abstract = {The objective of the present paper is to provide
             experimental evidence of isolated resonances in the
             frequency response of nonlinear mechanical systems. More
             specifically, this work explores the presence of isolas,
             which are periodic solutions detached from the main
             frequency response, in the case of a nonlinear set-up
             consisting of two masses sliding on a horizontal guide. A
             careful experimental investigation of isolas is carried out
             using responses to swept-sine and stepped-sine excitations.
             The experimental findings are validated with advanced
             numerical simulations combining nonlinear modal analysis and
             bifurcation monitoring. In particular, the interactions
             between two nonlinear normal modes are shown to be
             responsible for the creation of the isolas.},
   Doi = {10.1371/journal.pone.0194452},
   Key = {fds333792}
}

@article{fds330069,
   Author = {Virgin, L},
   Title = {Enhancing the teaching of structural dynamics using additive
             manufacturing},
   Journal = {Engineering Structures},
   Volume = {152},
   Pages = {750-757},
   Publisher = {Elsevier BV},
   Year = {2017},
   Month = {December},
   url = {http://dx.doi.org/10.1016/j.engstruct.2017.09.052},
   Abstract = {© 2017 Elsevier Ltd This paper provides a companion study
             to a previous paper by the same author (Virgin, 2017). In
             that paper, 3D printing was used to provide a hands-on
             experience for students of (linear) structural analysis
             based on the lateral stiffness of plane frames. In this
             paper, a related set of structural plane frames is
             investigated in terms of their natural frequencies, perhaps
             the fundamental feature in structural dynamics. Again, a 3D
             printer is used to provide a variety of parameter
             variations, and the extent to which certain simplifying
             analytical assumptions are justified is assessed.},
   Doi = {10.1016/j.engstruct.2017.09.052},
   Key = {fds330069}
}

@article{fds340378,
   Author = {Brzeski, P and Virgin, LN},
   Title = {Experimental investigation of perpetual points in mechanical
             systems},
   Journal = {Nonlinear Dynamics},
   Volume = {90},
   Number = {4},
   Pages = {2917-2928},
   Publisher = {Springer Nature},
   Year = {2017},
   Month = {December},
   url = {http://dx.doi.org/10.1007/s11071-017-3852-z},
   Abstract = {© 2017, The Author(s). In dissipative dynamical systems,
             equilibrium (stationary) points have a dominant organizing
             effect on transient motion in phase space, especially in
             nonlinear systems. These time-independent solutions are
             readily defined in the context of ordinary differential
             equations, that is, they occur when all the time derivatives
             are simultaneously zero. However, there has been some recent
             interest in perpetual points: points at which the higher
             time derivatives are zero, but not necessarily the first.
             Previous work has focused on analytic work (including
             simulation) and some experimental studies of electric
             circuits. This paper focuses attention on the occurrence of
             these points in a simple mechanical system, including
             experimental verification. Thus, points of zero acceleration
             can be found in which the corresponding velocity is a
             maximum or minimum, but not zero. Specifically, the
             rigid-arm pendulum is used to generate data for which
             acceleration (and its derivative) can be evaluated. In this
             paper an experimental (mechanical) setup is described,
             specifically designed to investigate perpetual points,
             including a description of the data analysis approaches
             developed to identify their location.},
   Doi = {10.1007/s11071-017-3852-z},
   Key = {fds340378}
}

@article{fds330070,
   Author = {Plaut, RH and Virgin, LN and Knight, JD},
   Title = {Predicting critical speeds in various rotordynamics
             problems},
   Journal = {Proceedings of the Institution of Mechanical Engineers, Part
             C: Journal of Mechanical Engineering Science},
   Volume = {231},
   Number = {21},
   Pages = {3913-3922},
   Publisher = {SAGE Publications},
   Year = {2017},
   Month = {November},
   url = {http://dx.doi.org/10.1177/0954406216659680},
   Abstract = {© Institution of Mechanical Engineers. Rotating shafts
             often experience undesirable large-amplitude whirling
             oscillations associated with resonance at critical speeds.
             This paper further develops a nondestructive technique in
             which measured information about the growing nature of the
             response is used to predict an incipient critical speed. A
             number of models of varying degrees of sophistication are
             developed and tested using the new approach, but the main
             advantage of the method is that it is model-free and thus
             possesses considerable practical utility. In addition,
             further experimental results are presented for the case of
             two disks mounted on a shaft, and the technique is
             successfully demonstrated in predicting a critical speed
             associated with a higher mode.},
   Doi = {10.1177/0954406216659680},
   Key = {fds330070}
}

@article{fds327427,
   Author = {Virgin, L},
   Title = {Enhancing the teaching of linear structural analysis using
             additive manufacturing},
   Journal = {Engineering Structures},
   Volume = {150},
   Pages = {135-142},
   Publisher = {Elsevier BV},
   Year = {2017},
   Month = {November},
   url = {http://dx.doi.org/10.1016/j.engstruct.2017.07.054},
   Abstract = {© 2017 Elsevier Ltd Structural analysis forms a key
             component in many courses in civil, mechanical and aerospace
             engineering. Conventionally, the matrix stiffness method, a
             subset of finite element analysis, tends to occupy a central
             position in a typical syllabus, with a special focus on
             plane frames providing a bridge between basic structural
             components with pedagogical clarity and real-world
             structures. Equations of equilibrium are set-up and the full
             force of linear algebra brought to bear using the
             capabilities of Matlab or more specialized FEA packages.
             Such classes have a tendency to become a little dry and
             suffer from the usual shortcomings of numerical analysis and
             a black box approach - shortcomings in the sense of
             conceptual understanding as opposed to usefulness in the
             hands of experienced practitioners. The relatively recent
             advent of additive manufacturing is an exciting opportunity
             to incorporate a practical aspect to structural analysis.
             This paper describes the use of 3D printing, via the
             flexural stiffness of plane frames, to develop a structural
             feel for students, augmenting theoretical analyses. In
             addition to directly addressing the role of modeling,
             approximation, applicability of the underlying theory, and
             measurement uncertainty, it is thoroughly hands-on and
             initial anecdotal evidence suggests a higher degree of
             student buy-in.},
   Doi = {10.1016/j.engstruct.2017.07.054},
   Key = {fds327427}
}

@article{fds323883,
   Author = {Plaut, RH and Virgin, LN},
   Title = {Snap-through under unilateral displacement control with
             constant velocity},
   Journal = {International Journal of Non Linear Mechanics},
   Volume = {94},
   Pages = {292-299},
   Publisher = {Elsevier BV},
   Year = {2017},
   Month = {September},
   url = {http://dx.doi.org/10.1016/j.ijnonlinmec.2017.01.015},
   Abstract = {© 2017 Elsevier Ltd When the side of a beverage can or the
             domed lid of a jar is pushed inward, all or part of the
             structure may suddenly snap into an inverted configuration.
             The velocity of the pushing motion affects this instability.
             Most previous analyses of snap-through have considered force
             control (increasing the pushing force, e.g., a weight).
             Snap-through under dynamic, unilateral displacement control
             is investigated here, with the indentor moving at constant
             velocity (as in a universal testing machine) until
             snap-through occurs. Shallow elastic arches with immovable
             pinned ends are analyzed. Attention is focused on the
             critical height of the indentor at which snap-through is
             initiated. The effects of the indentor velocity, indentor
             location along the span, initial arch height, and damping
             magnitude are investigated. In addition, experiments are
             conducted on shallow buckled beams, which behave similarly
             to arches. Usually, the higher the indentor velocity, the
             further the indentor must move before snap-through
             occurs.},
   Doi = {10.1016/j.ijnonlinmec.2017.01.015},
   Key = {fds323883}
}

@article{fds326067,
   Author = {Plaut, RH and Virgin, LN},
   Title = {Furthest reach of a uniform cantilevered
             elastica},
   Journal = {Mechanics Research Communications},
   Volume = {83},
   Pages = {18-21},
   Publisher = {Elsevier BV},
   Year = {2017},
   Month = {July},
   url = {http://dx.doi.org/10.1016/j.mechrescom.2017.03.002},
   Abstract = {© 2017 Elsevier Ltd A uniform elastic cantilever is
             subjected to a uniformly distributed load or a concentrated
             load at its tip. The angle of the fixed end with the
             horizontal is varied until the maximum horizontal distance
             (projection) from the fixed end to the horizontal location
             of the tip is attained. The beam is modeled as an
             inextensible elastica, and numerical results are obtained
             with the use of a shooting method. For the optimal solution
             (furthest reach), the tip is below the level of the fixed
             end. Experiments are conducted to verify the analysis for a
             heavy cantilever (i.e., only subjected to its
             self-weight).},
   Doi = {10.1016/j.mechrescom.2017.03.002},
   Key = {fds326067}
}

@article{fds325522,
   Author = {Virgin, LN and Guan, Y and Plaut, RH},
   Title = {On the geometric conditions for multiple stable equilibria
             in clamped arches},
   Journal = {International Journal of Non Linear Mechanics},
   Volume = {92},
   Pages = {8-14},
   Publisher = {Elsevier BV},
   Year = {2017},
   Month = {June},
   url = {http://dx.doi.org/10.1016/j.ijnonlinmec.2017.03.009},
   Abstract = {© 2017 Elsevier Ltd Curved structures, such as beams,
             arches, and panels are capable of exhibiting snap-through
             buckling behavior when loaded laterally, that is they can
             exhibit multiple stable equilibria, sometimes after any
             external loading is removed. This is a consequence of highly
             nonlinear force-deflection relations with perhaps multiple
             crossings of the zero-force axis for typical equilibrium
             paths. However, the propensity to maintain a stable
             snapped-through equilibrium position (in addition to the
             nominally unloaded equilibrium configuration) after the load
             is removed depends on certain geometric properties. A number
             of clamped arches are used to illustrate the relation
             between geometry (essentially the shape) and corresponding
             equilibrium configuration(s), and especially those
             conditions for which the initial equilibrium configuration
             is the only stable shape possible. Furthermore, related
             results are obtained when a change in the thermal
             environment may cause a system to exhibit a stable
             snapped-through equilibrium even when the system at ambient
             thermal conditions does not. Some representative examples
             are produced using a 3D printer for verification
             purposes.},
   Doi = {10.1016/j.ijnonlinmec.2017.03.009},
   Key = {fds325522}
}

@article{fds323740,
   Author = {Virgin, L},
   Title = {On the flexural stiffness of 3D printer thermoplastic},
   Journal = {International Journal of Mechanical Engineering
             Education},
   Volume = {45},
   Number = {1},
   Pages = {59-75},
   Publisher = {SAGE Publications},
   Year = {2017},
   Month = {January},
   url = {http://dx.doi.org/10.1177/0306419016674140},
   Abstract = {© SAGE Publications. This paper describes the process of
             estimating Young's modulus for the thermoplastic material
             commonly used in a type of 3D printer. Its twin goals are to
             compare and contrast a number of simple techniques from
             elementary structural analysis and to assess the influence
             of the printer density settings and print orientation
             (effective material anisotropy). Since components printed
             using additive manufacturing are used extensively for
             student projects, often involving load-bearing components,
             this contribution seeks to shed some light on fundamental
             modeling issues.},
   Doi = {10.1177/0306419016674140},
   Key = {fds323740}
}

@article{fds343232,
   Author = {Bishop, SR and Virgin, LN},
   Title = {The onset of chaotic motions of a moored
             semi-submersible.},
   Journal = {In: Proc. Asme Sixth (1987) Int. Offshore Mechanics and
             Arctic Engineering Symp., (Houston, U.S.A.: Mar. 1 6,
             1987)},
   Volume = {II, J.S. Chung; S. Berg; S.K. Chakrabart},
   Year = {2017},
   Month = {January},
   Abstract = {This paper describes a combined numerical and geometric
             approach to study the dynamic behaviour of a moored
             semi-submersible based on solutions of the non-linear
             differential equation used to model the system. Complex
             features including competing steady states, subharmonic
             resonances and chaos are shown to be typical responses in
             regular seas. A qualitative overview was used to classify
             the computer data generated from direct time simulation with
             the aim of illustrating the inadequacies and limitations of
             a linear or a purely analytical approach.
             (A)},
   Key = {fds343232}
}

@article{fds321791,
   Author = {Plaut, RH and Virgin, LN},
   Title = {Equilibria and vibration of a buckled beam with attached
             masses or spring–mass systems},
   Journal = {Journal of Sound and Vibration},
   Volume = {379},
   Pages = {166-176},
   Publisher = {Elsevier BV},
   Year = {2016},
   Month = {September},
   url = {http://dx.doi.org/10.1016/j.jsv.2016.05.043},
   Abstract = {© 2016 Elsevier Ltd A buckled beam with immovable pinned
             ends is considered. Attached to the beam are either one
             concentrated mass, two concentrated masses, a spring–mass
             system (that could model a human, robot, or passive
             vibration absorber), or a horizontal rigid bar with two
             vertical end springs (a “bounce–pitch” system that
             could model an animal or a vehicle). In the theoretical
             analysis, the beam is modeled as an inextensible elastica.
             Equilibrium configurations are determined first. Then small
             free vibrations about equilibrium are examined, and the
             lowest frequencies and corresponding modes are computed. The
             effects of various parameters are investigated, such as the
             ratio of the span to the total arc length of the beam, the
             locations and weights of the attached masses and systems,
             and the stiffnesses of the springs. For the case of a single
             attached mass, experiments are conducted and the results are
             compared to the theoretical ones.},
   Doi = {10.1016/j.jsv.2016.05.043},
   Key = {fds321791}
}

@article{fds321794,
   Author = {Wiebe, R and Virgin, LN},
   Title = {On the experimental identification of unstable static
             equilibria.},
   Journal = {Proceedings. Mathematical, Physical, and Engineering
             Sciences},
   Volume = {472},
   Number = {2190},
   Pages = {20160172},
   Year = {2016},
   Month = {June},
   url = {http://dx.doi.org/10.1098/rspa.2016.0172},
   Abstract = {This paper shows how the presence of unstable equilibrium
             configurations of elastic continua is reflected in the
             behaviour of transients induced by large perturbations. A
             beam that is axially loaded beyond its critical state
             typically exhibits two buckled stable equilibrium
             configurations, separated by one or more unstable
             equilibria. If the beam is then loaded laterally
             (effectively like a shallow arch) it may snap-through
             between these states, including the case in which the
             loading is applied dynamically and of short duration, i.e.
             an impact. Such impacts, if applied at random locations and
             of random strength, will generate an ensemble of transient
             trajectories that explore the phase space. Given sufficient
             variety, some of these trajectories will possess initial
             energy that is close to (just less than or just greater
             than) the energy required to cause snap-through and will
             have a tendency to slowdown as they pass close to an
             unstable configuration: a saddle point in a potential energy
             surface, for example. Although this close-encounter is
             relatively straightforward in a system characterized by a
             single degree of freedom, it is more challenging to identify
             in a higher order or continuous system, especially in a
             (necessarily) noisy experimental system. This paper will
             show how the identification of unstable equilibrium
             configurations can be achieved using transient
             dynamics.},
   Doi = {10.1098/rspa.2016.0172},
   Key = {fds321794}
}

@article{fds321795,
   Author = {George, C and Virgin, LN and Witelski, T},
   Title = {Experimental study of regular and chaotic transients in a
             non-smooth system},
   Journal = {International Journal of Non Linear Mechanics},
   Volume = {81},
   Pages = {55-64},
   Publisher = {Elsevier BV},
   Year = {2016},
   Month = {May},
   url = {http://dx.doi.org/10.1016/j.ijnonlinmec.2015.12.006},
   Abstract = {© 2015 Elsevier Ltd. All rights reserved. This paper
             focuses on thoroughly exploring the finite-time transient
             behaviors occurring in a periodically driven non-smooth
             dynamical system. Prior to settling down into a long-term
             behavior, such as a periodic forced oscillation, or a
             chaotic attractor, responses may exhibit a variety of
             transient behaviors involving regular dynamics, co-existing
             attractors, and super-persistent chaotic transients. A
             simple and fundamental impacting mechanical system is used
             to demonstrate generic transient behavior in an experimental
             setting for a single degree of freedom non-smooth mechanical
             oscillator. Specifically, we consider a horizontally driven
             rigid-arm pendulum system that impacts an inclined rigid
             barrier. The forcing frequency of the horizontal
             oscillations is used as a bifurcation parameter. An
             important feature of this study is the systematic generation
             of generic experimental initial conditions, allowing a more
             thorough investigation of basins of attraction when multiple
             attractors are present. This approach also yields a
             perspective on some sensitive features associated with
             grazing bifurcations. In particular, super-persistent
             chaotic transients lasting much longer than the conventional
             settling time (associated with linear viscous damping) are
             characterized and distinguished from regular dynamics for
             the first time in an experimental mechanical
             system.},
   Doi = {10.1016/j.ijnonlinmec.2015.12.006},
   Key = {fds321795}
}

@article{fds282330,
   Author = {Virgin, LN and Knight, JD and Plaut, RH},
   Title = {A New Method for Predicting Critical Speeds in
             Rotordynamics},
   Journal = {Journal of Engineering for Gas Turbines and
             Power},
   Volume = {138},
   Number = {2},
   Pages = {022504-022504},
   Publisher = {ASME International},
   Year = {2016},
   Month = {February},
   ISSN = {0742-4795},
   url = {http://dx.doi.org/10.1115/1.4031308},
   Abstract = {© 2016 by ASME. The prediction of critical speeds of a
             rotating shaft is a crucial issue in a variety of industrial
             applications ranging from turbomachinery to disk storage
             systems. The modeling and analysis of rotordynamic systems
             is subject to a number of complications, but perhaps the
             most important characteristic is to pass through a critical
             speed under spin-up conditions. This is associated with
             classical resonance phenomena and high amplitudes, and is
             often a highly undesirable situation. However, given
             uncertainties in the modeling of such systems, it can be
             very difficult to predict critical speeds based on purely
             theoretical considerations. Thus, it is clearly useful to
             gain knowledge of the critical speeds of rotordynamic
             systems under in situ conditions. The present study
             describes a relatively simple method to predict the first
             critical speed using data from low rotational speeds. The
             method is shown to work well for two standard rotordynamic
             models, and with data from experiments conducted during this
             study.},
   Doi = {10.1115/1.4031308},
   Key = {fds282330}
}

@article{fds282329,
   Author = {Virgin, LN and George, C and Kini, A},
   Title = {Experiments on a non-smoothly-forced oscillator},
   Journal = {Physica D: Nonlinear Phenomena},
   Volume = {313},
   Pages = {1-10},
   Publisher = {Elsevier BV},
   Year = {2015},
   Month = {December},
   ISSN = {0167-2789},
   url = {http://dx.doi.org/10.1016/j.physd.2015.09.002},
   Abstract = {© 2015 Elsevier B.V. All rights reserved. This paper
             describes some typical behavior encountered in the response
             of a harmonically-excited mechanical system in which a
             severe nonlinearity occurs due to an impact. Although such
             systems have received considerable recent attention (most of
             it from a theoretical viewpoint), the system scrutinized in
             this paper also involves a discrete input of energy at the
             impact condition. That is, it is kicked when contact is
             made. One of the motivations for this work is related to a
             classic pinball machine in which a ball striking a bumper
             experiences a sudden impulse, introducing additional
             unpredictability to the motion of the ball. A
             one-dimensional analog of a pinball machine was the subject
             of a detailed mathematical study in Pring and Budd (2011),
             and the current paper details behavior obtained from a
             mechanical experiment and describes dynamics not observed in
             a conventional (passive) impact oscillator.},
   Doi = {10.1016/j.physd.2015.09.002},
   Key = {fds282329}
}

@article{fds282333,
   Author = {Virgin, LN and Plaut, RH and Cartee, EV},
   Title = {Adjacent Equilibria in Highly Flexible Upright Loop on Rigid
             Foundation},
   Journal = {Experimental Mechanics},
   Volume = {55},
   Number = {6},
   Pages = {1191-1197},
   Publisher = {Springer Nature},
   Year = {2015},
   Month = {July},
   ISSN = {0014-4851},
   url = {http://dx.doi.org/10.1007/s11340-015-0011-7},
   Abstract = {© 2015, Society for Experimental Mechanics. For very
             slender structural components, self-weight may compete with
             elastic flexural stiffness in determining equilibrium
             configurations. In cases where the inherent elastic
             stiffness is low (relative to self-weight) we observe a
             variety of types of highly nonlinear behavior in the
             equilibrium shapes, together with changes in the natural
             frequencies of small oscillations about these equilibrium
             configurations. This technical note describes a specific
             phenomenon observed in experiments on very slender
             polycarbonate loops. In addition to profound changes in
             equilibrium shapes as a function of weight-to-stiffness
             ratio, under some circumstances it is possible to have two
             adjacent, co-existing equilibrium configurations. This
             robust, highly nonlinear snap-through behavior is
             demonstrated by perturbing from one shape to the
             other.},
   Doi = {10.1007/s11340-015-0011-7},
   Key = {fds282333}
}

@article{fds282334,
   Author = {Virgin, LN},
   Title = {Comment on "mechanical properties of suspended graphene
             sheets" [J. Vac. Sci. Technol., B 25, 2558
             (2007)]},
   Journal = {Journal of Vacuum Science & Technology B, Nanotechnology and
             Microelectronics: Materials, Processing, Measurement, and
             Phenomena},
   Volume = {33},
   Number = {2},
   Pages = {023001-023001},
   Publisher = {American Vacuum Society},
   Year = {2015},
   Month = {March},
   ISSN = {2166-2746},
   url = {http://dx.doi.org/10.1116/1.4914967},
   Doi = {10.1116/1.4914967},
   Key = {fds282334}
}

@article{fds282337,
   Author = {Hartzell, S and Bartlett, MS and Virgin, L and Porporato,
             A},
   Title = {Nonlinear dynamics of the CAM circadian rhythm in response
             to environmental forcing.},
   Journal = {Journal of Theoretical Biology},
   Volume = {368},
   Pages = {83-94},
   Year = {2015},
   Month = {March},
   ISSN = {0022-5193},
   url = {http://dx.doi.org/10.1016/j.jtbi.2014.12.010},
   Abstract = {Crassulacean acid metabolism (CAM) photosynthesis functions
             as an endogenous circadian rhythm coupled to external
             environmental forcings of energy and water availability.
             This paper explores the nonlinear dynamics of a new CAM
             photosynthesis model (Bartlett et al., 2014) and
             investigates the responses of CAM plant carbon assimilation
             to different combinations of environmental conditions. The
             CAM model (Bartlett et al., 2014) consists of a Calvin cycle
             typical of C3 plants coupled to an oscillator of the type
             employed in the Van der Pol and FitzHugh-Nagumo systems.
             This coupled system is a function of environmental variables
             including leaf temperature, leaf moisture potential, and
             irradiance. Here, we explore the qualitative response of the
             system and the expected carbon assimilation under constant
             and periodically forced environmental conditions. The model
             results show how the diurnal evolution of these variables
             entrains the CAM cycle with prevailing environmental
             conditions. While constant environmental conditions generate
             either steady-state or periodically oscillating responses in
             malic acid uptake and release, forcing the CAM system with
             periodic daily fluctuations in light exposure and leaf
             temperature results in quasi-periodicity and possible chaos
             for certain ranges of these variables. This analysis is a
             first step in quantifying changes in CAM plant productivity
             with variables such as the mean temperature, daily
             temperature range, irradiance, and leaf moisture potential.
             Results may also be used to inform model parametrization
             based on the observed fluctuating regime.},
   Doi = {10.1016/j.jtbi.2014.12.010},
   Key = {fds282337}
}

@article{fds282332,
   Author = {Phungpaingam, B and Virgin, LN and Chucheepsakul,
             S},
   Title = {Snap-Through Phenomenon and Self-Contact of Spatial Elastica
             Subjected to Mid-Torque},
   Journal = {International Journal of Applied Mechanics},
   Volume = {7},
   Number = {4},
   Pages = {1550057-1550057},
   Publisher = {World Scientific Pub Co Pte Lt},
   Year = {2015},
   Month = {January},
   ISSN = {1758-8251},
   url = {http://dx.doi.org/10.1142/S175882511550057X},
   Abstract = {© 2015 Imperial College Press. This paper presents the
             snap-through phenomenon and effect of self-contact of the
             spatial elastica subjected to mid-length torque. One end of
             the elastica is clamped while the other end is placed in a
             sleeve joint. The total arc-length of the elastica can be
             varied by sliding the end through the sleeve joint. At a
             certain value of total arc-length, the sleeve joint is
             clamped and an external torque is applied at the mid-length
             of the elastica. The system of governing differential
             equations is derived from the equilibrium of an elastica
             segment and geometric relations of the inextensible
             elastica. The transformation matrix formulated in terms of
             Euler parameters is utilized to avoid the kinematic
             singularity. To display the behavior of the elastica, the
             system of differential equations needs to be integrated
             numerically from one end to the other end. The integration
             is performed so that the boundary conditions and some
             constraint conditions of the problem are satisfied, i.e., a
             shooting method is used. The effect of self-contact is taken
             into account by considering the contact force as a point
             load applying at contact point. From the results, the
             snap-through phenomenon, effect of self-contact and
             equilibrium configurations are highlighted
             herein.},
   Doi = {10.1142/S175882511550057X},
   Key = {fds282332}
}

@article{fds282335,
   Author = {Wiebe, R and Virgin, LN and Spottswood, SM},
   Title = {Stochastic interrogation of competing responses in a
             nonlinear distributed system},
   Journal = {Nonlinear Dynamics},
   Volume = {79},
   Number = {1},
   Pages = {607-615},
   Year = {2015},
   Month = {January},
   ISSN = {0924-090X},
   url = {http://dx.doi.org/10.1007/s11071-014-1689-2},
   Abstract = {© 2014, Springer Science+Business Media Dordrecht. In this
             paper, we examine the potential for coexisting responses in
             a harmonically forced buckled beam. It is shown
             experimentally that such structures may present many more
             responses than might be observed using frequency sweep-up
             and sweep-down testing, with some responses being observed
             only very infrequently. The primary contribution of this
             work is the experimental approximation of the basins of
             attraction of the competing behaviors using stochastic
             interrogation, which uses strong, but random, perturbations
             to map out the initial conditions that tend to each
             attractor. This procedure is especially difficult in
             experimental studies of distributed systems; hence, we focus
             on the process of stochastic interrogation itself and
             strictly in an experimental context.},
   Doi = {10.1007/s11071-014-1689-2},
   Key = {fds282335}
}

@article{fds282336,
   Author = {Harvey, PS and Virgin, LN},
   Title = {Coexisting equilibria and stability of a shallow arch:
             Unilateral displacement-control experiments and
             theory},
   Journal = {International Journal of Solids and Structures},
   Volume = {54},
   Pages = {1-11},
   Year = {2015},
   Month = {January},
   ISSN = {0020-7683},
   url = {http://dx.doi.org/10.1016/j.ijsolstr.2014.11.016},
   Abstract = {© 2014 Elsevier Ltd. All rights reserved. The equilibria
             and stability of a shallow prestressed arch (beam-column)
             are investigated theoretically and experimentally. The
             deflection of the arch is unilaterally constrained by a
             displacement-control device. Both snap-through and remote
             coexisting equilibria are observed. Force-deflection curves
             for primary and secondary equilibrium branches are measured
             for varying constraint locations. The effect of the
             constraint location on the critical condition at which
             stability is lost, resulting in a jump to a remote
             equilibrium, is investigated. Good agreement is attained
             between experimental data and theoretical results (based on
             minimization of the constrained strain energy and an
             inextensibility assumption).},
   Doi = {10.1016/j.ijsolstr.2014.11.016},
   Key = {fds282336}
}

@article{fds282348,
   Author = {Witelski, T and Virgin, LN and George, C},
   Title = {A driven system of impacting pendulums: Experiments and
             simulations},
   Journal = {Journal of Sound and Vibration},
   Volume = {333},
   Number = {6},
   Pages = {1734-1753},
   Year = {2014},
   Month = {March},
   ISSN = {0022-460X},
   url = {http://dx.doi.org/10.1016/j.jsv.2013.11.004},
   Abstract = {This paper studies a system composed of two pendulums
             attached to a common base that is oscillated horizontally.
             The pendulums share a common pivot line, but move
             independently and are only coupled together through
             collisions. Impact dynamics for the collisions of the
             pendulums with each other and with fixed barriers yield
             complex nonlinear behaviors. Careful numerical simulation of
             the equations of motion demonstrates a close correlation
             with experimental data collected from the system. There are
             many independent parameters in this system, and one of the
             motivations for the present study is to establish the extent
             to which we can capture observed behavior with a relatively
             simple hybrid differential equation model in the face of
             several independent energy dissipation mechanisms coming
             from friction and impact. Comparison between experiments and
             simulations is based on the standard nonlinear dynamical
             system analyses of time series, phase projections, time-lag
             embedding, Poincaré sections, and frequency content.
             Grazing bifurcations and co-existence of
             impacting/non-impacting periodic/chaotic states are
             observed. © 2013 Elsevier Ltd.},
   Doi = {10.1016/j.jsv.2013.11.004},
   Key = {fds282348}
}

@article{fds282341,
   Author = {Plaut, RH and Virgin, LN},
   Title = {Deformation and vibration of upright loops on a foundation
             and of hanging loops},
   Journal = {International Journal of Solids and Structures},
   Volume = {51},
   Number = {18},
   Pages = {3067-3075},
   Year = {2014},
   Month = {January},
   ISSN = {0020-7683},
   url = {http://dx.doi.org/10.1016/j.ijsolstr.2014.05.003},
   Abstract = {The deformation and vibration of vertical flexible loops are
             investigated theoretically and experimentally. Both upright
             and hanging loops are considered. Potential applications
             include nanorings and carbon nanotubes as force sensors or
             structural components. The upright tubes rest on a rigid or
             linearly elastic (Winkler) foundation, and cases with
             adhesion and nonlocal elasticity are included in the
             analysis. The hanging loops are suspended by a clamp with
             zero or finite length. The effects of self-weight,
             foundation stiffness, work of adhesion, and nonlocal
             elasticity on the loop height or depth are determined, as
             well as the effects of self-weight and foundation stiffness
             on the lowest frequency for in-plane symmetric vibration.
             Good agreement is attained between theoretical results
             (based on an inextensible-elastica model) and experimental
             data. © 2014 Elsevier Ltd. All rights reserved.},
   Doi = {10.1016/j.ijsolstr.2014.05.003},
   Key = {fds282341}
}

@article{fds282347,
   Author = {Waite, JJ and Virgin, LN and Wiebe, R},
   Title = {Competing responses in a discrete mechanical
             system},
   Journal = {International Journal of Bifurcation and
             Chaos},
   Volume = {24},
   Number = {1},
   Pages = {1430003-1430003},
   Publisher = {World Scientific Pub Co Pte Lt},
   Year = {2014},
   Month = {January},
   ISSN = {0218-1274},
   url = {http://dx.doi.org/10.1142/S0218127414300031},
   Abstract = {This short paper takes a close look at a relatively simple
             harmonically-excited mechanical oscillator. Throughout the
             range of forcing frequencies the basins of attraction are
             investigated by applying strong perturbations to
             steady-state behavior. In this way, a more general solution
             space is mapped out. Numerical simulation of the equation of
             motion agrees very closely with data generated from a
             laboratory experiment. © 2014 World Scientific Publishing
             Company.},
   Doi = {10.1142/S0218127414300031},
   Key = {fds282347}
}

@article{fds282351,
   Author = {Virgin, LN and Wiebe, R and Spottswood, SM and Eason,
             TG},
   Title = {Sensitivity in the structural behavior of shallow
             arches},
   Journal = {International Journal of Non Linear Mechanics},
   Volume = {58},
   Pages = {212-221},
   Publisher = {Elsevier BV},
   Year = {2014},
   Month = {January},
   ISSN = {0020-7462},
   url = {http://dx.doi.org/10.1016/j.ijnonlinmec.2013.10.003},
   Abstract = {It is well established that certain structural buckling
             problems are extremely sensitive to small changes in
             configuration: geometric imperfections, load application,
             symmetry, boundary conditions, etc. This paper considers the
             behavior of a very shallow arch under lateral point loading,
             and specifically under the influence of changes in the
             thermal environment. In some ways the system under study is
             especially sensitive since small changes influence whether
             the arch 'snaps-through' or not. The experimental results
             provide insight into the challenges of understanding the
             behavior of these types of structural components in a
             practical, and thus necessarily imperfect, situation. The
             focus is on static loading or at least quasi-static loading,
             in which loading occurs on a slow time scale. This study
             also acts as a back-drop for studying the dynamic behavior
             of shallow arches, an area of concern in the context of
             aerospace structural components. © 2013 Elsevier
             Ltd.},
   Doi = {10.1016/j.ijnonlinmec.2013.10.003},
   Key = {fds282351}
}

@article{fds282352,
   Author = {Lyman, TC and Virgin, LN and Davis, RB},
   Title = {Application of continuation methods to uniaxially loaded
             postbuckled plates},
   Journal = {Journal of Applied Mechanics},
   Volume = {81},
   Number = {3},
   Pages = {031010-031010},
   Publisher = {ASME International},
   Year = {2014},
   Month = {January},
   ISSN = {0021-8936},
   url = {http://dx.doi.org/10.1115/1.4024672},
   Abstract = {Continuation methods are used to examine the static and
             dynamic postbuckled behavior of a uniaxially loaded, simply
             supported plate. Continuation methods have been extensively
             used to study problems in mathematics and physics; however,
             they have not been as widely applied to problems in
             engineering. When paired with a Galerkin approximation,
             continuation methods are shown to be well suited to solving
             nonlinear buckling problems. In addition to providing a
             robust solution method for nonlinear equations, the
             linearized Jacobians from the continuation steps will
             contain natural frequency and mode shape information for
             mechanical systems (provided inertia terms are included).
             Results for the primary buckling branch are compared to
             previously published results. Using the open-source
             continuation package Auto, stable, remote secondary buckling
             branches were discovered. These secondary stable equilibrium
             persist even in the presence of geometric imperfections and
             their existence is confirmed by experiment. Copyright ©
             2014 by ASME.},
   Doi = {10.1115/1.4024672},
   Key = {fds282352}
}

@article{fds282342,
   Author = {Plaut, RH and Virgin, LN},
   Title = {Deformation and vibration of upright loops on a foundation
             and of hanging loops},
   Journal = {International Journal of Solids and Structures},
   Volume = {51},
   Number = {18},
   Pages = {3067-3075},
   Publisher = {Elsevier BV},
   Year = {2014},
   ISSN = {0020-7683},
   url = {http://dx.doi.org/10.1016/j.ijsolstr.2014.05.003},
   Doi = {10.1016/j.ijsolstr.2014.05.003},
   Key = {fds282342}
}

@article{fds282356,
   Author = {Chandra, Y and Wiebe, R and Stanciulescu, I and Virgin, LN and Spottswood, SM and Eason, TG},
   Title = {Characterizing dynamic transitions associated with
             snap-through of clamped shallow arches},
   Journal = {Journal of Sound and Vibration},
   Volume = {332},
   Number = {22},
   Pages = {5837-5855},
   Publisher = {Elsevier BV},
   Year = {2013},
   Month = {October},
   ISSN = {0022-460X},
   url = {http://dx.doi.org/10.1016/j.jsv.2013.06.001},
   Abstract = {Slender curved structures can often be found as components
             of complex structures in civil, mechanical, and aerospace
             systems. Under extreme loadings, a curved structure might
             undergo snap-through buckling, i.e., the structure is forced
             to its inverted configuration, inducing fatigue. Therefore,
             it is important to identify the stability boundaries of
             structures and to obtain an accurate description of their
             performance if the response moves beyond those boundaries.
             In this paper, a combined experimental-computational
             framework is used to analyze the transient behavior of
             clamped-clamped shallow arches. We examine, both
             experimentally and using Finite Element Analysis (FEA), the
             response of shallow arches under harmonic distributed
             loading. Various types of responses are identified and
             regions in the forcing parameter space that lead to
             snap-through and chaotic responses are determined. © 2013
             Elsevier Ltd. All rights reserved.},
   Doi = {10.1016/j.jsv.2013.06.001},
   Key = {fds282356}
}

@article{fds282361,
   Author = {Plaut, RH and Virgin, LN},
   Title = {Pendulum models of ponytail motion during walking and
             running},
   Journal = {Journal of Sound and Vibration},
   Volume = {332},
   Number = {16},
   Pages = {3768-3780},
   Publisher = {Elsevier BV},
   Year = {2013},
   Month = {August},
   ISSN = {0022-460X},
   url = {http://dx.doi.org/10.1016/j.jsv.2013.02.016},
   Abstract = {Steady-state motions of a woman's ponytail during level,
             straight, walking and running are examined. Based on
             reported data, formulas have been developed for the
             relationship of the forward speed to the frequencies of
             vertical and sideways motion of the head, and of the form of
             that motion. The ponytail is modeled as a compound pendulum
             or a multi-bar pendulum with 2, 3, or 5 rigid bars. Motions
             in the vertical plane perpendicular to the direction of
             progression are analyzed. Rotational springs and dashpots
             are placed at the joints, and aerodynamic damping (air drag)
             is included. Attention is focused on the variation of the
             amplitudes of the bars as the woman's walking speed and then
             running speed increase. An example of three-dimensional
             motions of a spherical-pendulum model also is included.
             Experiments were conducted on a double pendulum with
             parabolic applied motion at the top. The damping is modeled
             by rotational friction (i.e., a constant resisting moment at
             the top and internal joints), and the numerical results
             agree well with the test data. © 2013 Elsevier
             Ltd.},
   Doi = {10.1016/j.jsv.2013.02.016},
   Key = {fds282361}
}

@article{fds282357,
   Author = {Hunt, G and Virgin, L},
   Title = {Michael Thompson: some personal recollections.},
   Journal = {Philosophical Transactions. Series A, Mathematical,
             Physical, and Engineering Sciences},
   Volume = {371},
   Number = {1993},
   Pages = {20120449},
   Year = {2013},
   Month = {June},
   ISSN = {1364-503X},
   url = {http://dx.doi.org/10.1098/rsta.2012.0449},
   Doi = {10.1098/rsta.2012.0449},
   Key = {fds282357}
}

@article{fds282359,
   Author = {Virgin, LN and Wiebe, R},
   Title = {On damping in the vicinity of critical points.},
   Journal = {Philosophical Transactions. Series A, Mathematical,
             Physical, and Engineering Sciences},
   Volume = {371},
   Number = {1993},
   Pages = {20120426},
   Year = {2013},
   Month = {June},
   ISSN = {1364-503X},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/23690637},
   Abstract = {The effect of damping on the behaviour of oscillations in
             the vicinity of bifurcations of nonlinear dynamical systems
             is investigated. Here, our primary focus is single
             degree-of-freedom conservative systems to which a small
             linear viscous energy dissipation has been added.
             Oscillators with saddle-node, pitchfork and transcritical
             bifurcations are shown analytically to exhibit several
             interesting characteristics in the free decay response near
             a bifurcation. A simple mechanical oscillator with a
             transcritical bifurcation is used to experimentally verify
             the analytical results. A transcritical bifurcation was
             selected because it may be used to represent generic
             bifurcation behaviour. It is shown that the damping ratio
             can be used to predict a change in the stability with
             respect to changing system parameters.},
   Doi = {10.1098/rsta.2012.0426},
   Key = {fds282359}
}

@article{fds282363,
   Author = {Wiebe, R and Virgin, LN and Stanciulescu, I and Spottswood, SM and Eason, TG},
   Title = {Characterizing dynamic transitions associated with
             snap-through: A discrete system},
   Journal = {Journal of Computational and Nonlinear Dynamics},
   Volume = {8},
   Number = {1},
   Pages = {011010-011010},
   Publisher = {ASME International},
   Year = {2013},
   Month = {January},
   ISSN = {1555-1423},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000313671300010&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Abstract = {Geometrically nonlinear structures often possess multiple
             equilibrium configurations. Under extreme conditions of
             excitation, it is possible for these structures to exhibit
             oscillations about and between these co-existing
             configurations. This behavior may have serious implications
             for fatigue in the context of aircraft surface panels.
             Snap-through is a name often given to sudden changes in
             dynamic behavior associated with mechanical instability
             (buckling). This is an often encountered problem in
             hypersonic vehicles in which severe thermal loading and
             acoustic excitation conspire to create an especially hostile
             environment for structural elements. In this paper, a simple
             link model is used, experimentally and numerically, to
             investigate the mechanisms of snap-through buckling from a
             phenomenological standpoint. © 2013 American Society of
             Mechanical Engineers.},
   Doi = {10.1115/1.4006201},
   Key = {fds282363}
}

@article{fds282362,
   Author = {Chandra, Y and Stanciulescu, I and Virgin, LN and Eason, TG and Spottswood, SM},
   Title = {A numerical investigation of snap-through in a shallow
             arch-like model},
   Journal = {Journal of Sound and Vibration},
   Volume = {332},
   Number = {10},
   Pages = {2532-2548},
   Publisher = {Elsevier BV},
   Year = {2013},
   Month = {January},
   ISSN = {0022-460X},
   url = {http://dx.doi.org/10.1016/j.jsv.2012.12.019},
   Abstract = {Slender curved structures may experience a loss of stability
             called snap-through, causing the curvature on part or all of
             the structure to invert inducing fatigue damage. This paper
             presents a framework for analyzing the transient responses
             of slender curved structures. A numerical study of
             snap-through in a shallow arch-like model under periodic
             excitations is performed on a simplified model and on a
             detailed finite element model. The boundaries that separate
             the snap-through and no snap-through regions in the forcing
             parameters space are identified. Various post-snap responses
             are analyzed. The effects of initial conditions on the
             snap-through boundaries and post-snap responses are
             examined. Forcing parameters that lead to chaotic response
             are identified. © 2013 Elsevier Ltd.},
   Doi = {10.1016/j.jsv.2012.12.019},
   Key = {fds282362}
}

@article{fds282346,
   Author = {Wiebe, R and Virgin, LN},
   Title = {A harmonic balance approximation of dynamic snap-through
             boundaries in a single-degree-of-freedom
             structure},
   Journal = {Proceedings of the Asme Design Engineering Technical
             Conference},
   Volume = {7 B},
   Publisher = {ASME},
   Year = {2013},
   Month = {January},
   url = {http://dx.doi.org/10.1115/DETC2013-12615},
   Abstract = {Under dynamic loading, systems with the requisite condition
             for snap-through buckling, that is co-existing equilibria,
             typically exhibit either small amplitude response about a
             single equilibrium configuration, or large amplitude
             response that transits between the static equilibria.
             Dynamic snap-through is the name given to the large
             amplitude response, which, in the context of structural
             systems, is obviously undesirable. Structures with
             underlying snap-through static behavior may exhibit highly
             nonlinear and unpredictable oscillations. Such systems
             rarely lend themselves to investigation by analytical means.
             This is not surprising as nonlinear phenomena such as chaos
             run counter to the predictability of an analytical closed
             form solution. However, many unexpected analytical
             approximations of global stability may be obtained for
             simple systems using the harmonic balance method. In this
             paper a simple single-degree-of-freedom arch is studied
             using the harmonic balance method. The equations developed
             with the harmonic balance approach are then solved using an
             arc-length method and an approximate snap-through boundary
             in forcing parameter space is obtained. The method is shown
             to exhibit excellent agreement with numerical results.
             Arches present an ideal avenue for the investigation of
             snap-through as they typically have multiple, often tunable,
             stable and unstable equilibria. They also have many
             applications in both civil engineering, where arches are a
             canonical structural element, and mechanical/aerospace
             engineering, where arches may be used to approximate the
             behavior of curved plates and panels such as those used on
             aircraft. Copyright © 2013 by ASME.},
   Doi = {10.1115/DETC2013-12615},
   Key = {fds282346}
}

@article{fds282350,
   Author = {Witelski, T and Virgin, LN and George, C},
   Title = {A driven system of impacting pendulums: Experiments and
             simulations},
   Journal = {Journal of Sound and Vibration},
   Year = {2013},
   ISSN = {0022-460X},
   Key = {fds282350}
}

@article{fds282412,
   Author = {Olson, CC and Nichols, JM and Virgin, LN},
   Title = {Parameter estimation for chaotic systems using a geometric
             approach: Theory and experiment},
   Journal = {Nonlinear Dynamics},
   Volume = {70},
   Number = {1},
   Pages = {381-391},
   Publisher = {Springer Nature},
   Year = {2012},
   Month = {October},
   ISSN = {0924-090X},
   url = {http://dx.doi.org/10.1007/s11071-012-0461-8},
   Abstract = {A method for estimating model parameters based on chaotic
             system response data is described. This estimation problem
             is made challenging by sensitive dependence to initial
             conditions. The standard maximum likelihood estimation
             method is practically infeasible due to the non-smooth
             nature of the likelihood function. We bypass the problem by
             introducing an alternative, smoother function that admits a
             better-defined maximum and show that the parameters that
             maximize this new function are asymptotically equivalent to
             maximum likelihood estimates. We use simulations to explore
             the influence of noise and available data on model Duffing
             and Lorenz oscillators. We then apply the approach to
             experimental data from a chaotic Duffing system. Our method
             does not require estimation of initial conditions and
             parameter estimates may be obtained even when system
             dynamics have been estimated from a delay embedding. © 2012
             Springer Science+Business Media B.V.},
   Doi = {10.1007/s11071-012-0461-8},
   Key = {fds282412}
}

@article{fds282409,
   Author = {Lyman, TC and Virgin, LN and Davis, RB},
   Title = {Application of continuation methods to nonlinear
             post-buckled structures},
   Journal = {Conference Proceedings of the Society for Experimental
             Mechanics Series},
   Volume = {3},
   Pages = {245-254},
   Publisher = {Springer New York},
   Year = {2012},
   Month = {June},
   ISSN = {2191-5644},
   url = {http://dx.doi.org/10.1007/978-1-4614-2416-1_20},
   Abstract = {Continuation and path following methods have been applied to
             many nonlinear problems in mathematics and physics. There is
             less widespread application of these methods, however, to
             structural systems. Since structural buckling and stability
             problems are primarily concerned with system behavior as a
             control parameter (most often the load) varies, they are
             particularly well suited for continuation methods and
             bifurcation analysis. In this work, the continuation package
             AUTO is utilized to calculate post-buckled configurations,
             natural frequencies, and mode shapes of flat plates.
             Additionally, the continuation analysis identifies
             bifurcation points and is also adapted to plate
             configurations that include slight initial imperfections.
             Finally, the path following methods are also applied to
             track the unstable snap-through solution and natural
             frequencies of post-buckled plates subject to a transverse
             load. © The Society for Experimental Mechanics, Inc.
             2012.},
   Doi = {10.1007/978-1-4614-2416-1_20},
   Key = {fds282409}
}

@article{fds282410,
   Author = {Phungpaingam, B and Virgin, LN and Chucheepsakul,
             S},
   Title = {Stability of spatial elastica in a gravitational
             field},
   Journal = {International Journal of Structural Stability and
             Dynamics},
   Volume = {12},
   Number = {2},
   Pages = {403-421},
   Publisher = {World Scientific Pub Co Pte Lt},
   Year = {2012},
   Month = {March},
   ISSN = {0219-4554},
   url = {http://dx.doi.org/10.1142/S0219455412500101},
   Abstract = {This paper considers the behavior of a spatial elastica in a
             gravitational field. The slenderness of the system
             considered is such that the weight becomes an important
             consideration in determining elastic equilibrium
             configurations. Both ends of the elastica are clamped in an
             initially (planar) horizontal orientation at a fixed
             distance apart. However, one of the ends allows an increase
             in arc-length, that is, it is a sleeve joint. Thus, the
             total arc-length is the primary control parameter. This kind
             of elastica typically loses stability, resulting in
             out-of-plane deflections, when the total arc-length is
             increased beyond a critical value. A small mid-length torque
             can used to perturb a planar equilibrium configuration in
             order to test for stability. The aim of this study is to
             assess the effect of self-weight of the elastica (which is
             typically ignored) on promoting or delaying the loss of
             stability. To this end, it is useful to compare and contrast
             the results of orientation, that is, the system is
             configured in both an initial "upright" orientation and then
             in an "upside-down" orientation to highlight the influence
             of gravity. The results of the weightless elastica are used
             as a reference. Analysis is based on Kirchhoff's rod theory
             and Euler parameters, and the resulting set of governing
             differential equations are solved using a shooting method.
             The results from an experimental system using a slender
             superelastic wire made from Nitinol (Nickel Titanium Naval
             Ordnance Laboratory) exhibit close agreement with the
             analytical results. © 2012 World Scientific Publishing
             Company.},
   Doi = {10.1142/S0219455412500101},
   Key = {fds282410}
}

@article{fds282426,
   Author = {Wiebe, R and Virgin, LN},
   Title = {A heuristic method for identifying chaos from frequency
             content.},
   Journal = {Chaos (Woodbury, N.Y.)},
   Volume = {22},
   Number = {1},
   Pages = {013136},
   Publisher = {AIP Publishing},
   Year = {2012},
   Month = {March},
   ISSN = {1054-1500},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/22463012},
   Abstract = {The sign of the largest Lyapunov exponent is the fundamental
             indicator of chaos in a dynamical system. However, although
             the extraction of Lyapunov exponents can be accomplished
             with (necessarily noisy) the experimental data, this is
             still a relatively data-intensive and sensitive endeavor.
             This paper presents an alternative pragmatic approach to
             identifying chaos using response frequency characteristics
             and extending the concept of the spectrogram. The method is
             shown to work well on both experimental and simulated time
             series.},
   Doi = {10.1063/1.3675624},
   Key = {fds282426}
}

@article{fds282434,
   Author = {Wiebe, R and Virgin, LN and Witelski, TP},
   Title = {A parametrically forced nonlinear system with reversible
             equilibria},
   Journal = {International Journal of Bifurcation and
             Chaos},
   Volume = {22},
   Number = {6},
   Pages = {1230020-1230020},
   Publisher = {World Scientific Pub Co Pte Lt},
   Year = {2012},
   Month = {January},
   ISSN = {0218-1274},
   url = {http://dx.doi.org/10.1142/S0218127412300200},
   Abstract = {A nonlinear Duffing-type dynamical system, in which the
             stability of equilibria is modulated in a time-dependent
             manner, is investigated both experimentally and numerically.
             This is a low-order dynamical system with some interesting
             available choices in the coordinate system. The system is
             found to exhibit a variety of interesting nonlinear behavior
             including ultrasubharmonic resonance. Frequency content is
             used to characterize periodic and chaotic behavior and their
             relation to the parameter space. © 2012 World Scientific
             Publishing Company.},
   Doi = {10.1142/S0218127412300200},
   Key = {fds282434}
}

@article{fds282360,
   Author = {Wiebe, R and Virgin, LN and Stanciulescu, I and Spottswood,
             SM},
   Title = {On snap-through buckling},
   Journal = {Collection of Technical Papers Aiaa/Asme/Asce/Ahs/Asc
             Structures, Structural Dynamics and Materials
             Conference},
   Publisher = {American Institute of Aeronautics and Astronautics},
   Year = {2011},
   Month = {December},
   ISSN = {0273-4508},
   url = {http://dx.doi.org/10.2514/6.2011-2083},
   Abstract = {Snap-through buckling can reduce the life-span of structural
             systems such as aircraft surface paneling. This is
             envisioned to be a specific problem in hypersonic vehicles
             in which severe thermal loading and acoustic excitation
             conspire to create an especially hostile environment for
             structural elements. A shallow arch, and two simplified link
             models are used to investigate the mechanisms of
             snap-through buckling from a fundamental, or
             phenomeno-logical, standpoint. The complexities introduced
             by modal interactions are introduced and a method for
             identifying snap-through buckling is developed. Copyright ©
             2011 by the American Institute of Aeronautics and
             Astronautics, Inc.},
   Doi = {10.2514/6.2011-2083},
   Key = {fds282360}
}

@article{fds282404,
   Author = {Wiebe, R and Virgin, LN},
   Title = {On the identification of chaos from frequency
             content},
   Journal = {Proceedings of the Asme Design Engineering Technical
             Conference},
   Volume = {4},
   Number = {PARTS A AND B},
   Pages = {823-828},
   Year = {2011},
   Month = {December},
   url = {http://dx.doi.org/10.1115/DETC2011-47473},
   Abstract = {The characterization of chaos as a random-like response from
             a deterministic dynamical system with an extreme sensitivity
             to initial conditions is well-established, and has provided
             a stimulus to research in nonlinear dynamical systems in
             general. In a formal sense, the computation of the Lyapunov
             Exponent spectrum establishes a quantitative measure, with
             at least one positive Lyapunov Exponent (and generally
             boundedmotion) indicating a local exponential divergence of
             adjacent trajectories. However, although the extraction of
             Lyapunov Exponents can be accomplished with (necessarily
             noisy) experimental data, this is still a relatively
             data-intensive and sensitive endeavor. We present here an
             alternative, pragmatic approach to identifying chaos as a
             function of system parameters using response frequency
             characteristics and extending the concept of the
             spectrogram. Copyright © 2011 by ASME.},
   Doi = {10.1115/DETC2011-47473},
   Key = {fds282404}
}

@article{fds282408,
   Author = {Gao, L and Tahir, MA and Virgin, LN and Yellen, BB},
   Title = {Multiplexing superparamagnetic beads driven by
             multi-frequency ratchets.},
   Journal = {Lab on a Chip},
   Volume = {11},
   Number = {24},
   Pages = {4214-4220},
   Year = {2011},
   Month = {December},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/22038314},
   Abstract = {Here, we explore the single particle dynamics of
             superparamagnetic beads exposed to multifrequency ratchets.
             Through a combination of theory, simulation, and experiment,
             we determine the important tuning parameters that can be
             used to implement multiplexed separation of polydisperse
             colloidal mixtures. In particular, our results demonstrate
             that the ratio of driving frequencies controls the
             transition between open and closed trajectories that allow
             particles to be transported across a substrate. We also
             demonstrate that the phase difference between the two
             frequencies controls not only the direction of motion but
             also which particles are allowed to move within a
             polydisperse mixture. These results represent a
             fundamentally different approach to colloidal separation
             than the previous methods which are based on controlling
             transitions between phase-locked and phase-slipping regimes,
             and have a higher degree of multiplexing capabilities that
             can benefit the fields of biological separation and sensing
             as well as provide crucial insights into general ratchet
             behavior.},
   Doi = {10.1039/c1lc20683d},
   Key = {fds282408}
}

@article{fds282435,
   Author = {Santillan, ST and Virgin, LN},
   Title = {Numerical and experimental analysis of the static behavior
             of highly deformed risers},
   Journal = {Ocean Engineering},
   Volume = {38},
   Number = {13},
   Pages = {1397-1402},
   Publisher = {Elsevier BV},
   Year = {2011},
   Month = {September},
   ISSN = {0029-8018},
   url = {http://dx.doi.org/10.1016/j.oceaneng.2011.06.009},
   Abstract = {This paper models a slender, flexible structure used as a
             drill string or riser in the offshore oil and gas industry
             that connects the well-head with a floating control vessel.
             These systems are used in deep-water drilling applications
             and present considerable design challenges due to their
             extreme flexibility and susceptibility to buckling and
             vibration. Two typical configurations are used (Bai and Bai,
             2005), with a common feature involving the attachment of a
             buoy designed to relieve some of the axial forces acting on
             the riser, especially at the attachment points. Previous
             work by the authors studied numerical results of
             small-amplitude vibrations and two other equilibrium
             configurations using parameter values that closely resemble
             the full-scale application (Santillan et al., 2008). Here,
             two new configurations are considered, and experiments are
             designed and conducted to verify these equilibrium results.
             © 2011 Elsevier Ltd. All rights reserved.},
   Doi = {10.1016/j.oceaneng.2011.06.009},
   Key = {fds282435}
}

@article{fds282403,
   Author = {Virgin, LN},
   Title = {A block rocking on a seesawing foundation},
   Journal = {Conference Proceedings of the Society for Experimental
             Mechanics Series},
   Volume = {2},
   Pages = {31-39},
   Year = {2011},
   Month = {August},
   ISSN = {2191-5644},
   Abstract = {Examples of vibro-impact mechanical and structural systems
             are not uncommon. Such systems are capable of exhibiting an
             interesting spectrum of non-smooth dynamic behavior when a
             characteristic changes abruptly. However, they present
             strong challenges to the analyst and designer trying to
             predict dynamic behavior. This paper considers an example of
             a rigid body (a rectangular block) that is placed on a flat
             surface that then oscillates in a seesawing, or tilting,
             motion. Given this kind of harmonic base excitation the
             free-standing block then responds accordingly, often by
             rocking. In this study the overturning characteristics of
             the block are of special interest. The motion is considered
             to take place in a vertical plane with no bouncing or
             sliding allowed. The outcome of experimental testing is
             compared with intensive numerical simulation. ©2010 Society
             for Experimental Mechanics Inc.},
   Key = {fds282403}
}

@article{fds304975,
   Author = {Tahir, MA and Gao, L and Virgin, LN and Yellen, BB},
   Title = {Transport of superparamagnetic beads through a
             two-dimensional potential energy landscape.},
   Journal = {Physical Review. E, Statistical, Nonlinear, and Soft Matter
             Physics},
   Volume = {84},
   Number = {1 Pt 1},
   Pages = {011403},
   Year = {2011},
   Month = {July},
   ISSN = {1539-3755},
   url = {http://dx.doi.org/10.1103/physreve.84.011403},
   Abstract = {The nonlinear dynamic behavior of superparamagnetic beads
             transported through a two-dimensional potential energy
             landscape is explored empirically and through numerical
             simulation. The beads are driven through a periodic array of
             micromagnets by an external rotating field oriented at an
             angle θ relative to the magnetization direction of the
             substrate. The bead's motion was highly sensitive to the
             angle of the driving field near critical angles and to
             various system parameters, including bead size, rotation
             frequency, and substrate pole density. Our results suggest
             the possibility of using this behavior in a highly
             discriminative colloidal separation system, in which two
             different bead types can be tuned to move in orthogonal
             directions.},
   Doi = {10.1103/physreve.84.011403},
   Key = {fds304975}
}

@article{fds282402,
   Author = {Virgin, LN and Lyman, TC},
   Title = {Structural dynamics of a frame including axial load
             effects},
   Journal = {Conference Proceedings of the Society for Experimental
             Mechanics Series},
   Volume = {4},
   Pages = {119-124},
   Year = {2011},
   Month = {July},
   ISSN = {2191-5644},
   Abstract = {This paper considers the free vibration of a plane,
             rectangular, portal frame consisting of slender members.
             Natural frequencies and mode shapes are influenced by the
             addition of mass at the corners of the frame. The members
             are sufficiently slender that axial effects occur, and may
             ultimately lead to buckling. The results from both
             theoretical and experimental studies are presented. ©2010
             Society for Experimental Mechanics Inc.},
   Key = {fds282402}
}

@article{fds343281,
   Author = {Srivastava, R and Panovsky, J and Kielb, R and Virgin, L and Ekici,
             K},
   Title = {Nonlinear flutter in fan stator vanes with time dependent
             fixity},
   Journal = {Journal of Turbomachinery},
   Volume = {134},
   Number = {2},
   Year = {2011},
   Month = {June},
   url = {http://dx.doi.org/10.1115/1.4003253},
   Abstract = {A new mechanism for fan stator vane failure in turbofan
             engines at high speed and high loading has been identified
             and reported in this paper. Highly destructive vane failures
             have been encountered at Honeywell in a development fan with
             composite stator vanes. Measured data indicated nonlinear
             high amplitude vibratory response in fan stator vanes on the
             stall side of the fan map at high speeds. Analysis showed
             that under certain steady loading, vane fixity at the hub
             could change, significantly reducing the vane natural
             frequency. At this lower natural frequency, the vane was
             found to be aeroelastically unstable, and calculated
             response exhibited characteristics similar to those observed
             during failure. An engine test conducted to validate the
             role of hub fixity in vane failures showed the failure to be
             a self-excited phenomenon and not driven by an external
             source of excitation. It was also shown that failures occur
             in vanes that are not rigidly fixed, validating the role of
             hub fixity in vane failures. Test results along with
             analysis confirm the role of time dependent hub fixity
             leading to the highly destructive flutter responsible for
             vane failures. © 2012 American Society of Mechanical
             Engineers.},
   Doi = {10.1115/1.4003253},
   Key = {fds343281}
}

@article{fds282430,
   Author = {Plaut, RH and Virgin, LN},
   Title = {Optimal design of cantilevered elastica for minimum tip
             deflection under self-weight},
   Journal = {Structural and Multidisciplinary Optimization},
   Volume = {43},
   Number = {5},
   Pages = {657-664},
   Publisher = {Springer Nature},
   Year = {2011},
   Month = {May},
   ISSN = {1615-147X},
   url = {http://dx.doi.org/10.1007/s00158-010-0611-x},
   Abstract = {The optimal distribution of material to minimize the
             vertical deflection of the free end of a horizontal
             cantilever is determined. The beam is only subjected to its
             own weight. Large deflections are considered, and the
             structure is modeled as an inextensible elastica. A
             minimum-area constraint is included, and is active in a
             region near the tip. After the problem is formulated,
             numerical results are obtained with the use of a shooting
             method. The moment of inertia is assumed to be proportional
             to the area or its square or cube. The results depend on
             this relationship, the minimum-area constraint, and a
             nondimensional parameter depending on the beam's density,
             length, and modulus of elasticity. In the numerical results
             presented, if the minimum area is 1/20 of the area of the
             uniform beam, the tip deflection for the optimal design is
             78-89% smaller than that for the uniform beam. An experiment
             is conducted and the data are in close agreement with the
             numerical results. © 2010 Springer-Verlag.},
   Doi = {10.1007/s00158-010-0611-x},
   Key = {fds282430}
}

@article{fds282405,
   Author = {Budd, C and Champneys, A and Lord, G and Virgin, L},
   Title = {Introduction to special issue on reflections in nonlinear
             mechanics},
   Journal = {Ima Journal of Applied Mathematics},
   Volume = {76},
   Number = {1},
   Pages = {1},
   Publisher = {Oxford University Press (OUP)},
   Year = {2011},
   Month = {February},
   ISSN = {0272-4960},
   url = {http://dx.doi.org/10.1093/imamat/hxq071},
   Doi = {10.1093/imamat/hxq071},
   Key = {fds282405}
}

@article{fds282428,
   Author = {Gao, L and Tahir, MA and Virgin, LN and Yellen, BB},
   Title = {Multiplexing Superparamagnetic Beads Using Phase-Modulated
             Multi-Frequency Ratchets},
   Journal = {Lab on a Chip},
   Volume = {11},
   Number = {4214-4220},
   Year = {2011},
   Key = {fds282428}
}

@article{fds282431,
   Author = {Tahir, MA and Guo, L and Virgin, LN and Yellen, BB},
   Title = {Transport of superparamagnetic beads through a
             two-dimensional potential energy landscape},
   Journal = {Physical Review E},
   Volume = {84},
   Number = {011403},
   Pages = {011403},
   Year = {2011},
   ISSN = {1539-3755},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/21867167},
   Abstract = {The nonlinear dynamic behavior of superparamagnetic beads
             transported through a two-dimensional potential energy
             landscape is explored empirically and through numerical
             simulation. The beads are driven through a periodic array of
             micromagnets by an external rotating field oriented at an
             angle θ relative to the magnetization direction of the
             substrate. The bead's motion was highly sensitive to the
             angle of the driving field near critical angles and to
             various system parameters, including bead size, rotation
             frequency, and substrate pole density. Our results suggest
             the possibility of using this behavior in a highly
             discriminative colloidal separation system, in which two
             different bead types can be tuned to move in orthogonal
             directions. © 2011 American Physical Society.},
   Doi = {10.1103/PhysRevE.84.011403},
   Key = {fds282431}
}

@article{fds282436,
   Author = {Phungpaingam, B and Virgin, LN and Chucheepsakul,
             S},
   Title = {Stability of spatial elastica including weight
             effects},
   Journal = {International Journal of Structural Stability and
             Dynamics},
   Volume = {11},
   Number = {6},
   Year = {2011},
   Key = {fds282436}
}

@article{fds282400,
   Author = {Srivastava, R and Panovsky, J and Kielb, R and Virgin, L and Ekici,
             K},
   Title = {Non-linear flutter in fan stator vanes with time dependent
             fixity},
   Journal = {Proceedings of the Asme Turbo Expo},
   Volume = {6},
   Number = {PARTS A AND B},
   Pages = {1189-1199},
   Publisher = {ASME},
   Year = {2010},
   Month = {December},
   ISSN = {0889-504X},
   url = {http://dx.doi.org/10.1115/GT2010-22555},
   Abstract = {A new mechanism for fan stator vane failure in turbofan
             engines at high speed and high loading has been identified
             and reported in this paper. Highly destructive vane failures
             have been encountered at Honeywell in one of the development
             fans with composite stator vanes. Measured data indicated
             non-linear high amplitude vibratory response in fan stator
             vanes on stall side of the fan map at high speeds. Analysis
             showed that under certain vane steady loading vane fixity at
             hub could change, significantly reducing the vane natural
             frequency. At lower natural frequency the vane was found to
             be aeroelastically unstable and calculated response
             exhibited behavior observed during failure. An engine test
             was conducted to validate the role of hub fixity in vane
             failures. Test results showed failure to be a self-excited
             phenomenon and not driven by an external source of
             excitation. It was also shown that failures occur in vanes
             that are not rigidly fixed, validating the role of hub
             fixity in vane failures. Test results along with the
             analysis confirm the role of time dependent hub fixity
             leading to the highly destructive flutter responsible for
             vane failures. Copyright © 2010 by ASME.},
   Doi = {10.1115/GT2010-22555},
   Key = {fds282400}
}

@article{fds282437,
   Author = {Gao, L and Gottron, NJ and Virgin, LN and Yellen,
             BB},
   Title = {The synchronization of superparamagnetic beads driven by a
             micro-magnetic ratchet.},
   Journal = {Lab on a Chip},
   Volume = {10},
   Number = {16},
   Pages = {2108-2114},
   Year = {2010},
   Month = {August},
   ISSN = {1473-0197},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/20556295},
   Abstract = {We present theoretical, numerical, and experimental analyses
             on the non-linear dynamic behavior of superparamagnetic
             beads exposed to a periodic array of micro-magnets and an
             external rotating field. The agreement between theoretical
             and experimental results revealed that non-linear magnetic
             forcing dynamics are responsible for transitions between
             phase-locked orbits, sub-harmonic orbits, and closed orbits,
             representing different mobility regimes of colloidal beads.
             These results suggest that the non-linear behavior can be
             exploited to construct a novel colloidal separation device
             that can achieve effectively infinite separation resolution
             for different types of beads, by exploiting minor
             differences in their bead's properties. We also identify a
             unique set of initial conditions, which we denote the
             "devil's gate" which can be used to expeditiously identify
             the full range of mobility for a given bead
             type.},
   Doi = {10.1039/c003836a},
   Key = {fds282437}
}

@article{fds282401,
   Author = {Santillan, ST and Virgin, LN and Plaut, RH},
   Title = {Static and dynamic behavior of highly deformed risers and
             pipelines},
   Journal = {Journal of Offshore Mechanics and Arctic
             Engineering},
   Volume = {132},
   Number = {2},
   Pages = {1-6},
   Publisher = {ASME International},
   Year = {2010},
   Month = {May},
   ISSN = {0892-7219},
   url = {http://dx.doi.org/10.1115/1.4000555},
   Abstract = {This paper models flexible risers and pipelines as slender
             elastica structures. The theoretical formulation leads to a
             type of nonlinear boundary value problem that can be solved
             numerically given appropriate boundary conditions. The
             offsetting effects of gravity and buoyancy are included in
             the analysis. These forces can provide considerable axial
             loading (as can thermal changes), and hence, stability
             (buckling) is a major concern. Initial studies are based on
             the planar problem. A free-vibration analysis is also
             conducted for small-amplitude oscillations about various
             deflected equilibrium configurations in terms of natural
             frequencies and corresponding mode shapes. Energy
             dissipation and fluid forces are key issues in the forced
             problem, especially when large deformations are involved.
             Free vibration information is a vital prerequisite in
             understanding the response of these types of structures in
             practice. Copyright © 2010 by ASME.},
   Doi = {10.1115/1.4000555},
   Key = {fds282401}
}

@article{fds282432,
   Author = {Virgin, LN and Lyman, TC and Davis, RB},
   Title = {Nonlinear dynamics of a ball rolling on a
             surface},
   Journal = {American Journal of Physics},
   Volume = {78},
   Number = {3},
   Pages = {250-257},
   Publisher = {American Association of Physics Teachers
             (AAPT)},
   Year = {2010},
   Month = {March},
   ISSN = {0002-9505},
   url = {http://dx.doi.org/10.1119/1.3263169},
   Abstract = {An underlying potential energy function can provide visual
             and intuitive insight into a system's stability and overall
             behavior. In particular, the motion of a ball moving along a
             curve or surface in a gravitational field provides a
             macroscale demonstration of interesting dynamics. We
             investigate the motion of a small ball rolling along a
             smooth two-dimensional potential surface. A direct
             experimental realization of this situation is suitable for
             demonstrating some classic features of nonlinear dynamics.
             The results of numerical simulations are directly compared
             with experimental data. To better characterize the dynamical
             behavior of the ball, especially when it is undergoing
             chaotic motion, several descriptive measures are discussed,
             including time-lag embedding, initial condition maps, power
             spectra, Lyapunov exponents, and fractal dimensions. © 2010
             American Association of Physics Teachers.},
   Doi = {10.1119/1.3263169},
   Key = {fds282432}
}

@article{fds282429,
   Author = {Srivastava, R and Panovsky, J and Kielb, R and Virgin, L and Ekici,
             K},
   Title = {NON-LINEAR FLUTTER IN FAN STATOR VANES WITH TIME DEPENDENT
             FIXITY},
   Journal = {Proceedings of the Asme Turbo Expo 2010, Vol 6, Pts a and
             B},
   Volume = {134},
   Number = {2},
   Pages = {1189-1199},
   Publisher = {AMER SOC MECHANICAL ENGINEERS},
   Year = {2010},
   Month = {January},
   ISSN = {0889-504X},
   url = {http://dx.doi.org/10.1115/1.4003253},
   Abstract = {A new mechanism for fan stator vane failure in turbofan
             engines at high speed and high loading has been identified
             and reported in this paper. Highly destructive vane failures
             have been encountered at Honeywell in a development fan with
             composite stator vanes. Measured data indicated nonlinear
             high amplitude vibratory response in fan stator vanes on the
             stall side of the fan map at high speeds. Analysis showed
             that under certain steady loading, vane fixity at the hub
             could change, significantly reducing the vane natural
             frequency. At this lower natural frequency, the vane was
             found to be aeroelastically unstable, and calculated
             response exhibited characteristics similar to those observed
             during failure. An engine test conducted to validate the
             role of hub fixity in vane failures showed the failure to be
             a self-excited phenomenon and not driven by an external
             source of excitation. It was also shown that failures occur
             in vanes that are not rigidly fixed, validating the role of
             hub fixity in vane failures. Test results along with
             analysis confirm the role of time dependent hub fixity
             leading to the highly destructive flutter responsible for
             vane failures. © 2012 American Society of Mechanical
             Engineers.},
   Doi = {10.1115/1.4003253},
   Key = {fds282429}
}

@article{fds282433,
   Author = {Plaut, RH and Virgin, LN},
   Title = {Vibrations and large postbuckling deflections of optimal
             pinned columns with elastic foundations},
   Journal = {Structural and Multidisciplinary Optimization},
   Volume = {40},
   Number = {1-6},
   Pages = {157-164},
   Publisher = {Springer Nature},
   Year = {2010},
   Month = {January},
   ISSN = {1615-147X},
   url = {http://dx.doi.org/10.1007/s00158-008-0354-0},
   Abstract = {The optimal distribution of material to maximize the
             critical load of columns has been studied extensively in the
             past, along with initial postbuckling behavior. Here, large
             postbuckling deflections are analyzed for optimal columns
             with pinned ends. Small vibrations of the optimal columns
             about postbuckled equilibrium shapes are also investigated.
             A shooting method is utilized to obtain numerical solutions.
             In some examples, an elastic foundation is attached to the
             column. The foundation includes the usual transverse
             resistance and an axial resisting force. The bifurcation is
             subcritical in some cases, and then the column is
             imperfection-sensitive. Results are compared to those for
             the corresponding uniform column with the same total volume.
             © 2009 US Government.},
   Doi = {10.1007/s00158-008-0354-0},
   Key = {fds282433}
}

@article{fds282438,
   Author = {Santillan, ST and Virgin, LN and Plaut, RH},
   Title = {Dynamic behavior of highly-deformed risers and
             pipelines},
   Journal = {Asme Journal of Offshore Mechanics and Arctic
             Engineering},
   Volume = {132},
   Pages = {021401},
   Year = {2010},
   Key = {fds282438}
}

@article{fds282398,
   Author = {Virgin, L and Holland, D},
   Title = {Effect of weight on the experimental modal analysis of
             slender cantilever beams},
   Journal = {Proceedings of the Asme Design Engineering Technical
             Conference},
   Volume = {1},
   Number = {PARTS A AND B},
   Pages = {557-560},
   Year = {2009},
   Month = {December},
   url = {http://dx.doi.org/10.1115/DETC2009-86149},
   Abstract = {It is relatively well known that axial loads tend to
             influence lateral stiffness and hence natural frequencies of
             slender structural components. Tensile forces tend to
             increase the lateral stiffness and compressive forces tend
             to reduce lateral stiffness, bringing with it the
             possibility of buckling. In many practical situations this
             is a negligible effect. But for very slender structures it
             can be important, including the effect of self-weight. This
             paper will focus attention on a form of double cantilever
             beam system, i.e., two cantilevers sharing a common hub. A
             differential axial load can be applied to this system via
             orientation in a gravitational field. We shall neglect the
             effect of gravity when the beams are in their horizontal
             orientation from a limited theoretical standpoint. It is of
             course present in the experiments but the cantilevers are
             much stiffer in one direction than the other, and the beams
             are clamped with their stiffer resistance in the vertical
             direction. The focus of the current paper is on the natural
             frequencies and mode shapes of a two-beam system from an
             experimental modal analysis perspective. Copyright © 2009
             by ASME.},
   Doi = {10.1115/DETC2009-86149},
   Key = {fds282398}
}

@article{fds304973,
   Author = {Plaut, RH and Virgin, LN},
   Title = {Vibration and snap-through of bent elastica strips subjected
             to end rotations},
   Journal = {Journal of Applied Mechanics},
   Volume = {76},
   Number = {4},
   Pages = {1-7},
   Publisher = {ASME International},
   Year = {2009},
   Month = {December},
   ISSN = {0021-8936},
   url = {http://dx.doi.org/10.1115/1.3086783},
   Abstract = {A flexible strip is rotated at its ends until it forms a
             deep circular arc above its ends. Then the ends are kept
             immovable and are rotated downward until the arch suddenly
             snaps into an inverted configuration. The strip is analyzed
             as an inextensible elastica. Twodimensional equilibrium
             shapes, vibration modes and frequencies, and critical
             rotations for snap-through are determined using a shooting
             method. Experiments are also conducted and results are
             compared with those from the analysis. The agreement is
             good. In addition, a microelectromechanical systems (MEMS)
             example is analyzed, in which an electrostatic force below a
             buckled strip causes the strip to snap downward, and the
             critical force is obtained as a function of the vertical
             gap. © 2009 by ASME.},
   Doi = {10.1115/1.3086783},
   Key = {fds304973}
}

@article{fds304974,
   Author = {Yellen, BB and Virgin, LN},
   Title = {Nonlinear dynamics of superparamagnetic beads in a traveling
             magnetic-field wave.},
   Journal = {Physical Review. E, Statistical, Nonlinear, and Soft Matter
             Physics},
   Volume = {80},
   Number = {1 Pt 1},
   Pages = {011402},
   Year = {2009},
   Month = {July},
   ISSN = {1539-3755},
   url = {http://dx.doi.org/10.1103/physreve.80.011402},
   Abstract = {The nonlinear dynamic behavior of superparamagnetic beads
             exposed to a periodic array of micromagnets and an external
             rotating field is simulated as a function of the relative
             size of the bead with respect to the micromagnet size and
             the strength of the external field relative to the pole
             density of the substrate. For large bead sizes, it is
             confirmed that the motion of the beads corresponds to the
             dynamics of an overdamped nonlinear harmonic oscillator. For
             lower bead sizes, additional subharmonic locking effects are
             observed along with the emergence of bounded orbits. These
             results qualitatively support previous experimental
             investigations of traveling-wave magnetophoresis and provide
             guidelines for achieving nearly infinite separation
             resolution between differently sized beads.},
   Doi = {10.1103/physreve.80.011402},
   Key = {fds304974}
}

@article{fds282450,
   Author = {Yellen, B and Virgin, LN},
   Title = {Non-linear dynamics of superparamagnetic beads in a
             traveling magnetic field wave},
   Journal = {Physical Review E},
   Volume = {80},
   Number = {011402},
   Pages = {011402},
   Year = {2009},
   ISSN = {1539-3755},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/19658704},
   Abstract = {The nonlinear dynamic behavior of superparamagnetic beads
             exposed to a periodic array of micromagnets and an external
             rotating field is simulated as a function of the relative
             size of the bead with respect to the micromagnet size and
             the strength of the external field relative to the pole
             density of the substrate. For large bead sizes, it is
             confirmed that the motion of the beads corresponds to the
             dynamics of an overdamped nonlinear harmonic oscillator. For
             lower bead sizes, additional subharmonic locking effects are
             observed along with the emergence of bounded orbits. These
             results qualitatively support previous experimental
             investigations of traveling-wave magnetophoresis and provide
             guidelines for achieving nearly infinite separation
             resolution between differently sized beads. © 2009 The
             American Physical Society.},
   Doi = {10.1103/PhysRevE.80.011402},
   Key = {fds282450}
}

@article{fds282451,
   Author = {Plaut, RH and Virgin, LN},
   Title = {Vibration and snap-through of bent elastica strips subjected
             to end rotations},
   Journal = {Journal of Applied Mechanics},
   Volume = {76},
   Number = {041011},
   Pages = {1-7},
   Year = {2009},
   ISSN = {0021-8936},
   url = {http://dx.doi.org/10.1115/1.3086783},
   Abstract = {A flexible strip is rotated at its ends until it forms a
             deep circular arc above its ends. Then the ends are kept
             immovable and are rotated downward until the arch suddenly
             snaps into an inverted configuration. The strip is analyzed
             as an inextensible elastica. Twodimensional equilibrium
             shapes, vibration modes and frequencies, and critical
             rotations for snap-through are determined using a shooting
             method. Experiments are also conducted and results are
             compared with those from the analysis. The agreement is
             good. In addition, a microelectromechanical systems (MEMS)
             example is analyzed, in which an electrostatic force below a
             buckled strip causes the strip to snap downward, and the
             critical force is obtained as a function of the vertical
             gap. © 2009 by ASME.},
   Doi = {10.1115/1.3086783},
   Key = {fds282451}
}

@article{fds282454,
   Author = {Santillan, ST and Plaut, RH and Witelski, TP and Virgin,
             LN},
   Title = {Large oscillations of beams and columns including
             self-weight},
   Journal = {International Journal of Non Linear Mechanics},
   Volume = {43},
   Number = {8},
   Pages = {761-771},
   Publisher = {Elsevier BV},
   Year = {2008},
   Month = {October},
   ISSN = {0020-7462},
   url = {http://dx.doi.org/10.1016/j.ijnonlinmec.2008.04.007},
   Abstract = {Large-amplitude, in-plane beam vibration is investigated
             using numerical simulations and a perturbation analysis
             applied to the dynamic elastica model. The governing
             non-linear boundary value problem is described in terms of
             the arclength, and the beam is treated as inextensible. The
             self-weight of the beam is included in the equations. First,
             a finite difference numerical method is introduced. The
             system is discretized along the arclength, and
             second-order-accurate finite difference formulas are used to
             generate time series of large-amplitude motion of an upright
             cantilever. Secondly, a perturbation method (the method of
             multiple scales) is applied to obtain approximate solutions.
             An analytical backbone curve is generated, and the results
             are compared with those in the literature for various
             boundary conditions where the self-weight of the beam is
             neglected. The method is also used to characterize
             large-amplitude first-mode vibration of a cantilever with
             non-zero self-weight. The perturbation and finite difference
             results are compared for these cases and are seen to agree
             for a large range of vibration amplitudes. Finally,
             large-amplitude motion of a postbuckled, clamped-clamped
             beam is simulated for varying degrees of buckling and
             self-weight using the finite difference method, and backbone
             curves are obtained. © 2008 Elsevier Ltd.},
   Doi = {10.1016/j.ijnonlinmec.2008.04.007},
   Key = {fds282454}
}

@article{fds282453,
   Author = {Virgin, LN and Santillan, ST and Plaut, RH},
   Title = {Vibration isolation using extreme geometric
             nonlinearity},
   Journal = {Journal of Sound and Vibration},
   Volume = {315},
   Number = {3},
   Pages = {721-731},
   Publisher = {Elsevier BV},
   Year = {2008},
   Month = {August},
   ISSN = {0022-460X},
   url = {http://dx.doi.org/10.1016/j.jsv.2007.12.025},
   Abstract = {A highly deformed, slender beam (or strip), attached to a
             vertically oscillating base, is used in a vibration
             isolation application to reduce the motion of a supported
             mass. The isolator is a thin strip that is bent so that the
             two ends are clamped together, forming a loop. The clamped
             ends are attached to an excitation source and the supported
             system is attached at the loop midpoint directly above the
             base. The strip is modeled as an elastica, and the resulting
             nonlinear boundary value problem is solved numerically using
             a shooting method. First the equilibrium shapes of the loop
             with varying static loads and lengths are studied. The
             analysis reveals a large degree of stiffness tunability; the
             stiffness is dependent on the geometric configuration, which
             itself is determined by the supported mass, loop length, and
             loop self-weight. Free vibration frequencies and mode shapes
             are also found. Finally, the case of forced vibration is
             studied, and the displacement transmissibility over a large
             range of forcing frequencies is determined for varying
             parameter values. Experiments using polycarbonate strips are
             conducted to verify equilibrium and dynamic behavior. ©
             2008 Elsevier Ltd. All rights reserved.},
   Doi = {10.1016/j.jsv.2007.12.025},
   Key = {fds282453}
}

@article{fds282395,
   Author = {Holland, D and Virgin, L},
   Title = {Experimental modal analysis of solar sail
             booms},
   Journal = {Collection of Technical Papers Aiaa/Asme/Asce/Ahs/Asc
             Structures, Structural Dynamics and Materials
             Conference},
   Year = {2008},
   Month = {July},
   ISSN = {0273-4508},
   Abstract = {This paper presents the results of experimental modal
             analysis of a system of two very slender cantilever beams
             connected by a rigid hub. The effect of gravity is examined
             together with the influence of an attached cable. Natural
             frequencies and mode shapes are determined for a number of
             configurations. The practical application of these types of
             systems is as the structural support frame for solar sails,
             in which the current set of results represents an
             intermediate step in going from the behavior of an isolated
             solar sail boom towards the four boom configuration favored
             by many current designs. Copyright © 2008 by the American
             Institute of Aeronautics and Astronautics, Inc. All rights
             reserved.},
   Key = {fds282395}
}

@article{fds282349,
   Author = {Virgin, LN and Dowell, EH and Flowers, G},
   Title = {Nonlinear Vibration},
   Pages = {255-267},
   Publisher = {JOHN WILEY & SONS INC},
   Year = {2008},
   Month = {April},
   url = {http://dx.doi.org/10.1002/9780470209707.ch18},
   Doi = {10.1002/9780470209707.ch18},
   Key = {fds282349}
}

@article{fds282452,
   Author = {Davis, RB and Virgin, LN and Brown, AM},
   Title = {Cylindrical shell submerged in bounded acoustic media: A
             modal approach},
   Journal = {Aiaa Journal},
   Volume = {46},
   Number = {3},
   Pages = {752-763},
   Publisher = {American Institute of Aeronautics and Astronautics
             (AIAA)},
   Year = {2008},
   Month = {March},
   ISSN = {0001-1452},
   url = {http://dx.doi.org/10.2514/1.31706},
   Abstract = {The dynamics of a simply supported cylindrical shell
             submerged in liquid hydrogen and liquid oxygen are
             considered. The shell itself is bounded by a rigid outer
             cylinder with closed rigid ends. This configuration gives
             rise to two fluid-filled cavities - an inner cylindrical
             cavity and an outer annular cavity. Such geometries are
             common in rocket engine design. The natural frequencies and
             modes of the fluid-structure system are computed by
             combining the rigid wall acoustic cavity modes and the in
             vacuo structural modes into a system of coupled ordinary
             differential equations. Eigenvalue veering is observed near
             the intersections of the curves representing natural
             frequencies of the rigid wall acoustic and the in vacuo
             structural modes. In the case of a shell submerged in liquid
             hydrogen, system frequencies near these intersections are as
             much as 30% lower than the corresponding in vacuo structural
             frequencies. Because of its high density, the frequency
             reductions in the presence of liquid oxygen are even more
             dramatic. The forced responses of a shell submerged in
             liquid hydrogen and liquid oxygen, while subject to a
             harmonic point excitation, are also presented. The responses
             in the presence of fluid are found to be quite distinct from
             those of the structure in vacuo.},
   Doi = {10.2514/1.31706},
   Key = {fds282452}
}

@article{fds282460,
   Author = {Jeffers, AE and Plaut, RH and Virgin, LN},
   Title = {Vibration isolation using buckled or pre-bent columns-Part
             2: Three-dimensional motions of horizontal rigid
             plate},
   Journal = {Journal of Sound and Vibration},
   Volume = {310},
   Number = {1-2},
   Pages = {421-432},
   Publisher = {Elsevier BV},
   Year = {2008},
   Month = {February},
   ISSN = {0022-460X},
   url = {http://dx.doi.org/10.1016/j.jsv.2007.09.039},
   Abstract = {This is a continuation of previous work to investigate the
             use of pairs of pre-bent columns, bonded with a viscoelastic
             filler, as vibration isolators. In this paper, four of these
             devices support the corners of a square, rigid plate. When
             the system is in equilibrium, small harmonic vibrations are
             applied vertically to the base of the isolators, and the
             steady-state response of the system is determined. First,
             the system is analyzed for the fully symmetric case, i.e.,
             the center of mass of the plate coincides with the geometric
             center. Then, the system is analyzed for various cases in
             which the center of mass has some eccentricity. The
             eccentric weight introduces rotational motions of the plate.
             The governing equations are formulated and then numerically
             solved in Mathematica using a shooting method. The
             displacement transmissibility is plotted over a range of
             excitation frequencies, and the mode shapes are shown for
             the first few resonant frequencies. Free vibration of the
             system is also considered. For this three-dimensional
             system, the pre-bent columns can be effective at isolating
             vibrations for a wide range of excitation frequencies. ©
             2007 Elsevier Ltd. All rights reserved.},
   Doi = {10.1016/j.jsv.2007.09.039},
   Key = {fds282460}
}

@article{fds282461,
   Author = {Holland, DB and Virgin, LN and Plaut, RH},
   Title = {Large deflections and vibration of a tapered cantilever
             pulled at its tip by a cable},
   Journal = {Journal of Sound and Vibration},
   Volume = {310},
   Number = {1-2},
   Pages = {433-441},
   Publisher = {Elsevier BV},
   Year = {2008},
   Month = {February},
   ISSN = {0022-460X},
   url = {http://dx.doi.org/10.1016/j.jsv.2007.06.075},
   Abstract = {The behavior of a slender, tapered, cantilever beam loaded
             through a cable attached to its free end is described. Large
             static deflections are computed (based on an elastica
             description) together with natural frequencies and mode
             shapes for small-amplitude vibrations about equilibrium.
             Experimental results exhibit good agreement with the
             theoretical results. © 2007.},
   Doi = {10.1016/j.jsv.2007.06.075},
   Key = {fds282461}
}

@article{fds282462,
   Author = {Plaut, RH and Favor, HM and Jeffers, AE and Virgin,
             LN},
   Title = {Vibration isolation using buckled or pre-bent columns-Part
             1: Two-dimensional motions of horizontal rigid
             bar},
   Journal = {Journal of Sound and Vibration},
   Volume = {310},
   Number = {1-2},
   Pages = {409-420},
   Publisher = {Elsevier BV},
   Year = {2008},
   Month = {February},
   ISSN = {0022-460X},
   url = {http://dx.doi.org/10.1016/j.jsv.2007.09.037},
   Abstract = {The use of buckled columns, or pairs of pre-bent columns
             bonded with a viscoelastic filler, as vibration isolators is
             analyzed. They support a horizontal rigid bar at its ends,
             and harmonic vertical motion is applied at the base of the
             isolators. The displacement transmissibility is analyzed for
             both symmetric and asymmetric bars. In the latter case, the
             bar exhibits rotational as well as translational motion.
             Each column is modeled as an elastica, allowing for large
             deflections. Small steady-state vibrations about the
             equilibrium configuration of the system are analyzed. After
             formulation of the governing equations, a shooting method is
             utilized to obtain numerical solutions in Mathematica. The
             transmissibility is plotted as a function of the excitation
             frequency, and vibration shapes associated with peaks in the
             transmissibility plots are shown. For the buckled
             single-column isolators, the effect of the amount of
             asymmetry of the bar is examined. For the bonded two-column
             pre-bent isolators, the effects of the filler stiffness,
             amount of initial curvature, and supported weight are
             determined. The isolators can be effective for a large range
             of excitation frequencies. © 2007 Elsevier Ltd. All rights
             reserved.},
   Doi = {10.1016/j.jsv.2007.09.037},
   Key = {fds282462}
}

@article{fds150317,
   Author = {L.N. Virgin and S.T. Santillan and R.H. Plaut},
   Title = {Vibration isolation using extreme geometric
             nonlinearity},
   Journal = {Journal of Sound and Vibration},
   Volume = {315},
   Pages = {721-731},
   Year = {2008},
   Key = {fds150317}
}

@article{fds282394,
   Author = {Santillan, ST and Virgin, LN and Plaut, RH},
   Title = {Static and dynamic behavior of highly-deformed risers and
             pipelines},
   Journal = {Proceedings of the International Conference on Offshore
             Mechanics and Arctic Engineering Omae},
   Volume = {3},
   Pages = {143-149},
   Publisher = {ASME},
   Year = {2007},
   Month = {December},
   url = {http://dx.doi.org/10.1115/OMAE2007-29180},
   Abstract = {This paper models flexible risers and pipelines as slender
             elastica structures. The theoretical formulation leads to a
             type of nonlinear boundary value problem that can be solved
             numerically given appropriate boundary conditions. The
             offsetting effects of gravity and buoyancy are included in
             the analysis. These forces can provide considerable axial
             loading (as can thermal changes) and hence stability
             (buckling) is a major concern. Initial studies are based on
             the planar problem. A free-vibration analysis is also
             conducted for small-amplitude oscillations about various
             deflected equilibrium configurations in terms of natural
             frequencies and corresponding mode shapes [1]. Energy
             dissipation and fluid forces are a key issue in the forced
             problem, especially when large deformations are involved [2,
             3]. Free vibration information is a vital prerequisite in
             understanding the response of these types of structures in
             practice [4]. Copyright © 2007 by ASME.},
   Doi = {10.1115/OMAE2007-29180},
   Key = {fds282394}
}

@article{fds282392,
   Author = {Virgin, LN and Nichols, JM},
   Title = {An experimental nonlinear oscillator subject to
             two-frequency excitation},
   Journal = {Conference Proceedings of the Society for Experimental
             Mechanics Series},
   Year = {2007},
   Month = {December},
   ISSN = {2191-5644},
   Abstract = {This paper describes some interesting nonlinear behavior in
             the response of an experimental mechanical oscillator. The
             focusis on the characterization of nonlinear response
             (subharmonic, quasiperiodic and chaotic) of a discrete
             mechanical oscillator subject to two-frequency excitation. A
             variety of analysis tools are illustrated, including power
             spectra, time-lag embedding, dimension,and Poincaré
             sectioning. A key element in this study is whether the
             frequencies are commensurate or not. An excellent agreement
             is shown between experimental data and the output from
             numerical simulation.},
   Key = {fds282392}
}

@article{fds319934,
   Author = {Davis, RB and Virgin, LN and Brown, AM},
   Title = {Cylindrical shell submerged in bounded acoustic media: A
             modal approach},
   Journal = {Collection of Technical Papers Aiaa/Asme/Asce/Ahs/Asc
             Structures, Structural Dynamics and Materials
             Conference},
   Volume = {5},
   Pages = {4871-4887},
   Year = {2007},
   Month = {August},
   Abstract = {The dynamics of a simply-supported cylindrical shell
             submerged in liquid hydrogen (LH2) and liquid oxygen (LOX)
             are considered. The shell itself is bounded by a rigid outer
             cylinder with closed rigid ends. This configuration gives
             rise to two fluid-filled cavitiesan inner cylindrical cavity
             and an outer annular cavity. Such geometries are common in
             rocket engine design. This study computes the natural
             frequencies and modes of the fluid-structure system by
             combining the rigid wall acoustic cavity modes and the in
             vacuo structural modes into a system of coupled ordinary
             differential equations. Eigenvalue veering is observed near
             the intersections of the curves representing natural
             frequencies of the rigid wall acoustic and the in vacuo
             structural modes. In the case of a shell submerged in LH2,
             system frequencies near these intersections are as much as
             30% lower than the corresponding in vacuo structural
             frequencies. Due to its high density, the frequency
             reductions in the presence of LOX are even more dramatic.
             The forced response of the fluid-loaded shell subject to a
             harmonic point excitation is also presented. The forced
             response in the presence of fluid is different from the
             response of the structure in vacuo in a variety of ways. The
             frequency shifts that arise from consideration of the fluid
             alter the order of the resonant response peaks. In some
             cases, modes that are well separated in the in vacuo case
             are within close proximity in the fluid-loaded case (and
             vice-versa). The fluid-loaded structural responses also
             contain relatively small resonant peaks corresponding to
             system modes that are dominated by contributions from the
             fluid.},
   Key = {fds319934}
}

@article{fds282463,
   Author = {Davis, RB and Virgin, LN},
   Title = {Non-linear behavior in a discretely forced
             oscillator},
   Journal = {International Journal of Non Linear Mechanics},
   Volume = {42},
   Number = {5},
   Pages = {744-753},
   Publisher = {Elsevier BV},
   Year = {2007},
   Month = {June},
   ISSN = {0020-7462},
   url = {http://dx.doi.org/10.1016/j.ijnonlinmec.2007.02.012},
   Abstract = {The simulated and experimental responses of a rigid-arm
             pendulum driven by an external impactor are considered.
             Here, impact occurs if the trajectory of a rotating impactor
             intersects that of the pendulum. Using the rotation rate of
             the impactor as the control parameter, experimental trials
             have demonstrated much of the dynamic behavior predicted by
             numerical simulations. The system exhibits chatter (i.e.,
             multiple impacts within a single forcing period), sticking
             (i.e., contact between the pendulum and the impactor for
             non-negligible amounts of time), high-order periodicity, and
             behavior suggestive of chaos. A new convention for
             classifying periodic motions as well as insights regarding
             the nature of the coefficient of restitution (COR) in an
             experimental impacting system are also presented. © 2007
             Elsevier Ltd. All rights reserved.},
   Doi = {10.1016/j.ijnonlinmec.2007.02.012},
   Key = {fds282463}
}

@article{fds282415,
   Author = {Stanciulescu, I and Virgin, LN and Laursen, TA},
   Title = {Slender solar sail booms: Finite element
             analysis},
   Journal = {Journal of Spacecraft and Rockets},
   Volume = {44},
   Number = {3},
   Pages = {528-537},
   Publisher = {American Institute of Aeronautics and Astronautics
             (AIAA)},
   Year = {2007},
   Month = {May},
   ISSN = {0022-4650},
   url = {http://dx.doi.org/10.2514/1.20526},
   Abstract = {Various aspects related to the numerical (finite element)
             analysis of the support structure for solar sails are
             analyzed. Static analyses of single booms (simple beam and
             isogrid configurations) are presented and dynamic properties
             are extracted before and beyond the buckling load. Numerical
             difficulties associated with the case of buckling under
             nonconservative loading are also explored using as a
             reference example von Beck's problem, for which a
             closed-form solution for comparison is available. A study of
             the entire support structure for a square solar sail (four
             connected booms) is also presented. In all analyses,
             attention is focused on the prediction of the postbuckling
             (large deflection) behavior, including dynamics. Copyright
             © 2007 by the American Institute of Aeronautics and
             Astronautics, Inc. All rights reserved.},
   Doi = {10.2514/1.20526},
   Key = {fds282415}
}

@article{fds282465,
   Author = {Virgin, LN and Santillan, ST and Holland, DB},
   Title = {Effect of gravity on the vibration of vertical
             cantilevers},
   Journal = {Mechanics Research Communications},
   Volume = {34},
   Number = {3},
   Pages = {312-317},
   Publisher = {Elsevier BV},
   Year = {2007},
   Month = {April},
   ISSN = {0093-6413},
   url = {http://dx.doi.org/10.1016/j.mechrescom.2006.12.006},
   Abstract = {The free vibration of a vertically-oriented, thin, prismatic
             cantilever is influenced by weight. That is, the natural
             frequencies (and to a lesser extent, mode shapes) are
             affected by the application of a linearly varying axial
             load. A beam with an "upward" orientation, i.e., with the
             free end above the clamped end, will experience a
             de-stiffening effect, up to the point of self-weight
             buckling (at zero effective stiffness). A beam in a
             "downward" orientation will be stiffened by the weight of
             the beam. This technical note describes some simple
             experiments on very slender strips and their (vertical)
             orientation and shows a close correlation with theory. ©
             2007 Elsevier Ltd. All rights reserved.},
   Doi = {10.1016/j.mechrescom.2006.12.006},
   Key = {fds282465}
}

@article{fds282464,
   Author = {Todd, MD and Nichols, JM and Trickey, ST and Seaver, M and Nichols, CJ and Virgin, LN},
   Title = {Bragg grating-based fibre optic sensors in structural health
             monitoring.},
   Journal = {Philosophical Transactions. Series A, Mathematical,
             Physical, and Engineering Sciences},
   Volume = {365},
   Number = {1851},
   Pages = {317-343},
   Year = {2007},
   Month = {February},
   ISSN = {1364-503X},
   url = {http://dx.doi.org/10.1098/rsta.2006.1937},
   Abstract = {This work first considers a review of the dominant current
             methods for fibre Bragg grating wavelength interrogation.
             These methods include WDM interferometry, tunable filter
             (both Fabry-Perot and acousto-optic) demultiplexing,
             CCD/prism technique and a newer hybrid method utilizing
             Fabry-Perot and interferometric techniques. Two applications
             using these techniques are described: hull loads monitoring
             on an all-composite fast patrol boat and bolt pre-load loss
             monitoring in a composite beam in conjunction with a
             state-space modelling data analysis technique.},
   Doi = {10.1098/rsta.2006.1937},
   Key = {fds282464}
}

@article{fds282459,
   Author = {Stanciulescu, I and Virgin, LN and Laursen, TA},
   Title = {Finite element analysis of a slender isogrid
             structure},
   Journal = {Journal of Spacecraft and Rockets},
   Volume = {44},
   Pages = {529-537},
   Year = {2007},
   Key = {fds282459}
}

@article{063010018842,
   Author = {Plaut, RH and Dillard, DA and Virgin, LN},
   Title = {Postbuckling of elastic columns with second-mode
             imperfection},
   Journal = {Journal of Engineering Mechanics},
   Volume = {132},
   Number = {8},
   Pages = {898-901},
   Publisher = {American Society of Civil Engineers (ASCE)},
   Year = {2006},
   Month = {August},
   ISSN = {0733-9399},
   url = {http://dx.doi.org/10.1061/(ASCE)0733-9399(2006)132:8(898)},
   Keywords = {Buckling;Elasticity;Deflection (structures);Structural
             analysis;Mathematical models;},
   Abstract = {Initial imperfections of columns are often assumed to have
             the shape of the first buckling mode. In this technical
             note, the imperfection has the shape of the second mode. An
             elastica analysis is performed, and numerical results are
             obtained for two cases with the use of a shooting method.
             For the example of a pinned column, bifurcation occurs at a
             load slightly higher than the critical load for the perfect
             system. With further increase in load, the deflection
             changes smoothly from an antisymmetric shape with one node
             to a shape with no nodes. For the cantilevered-column
             example, a limit point occurs just beyond the critical load
             for the perfect system, and the equilibrium shape jumps from
             one state to another. As the load is increased further, the
             deflection passes smoothly to the other side of the column
             and loses its inflection point. © ASCE.},
   Doi = {10.1061/(ASCE)0733-9399(2006)132:8(898)},
   Key = {063010018842}
}

@article{063310069781,
   Author = {Holland, DB and Stanciulescu, I and Virgin, LN and Plaut,
             RH},
   Title = {Vibration and large deflection of cantilevered elastica
             compressed by angled cable},
   Journal = {Aiaa Journal},
   Volume = {44},
   Number = {7},
   Pages = {1468-1476},
   Publisher = {American Institute of Aeronautics and Astronautics
             (AIAA)},
   Year = {2006},
   Month = {July},
   ISSN = {0001-1452},
   url = {http://dx.doi.org/10.2514/1.18000},
   Keywords = {Vibrations (mechanical);Deflection (structures);Finite
             element method;Numerical methods;Frequencies;},
   Abstract = {A thin cantilevered beam is compressed by a cable attached
             to the tip of the beam and terminating near the base.
             Large-deflection equilibrium configurations and small
             vibrations about equilibrium are investigated. This system
             has a direct application to solar-sail structures, where the
             structural booms could be designed to bend to supply tension
             loading in the sail membrane. The equilibrium and vibration
             properties are examined in three ways: numerical integration
             of the governing elastica equations using a shooting method,
             finite element analysis using ABAQUS, and experiments with a
             polycarbonate strip bent by a cable that is tightened with a
             turnbuckle. Equilibrium shapes and vibration mode shapes and
             frequencies are obtained for two different cable attachment
             points offset slightly from the beam's base in the axial and
             transverse directions. Frequencies obtained from a
             three-dimensional finite element analysis are also
             presented. Copyright © 2006 by the American Institute of
             Aeronautics and Astronautics, Inc. All rights
             reserved.},
   Doi = {10.2514/1.18000},
   Key = {063310069781}
}

@article{064210171593,
   Author = {Santillan, ST and Virgin, LN and Plaut, RH},
   Title = {Post-buckling and vibration of heavy beam on horizontal or
             inclined rigid foundation},
   Journal = {Journal of Applied Mechanics},
   Volume = {73},
   Number = {4},
   Pages = {664-671},
   Publisher = {ASME International},
   Year = {2006},
   Month = {July},
   ISSN = {0021-8936},
   url = {http://dx.doi.org/10.1115/1.2165237},
   Keywords = {Vibrations (mechanical);Foundations;Structural loads;Phase
             equilibria;Natural frequencies;Mathematical
             models;},
   Abstract = {A slender, straight beam resting on a flat, rigid foundation
             does not buckle when subjected to a compressive load, since
             the load cannot overcome the effect of the beam's weight.
             However, it buckles if its ends are moved toward each other.
             Post-buckling of such a beam is examined, both theoretically
             and experimentally, for horizontal and inclined foundations.
             The beam is modeled as an elastica, and equilibrium states
             with large deflections are computed, including cases in
             which self-contact occurs. Frequencies and mode shapes for
             small vibrations about equilibrium are also determined.
             Agreement between the theoretical and experimental results
             is very good. Copyright © 2006 by ASME.},
   Doi = {10.1115/1.2165237},
   Key = {064210171593}
}

@article{06209877905,
   Author = {Chen, H and Virgin, LN},
   Title = {Finite element analysis of post-buckling dynamics in plates.
             Part II: A non-stationary analysis},
   Journal = {International Journal of Solids and Structures},
   Volume = {43},
   Number = {13},
   Pages = {4008-4027},
   Publisher = {Elsevier BV},
   Year = {2006},
   Month = {June},
   ISSN = {0020-7683},
   url = {http://dx.doi.org/10.1016/j.ijsolstr.2005.04.037},
   Keywords = {Finite element method;Buckling;Adaptive algorithms;Computational
             complexity;Bifurcation (mathematics);Stiffness;},
   Abstract = {With the secondary bifurcation and the local post-secondary
             buckling behavior being analyzed in Part I, Part II of this
             study consists of developing an adaptive non-stationary load
             sweeping algorithm to investigate post-buckling dynamics and
             mode jumping phenomena of generally (mechanically and
             thermally) loaded thin plates in a global context. The
             non-stationary sweeping procedure has the merits of adapting
             large load steps to capture static characteristics of stable
             equilibrium paths both before and after mode jumping and
             reduce automatically the step size to ensure a dynamic
             transition between the two stable branches. Thus, it is
             computationally effective. Furthermore, by adopting the
             non-stationary sweeping scheme, this procedure can avoid
             spurious convergence of the transient response to an
             unstable equilibrium. Corresponding to different
             post-secondary bifurcation forms, which are determined using
             asymptotical finite element analysis developed in Part I,
             subsequent buckling patterns of various complexity occurring
             after mode jumping are obtained using the method developed
             in this article. Qualitative changes in post-buckled
             patterns are observed after the occurrence of the secondary
             bifurcation or the mode jumping. Free vibration analysis
             using the tangent stiffness matrix obtained from the
             converged static or dynamic solutions shows a vibration
             modal shifting phenomena occurs during the process of the
             load sweep. The spurious convergence phenomenon caused by
             the application of the traditional hybrid static-dynamic
             method is found and explained. © 2005 Elsevier Ltd. All
             rights reserved.},
   Doi = {10.1016/j.ijsolstr.2005.04.037},
   Key = {06209877905}
}

@article{06209877914,
   Author = {Chen, H and Virgin, LN},
   Title = {Finite element analysis of post-buckling dynamics in
             plates-Part I: An asymptotic approach},
   Journal = {International Journal of Solids and Structures},
   Volume = {43},
   Number = {13},
   Pages = {3983-4007},
   Publisher = {Elsevier BV},
   Year = {2006},
   Month = {June},
   ISSN = {0020-7683},
   url = {http://dx.doi.org/10.1016/j.ijsolstr.2005.04.036},
   Keywords = {Dynamic response;Finite element method;Numerical
             methods;Perturbation techniques;Bifurcation
             (mathematics);},
   Abstract = {Various static and dynamic aspects of post-buckled thin
             plates, including the transition of buckled patterns,
             post-buckling dynamics, secondary bifurcation, and dynamic
             snapping (mode jumping phenomenon), are investigated
             systematically using asymptotical and non-stationary finite
             element methods. In part I, the secondary dynamic
             instability and the local post-secondary buckling behavior
             of thin rectangular plates under generalized (mechanical and
             thermal) loading is investigated using an asymptotic
             numerical method which combines Koiter's nonlinear
             instability theory with the finite element technique. A
             dynamic multi-mode reduction method-similar to its static
             single-mode counterpart: Liapunov-Schmidt reduction-is
             developed in this perturbation approach. Post-secondary
             buckling equilibrium branches are obtained by solving the
             reduced low-dimensional parametric equations and their
             stability properties are determined directly by checking the
             eigenvalues of the resulting Jacobian matrix. Typical
             post-secondary buckling forms-transcritical, supercritical
             and subcritical bifurcations are observed according to
             different combinations of boundary conditions and load
             types. Geometric imperfection analysis shows that not only
             the secondary bifurcation load but also changes in the
             fundamental post-secondary buckling behavior are affected.
             The post-buckling dynamics and the global analysis of mode
             jumping of the plates are addressed in part II. © 2005
             Elsevier Ltd. All rights reserved.},
   Doi = {10.1016/j.ijsolstr.2005.04.036},
   Key = {06209877914}
}

@article{fds282366,
   Author = {Virgin, LN},
   Title = {A reflection on nonlinear oscillations, dynamical systems,
             and bifurcations of vector fields},
   Journal = {Journal of Computational and Nonlinear Dynamics},
   Volume = {1},
   Number = {4},
   Pages = {277-278},
   Publisher = {ASME International},
   Year = {2006},
   Month = {January},
   ISSN = {1555-1423},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000204234100003&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Doi = {10.1115/1.2338659},
   Key = {fds282366}
}

@article{fds71105,
   Author = {S. Santillan and L.N. Virgin and R.H. Plaut},
   Title = {Postbuckling and vibration of heavy beam on horizontal or
             inclined rigid foundation’},
   Journal = {Journal of Applied Mechanics},
   Volume = {73},
   Pages = {664-671},
   Year = {2006},
   Key = {fds71105}
}

@article{fds282390,
   Author = {Holland, DB and Stanciulescu, I and Virgin, LN and Plaut,
             RH},
   Title = {Vibration and large deflection of a beam-cable
             system},
   Journal = {Collection of Technical Papers Aiaa/Asme/Asce/Ahs/Asc
             Structures, Structural Dynamics and Materials
             Conference},
   Volume = {3},
   Pages = {2130-2142},
   Year = {2005},
   Month = {December},
   ISSN = {0273-4508},
   Abstract = {This paper studies the large-deflection static and dynamic
             characteristics of a slender prismatic cantilevered beam
             loaded by a cable attached at the tip and terminating near
             the base. This system has a direct application to square
             solar-sail structures where the structural booms could be
             designed to buckle in order to supply tension loading in the
             sail membrane. The beam and cable configuration can be
             considered a two-dimensional analogy of this
             three-dimensional problem. The equilibrium and vibration
             properties are investigated using three methods: numerical
             integration of the governing equations using a shooting
             method; finite element analysis using ABAQUS; and
             experiments using a laser vibrometer. Two different cable
             attachment points are considered. Significant results show a
             buckling load much higher than for a cantilever beam under
             axial end load, and sensitivity of the vibration frequencies
             near the buckling load. In addition, anomalies discovered
             while analyzing the system using the finite element method
             are discussed. Copyright © 2005 by the American Institute
             of Aeronautics and Astronautics, Inc. All rights
             reserved.},
   Key = {fds282390}
}

@article{fds282414,
   Author = {Stanciulescu, I and Virgin, LN and Laursen, TA},
   Title = {Finite element analysis of slender solar sail
             booms},
   Journal = {Collection of Technical Papers Aiaa/Asme/Asce/Ahs/Asc
             Structures, Structural Dynamics and Materials
             Conference},
   Volume = {3},
   Pages = {2121-2129},
   Year = {2005},
   Month = {December},
   ISSN = {0273-4508},
   Key = {fds282414}
}

@article{fds282353,
   Author = {Plaut, RH and Alloway, LA and Virgin, LN},
   Title = {Nonlinear oscillations of a buckled mechanism used as a
             vibration isolator},
   Journal = {Solid Mechanics and Its Applications},
   Volume = {122},
   Pages = {241-250},
   Year = {2005},
   Month = {December},
   ISSN = {0925-0042},
   url = {http://dx.doi.org/10.1007/1-4020-3268-4-23},
   Abstract = {Various devices have been used to reduce the dynamic
             response of mechanical and structural systems connected to
             moving sources. A vibration isolator can be inserted between
             a system and source to absorb energy and reduce the system's
             motion. The application of a buckled mechanism as a
             vibration isolator is investigated here. Harmonic motion is
             applied to the base, and the response of the supported
             weight is examined. Both parametric and external (forcing)
             excitations are present. Small applied motions and responses
             are considered first, and the steady-state harmonic motion
             of the weight is plotted as a function of the applied
             frequency. Then large responses are investigated. The
             buckled mechanism may snap from one side to the other. After
             some initial transient response, period-one, period-two,
             period-four, and chaotic responses are observed for various
             applied frequencies and given values of the applied
             amplitude, supported weight, damping coefficient, and
             stiffness parameter. © 2005 Springer.},
   Doi = {10.1007/1-4020-3268-4-23},
   Key = {fds282353}
}

@article{05379362674,
   Author = {Santillan, S and Virgin, LN and Plaut, RH},
   Title = {Equilibria and vibration of a heavy pinched
             loop},
   Journal = {Journal of Sound and Vibration},
   Volume = {288},
   Number = {1-2},
   Pages = {81-90},
   Publisher = {Elsevier BV},
   Year = {2005},
   Month = {November},
   url = {http://dx.doi.org/10.1016/j.jsv.2004.12.016},
   Keywords = {Pinch effect;Clamping devices;Deflection
             (structures);Boundary value problems;Polycarbonates;Elasticity;Natural
             frequencies;Laser applications;},
   Abstract = {A thin strip is bent such that the two ends are brought
             together and clamped (pinched) to form a teardrop shape. The
             clamped end is held at various angles with the loop either
             upright, horizontal, downward, or halfway between these
             positions. The length of the loop is increased, and the
             resulting equilibrium shapes, as well as small in-plane
             vibrations about equilibrium, are investigated analytically
             and experimentally. When the loop is held upright, in-plane
             buckling occurs at a critical length, and subsequent
             postbuckling deflections can be large. For the other
             orientations, except the hanging one, deflections also
             become large as the length is increased. In the analysis,
             the strip is assumed to be an inextensible elastica which is
             unstrained when straight, and its self-weight is included. A
             shooting method is applied to obtain numerical solutions to
             the nonlinear equilibrium boundary value problem and the
             linear vibration boundary value problem. Polycarbonate
             strips are used in the experiments, and data are acquired
             with a laser vibrometer. The experimental deflections,
             frequencies, and mode shapes exhibit excellent agreement
             with the analytical solutions. © 2005 Elsevier Ltd. All
             rights reserved.},
   Doi = {10.1016/j.jsv.2004.12.016},
   Key = {05379362674}
}

@article{05429423508,
   Author = {Xie, J and Ding, W and Dowell, EH and Virgin, LN},
   Title = {Hopf-flip bifurcation of high dimensional maps and
             application to vibro-impact systems},
   Journal = {Acta Mechanica Sinica},
   Volume = {21},
   Number = {4},
   Pages = {402-410},
   Publisher = {Springer Nature},
   Year = {2005},
   Month = {August},
   ISSN = {0567-7718},
   url = {http://dx.doi.org/10.1007/s10409-005-0045-7},
   Keywords = {Impact testing;Bifurcation (mathematics);Applications;Dynamics;Chaos
             theory;Three dimensional;Differential equations;Eigenvalues
             and eigenfunctions;Degrees of freedom (mechanics);Vectors;},
   Abstract = {This paper addresses the problem of Hopf-flip bifurcation of
             high dimensional maps. Using the center manifold theorem, we
             obtain a three dimensional reduced map through the
             projection technique. The reduced map is further transformed
             into its normal form whose coefficients are determined by
             that of the original system. The dynamics of the map near
             the Hopf-flip bifurcation point is approximated by a so
             called time-2τ2 map of a planar autonomous differential
             equation. It is shown that high dimensional maps may result
             in cycles of period two, tori T1 (Hopf invariant circles),
             tori 2T1 and tori 2T2 depending both on how the critical
             eigenvalues pass the unit circle and on the signs of
             resonant terms' coefficients. A two-degree-of-freedom
             vibro-impact system is given as an example to show how the
             procedure of this paper works. It reveals that through
             Hopf-flip bifurcations, periodic motions may lead directly
             to different types of motion, such as subharmonic motions,
             quasi-periodic motions, motions on high dimensional tori and
             even to chaotic motions depending both on change in
             direction of the parameter vector and on the nonlinear terms
             of the first three orders.},
   Doi = {10.1007/s10409-005-0045-7},
   Key = {05429423508}
}

@article{05159035755,
   Author = {Plaut, RH and Sidbury, JE and Virgin, LN},
   Title = {Analysis of buckled and pre-bent fixed-end columns used as
             vibration isolators},
   Journal = {Journal of Sound and Vibration},
   Volume = {283},
   Number = {3-5},
   Pages = {1216-1228},
   Publisher = {ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD},
   Year = {2005},
   Month = {May},
   ISSN = {0022-460X},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000228759300040&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Keywords = {Vibrations (mechanical);Stiffness;Buckling;Springs
             (components);Harmonic analysis;Approximation
             theory;Mathematical models;},
   Abstract = {The use of a buckled or pre-bent column with fixed ends as a
             vibration isolator is analyzed. The column is designed to
             have a high axial stiffness under the weight that it
             supports, so that the static displacement of the weight is
             not excessive, and then to have a low stiffness during
             excitation. The base of the column is assumed to have an
             axial motion which is simple harmonic or a linear
             combination of two simple harmonic functions. The column is
             modeled as an elastica. First the equilibrium shape under
             the supported weight is determined. Then small steady-state
             vibrations about the equilibrium configuration are obtained
             numerically using a shooting method. The inertia of the
             supported weight and the transverse and axial inertias of
             the column are included. The axial displacement
             transmissibility is computed, and the effects of external
             and internal damping, column stiffness, supported weight,
             and initial curvature are investigated. For the
             two-frequency excitation, the effects of the relative
             amplitudes and frequencies of the excitation components are
             considered. © 2004 Elsevier Ltd. All rights
             reserved.},
   Doi = {10.1016/j.jsv.2004.07.029},
   Key = {05159035755}
}

@article{05149017553,
   Author = {Moniz, L and Nichols, JM and Nichols, CJ and Seaver, M and Trickey, ST and Todd, MD and Pecora, LM and Virgin, LN},
   Title = {A multivariate, attractor-based approach to structural
             health monitoring},
   Journal = {Journal of Sound and Vibration},
   Volume = {283},
   Number = {1-2},
   Pages = {295-310},
   Publisher = {Elsevier BV},
   Year = {2005},
   Month = {May},
   url = {http://dx.doi.org/10.1016/j.jsv.2004.04.016},
   Keywords = {Plates (structural components);Steel structures;Time series
             analysis;Phase space methods;Chaos theory;Composite beams
             and girders;Damping;},
   Abstract = {In this work, recent advances in the use of nonlinear
             time-series analysis for structural health monitoring are
             extended to incorporate multivariate data. Structural
             response data recorded at multiple locations are combined
             using a multivariate time delay embedding in order to
             reconstruct the structure's dynamical attractor. Using this
             approach, a global phase-space representation of the
             dynamics may be realized for spatially extended systems. A
             new attractor-based metric, chaotic amplification of
             attractor distortion (CAAD), is then introduced as a damage
             sensitive feature. The approach is implemented using data
             acquired from a composite beam, bolted at either end to
             steel plates. Degradation to the system is introduced as a
             loosening of the bolts at one end of the structure. Results
             based on multivariate attractor reconstruction show a clear
             ability to detect both the presence and magnitude of damage
             to the connection. Comparisons are then drawn between this
             approach and one where the same feature is extracted from
             attractors reconstructed using data acquired from the
             individual sensor locations. These features are combined
             "post-extraction" using a linear discriminant coordinant
             analysis. Performing the analysis separately at the
             individual sensor locations results in a significant
             reduction in discriminating power. © 2004 Elsevier Ltd. All
             rights reserved.},
   Doi = {10.1016/j.jsv.2004.04.016},
   Key = {05149017553}
}

@article{04428406242,
   Author = {Chen, H and Virgin, LN},
   Title = {Dynamic analysis of modal shifting and mode jumping in
             thermally buckled plates},
   Journal = {Journal of Sound and Vibration},
   Volume = {278},
   Number = {1-2},
   Pages = {233-256},
   Publisher = {Elsevier BV},
   Year = {2004},
   Month = {November},
   ISSN = {0022-460X},
   url = {http://dx.doi.org/10.1016/j.jsv.2003.10.054},
   Keywords = {Plates (structural components);Bifurcation
             (mathematics);Transients;Computational methods;Boundary
             conditions;Eigenvalues and eigenfunctions;Numerical
             analysis;Finite element method;},
   Abstract = {Both analytical and finite element investigations are
             performed for the various static and dynamic aspects of the
             mode jumping phenomenon of a simply-supported rectangular
             plate heated deeply into the post-buckling regime. For the
             analytical method, the von Kármán plate equation is
             reduced to a system of non-linear ODEs by expressing the
             transverse deflection as a series of linear buckling modes.
             The ODEs, combined with the non-linear algebraic constraint
             equations obtained from in-plane boundary conditions, are
             then solved numerically under the parametric variation of
             the temperature. The results are checked by the finite
             element method, where a hybrid static-dynamic scheme is
             implemented. The contribution of each assumed (buckling)
             mode component is studied systematically. Characterized by
             the strong geometrical non-linearity, the secondary
             bifurcation point of the thermally loaded plate with fixed
             in-plane boundary conditions occurs far beyond the primary
             buckling point, and the jump behavior cannot be predicted
             correctly without sufficient assumed modes. Stationary
             bifurcation analysis indicates that while the post-buckling
             deflection before mode jumping is composed of pure symmetric
             modes, additional pure antisymmetric modes will appear after
             the occurrence of the snapping and they play the role of
             destabilizing the equilibrium. Furthermore, by monitoring
             natural frequencies and modal shapes, we find that a mode
             shifting phenomenon (the exchanging of vibration modes)
             exists in the primary post-buckling regime. Breaking of the
             symmetry of the dynamic modes is also found. By introducing
             a linear temperature sweeping scheme, transient analysis is
             performed to capture the snapping phenomenon dynamically,
             which occurs with moderate heating ratio. Comparison between
             the analytic and finite element results shows good
             agreement. © 2003 Elsevier Ltd. All rights
             reserved.},
   Doi = {10.1016/j.jsv.2003.10.054},
   Key = {04428406242}
}

@article{04288259395,
   Author = {Todd, MD and Nichols, JM and Nichols, CJ and Virgin,
             LN},
   Title = {An assessment of modal property effectiveness in detecting
             bolted joint degradation: Theory and experiment},
   Journal = {Journal of Sound and Vibration},
   Volume = {275},
   Number = {3-5},
   Pages = {1113-1126},
   Publisher = {Elsevier BV},
   Year = {2004},
   Month = {August},
   ISSN = {0022-460X},
   url = {http://dx.doi.org/10.1016/j.jsv.2003.10.037},
   Keywords = {Degradation;Modal analysis;Natural frequencies;Vibrations
             (mechanical);Nondestructive examination;Radiography;Thermography
             (imaging);Boundary conditions;},
   Abstract = {An experiment and a corresponding simple model were
             constructed to explore whether modal analysis is an
             appropriate tool for detecting bolted joint degradation. For
             the study, a beam is bolted to supports at its edges, and
             the spring encase the bolts such that greater control over
             the clamping force is retained. It was observed that the
             resonant frequencies and mode shapes are relatively
             insensitive to clamping force changes over wide ranges with
             a narrow region of sudden transition where there is greater
             sensitivity. It was suggested that the insensitivity may
             lead to poor prognostic capability if the modal properties
             are being used to track joint functionality loss for either
             maintenance or repair applications.},
   Doi = {10.1016/j.jsv.2003.10.037},
   Key = {04288259395}
}

@article{05279197528,
   Author = {Piiroinen, PT and Virgin, LN and Champneys, AR},
   Title = {Chaos and period-adding; experimental and numerical
             verification of the grazing bifurcation},
   Journal = {Journal of Nonlinear Science},
   Volume = {14},
   Number = {4},
   Pages = {383-404},
   Publisher = {Springer Nature},
   Year = {2004},
   Month = {August},
   ISSN = {0938-8974},
   url = {http://dx.doi.org/10.1007/s00332-004-0616-y},
   Abstract = {Experimental results are presented for a
             single-degree-of-freedom horizontally excited pendulum that
             is allowed to impact with a rigid stop at a fixed angle θ
             to the vertical. By inclining the apparatus, the pendulum is
             allowed to swing in an effectively reduced gravity, so that
             for each fixed θ less than a critical value, a forcing
             frequency is found such that a period-one limit cycle motion
             just grazes with the stop. Experimental measurements show
             the immediate onset of chaotic dynamics and a period-adding
             cascade for slightly higher frequencies. These results are
             compared with a numerical simulation and continuation of
             solutions to a mathematical model of the system, which shows
             the same qualitative effects. From the model, the theory of
             discontinuity mappings due to Nordmark is applied to derive
             the coefficients of the square-root normal form map of the
             grazing bifurcation for this system. The grazing periodic
             orbit and its linearisation are found using a numerical
             continuation method for hybrid systems. From this, the
             normal-form coefficients are computed, which in this case
             imply that a jump to chaos and period-adding cascade occurs.
             Excellent quantitative agreement is found between the model
             simulation and the map, even over wide parameter ranges.
             Qualitatively, both accurately predict the experimental
             results, and after a slight change in the effective damping
             value, a striking quantitative agreement is found too. ©
             2004 Springer-Verlag.},
   Doi = {10.1007/s00332-004-0616-y},
   Key = {05279197528}
}

@article{04208159109,
   Author = {Nichols, JM and Nichols, CJ and Todd, MD and Seaver, M and Trickey, ST and Virgin, LN},
   Title = {Use of data-driven phase space models in assessing the
             strength of a bolted connection in a composite
             beam},
   Journal = {Smart Materials and Structures},
   Volume = {13},
   Number = {2},
   Pages = {241-250},
   Publisher = {IOP Publishing},
   Year = {2004},
   Month = {April},
   url = {http://dx.doi.org/10.1088/0964-1726/13/2/001},
   Keywords = {Composite beams and girders;Robustness (control
             systems);Nonlinear systems;Monitoring;Natural
             frequencies;Vectors;Regression analysis;X ray
             radiography;Mathematical models;Algorithms;},
   Abstract = {This work explores the role of empirical dynamical models in
             deducing the level of preload loss in a bolted connection.
             Specifically, we examine the functional relationship between
             data gleaned from locations on either side of the connection
             using nonlinear predictive models. This relationship, as
             quantified by a measure of prediction error, changes as a
             function of bolt loosening, thus allowing both the presence
             and magnitude of the axial load to be identified. The models
             are based on a phase space portrayal of the system dynamics
             and require only that the structure's response be low
             dimensional. The technique is demonstrated experimentally on
             a composite beam fastened to steel plates with four
             instrumented bolts. Results are compared to a similar
             approach using an auto-regressive (AR) modeling
             technique.},
   Doi = {10.1088/0964-1726/13/2/001},
   Key = {04208159109}
}

@article{04538758636,
   Author = {Plaut, RH and Virgin, LN},
   Title = {Three-dimensional postbuckling and vibration of vertical
             half-loop under self-weight},
   Journal = {International Journal of Solids and Structures},
   Volume = {41},
   Number = {18-19},
   Pages = {4975-4988},
   Publisher = {Elsevier BV},
   Year = {2004},
   Month = {January},
   url = {http://dx.doi.org/10.1016/j.ijsolstr.2004.03.014},
   Keywords = {Vibration control;Fiber optics;Elastic moduli;Vectors;Velocity
             measurement;Approximation theory;Mathematical
             models;},
   Abstract = {The stability and vibration characteristics of a flexible
             and inextensible half-loop are investigated. The loop is
             fixed at two base points, which are separated by a specified
             distance, and is only subjected to gravity loading. If the
             length of the loop is sufficiently small, the loop stands
             upright in a vertical plane. If the length is increased past
             a critical value, the planar equilibrium shape becomes
             unstable and the loop droops to one side (i.e., laterally).
             This out-of-plane displacement may occur smoothly
             (supercritical bifurcation), or the loop may suddenly jump
             to a severely-drooped configuration (subcritical
             bifurcation), depending on the constitutive law.
             Linearly-elastic and softening materials are considered.
             Prebuckled and postbuckled equilibrium states are determined
             numerically with the use of a shooting method. Droop caused
             by an applied torsional moment is also analyzed. Then small
             vibrations about the prebuckled (planar) states are studied.
             Three basic types of vibration modes occur: in-plane,
             out-of-plane (symmetric), and twist about a vertical axis
             through the center of the loop. Experiments on a fiber-optic
             rod and a curtain wire are carried out to qualitatively
             verify the numerical results for both types of constitutive
             laws. © 2004 Elsevier Ltd. All rights reserved.},
   Doi = {10.1016/j.ijsolstr.2004.03.014},
   Key = {04538758636}
}

@article{04538758637,
   Author = {Virgin, LN and Plaut, RH},
   Title = {Postbuckling and vibration of linearly elastic and softening
             columns under self-weight},
   Journal = {International Journal of Solids and Structures},
   Volume = {41},
   Number = {18-19},
   Pages = {4989-5001},
   Publisher = {Elsevier BV},
   Year = {2004},
   Month = {January},
   url = {http://dx.doi.org/10.1016/j.ijsolstr.2004.03.023},
   Keywords = {Vibration control;Elastic moduli;Bending moments;Natural
             frequencies;Bessel functions;Linear equations;Mathematical
             models;},
   Abstract = {The critical height for buckling of a linearly elastic
             cantilevered column due to its self-weight was determined by
             Greenhill in 1881. Postbuckling behavior also has been
             studied, often assuming that the column is an elastica
             (inextensible, with its bending moment proportional to its
             curvature). The bifurcation point at the critical height is
             supercritical, so that the postbuckling path is stable as
             the height increases past its critical value. Subcritical
             bifurcation may occur if the column is nonlinearly elastic
             with a softening behavior. This results in a sudden jump
             from the straight vertical configuration to a
             severely-drooped shape. The governing equation is solved
             numerically with the use of a shooting method to obtain the
             equilibrium paths. Also, small vibrations about the straight
             and postbuckled equilibrium states are examined, and
             vibration frequencies (and hence stability properties) are
             obtained. An initial curvature of the column is included in
             the analysis. Experiments are conducted to verify the
             results qualitatively for linearly elastic and softening
             materials. © 2004 Elsevier Ltd. All rights
             reserved.},
   Doi = {10.1016/j.ijsolstr.2004.03.023},
   Key = {04538758637}
}

@article{fds282345,
   Author = {Holland, DB and Virgin, LN and Belvin, WK},
   Title = {Investigation of structural dynamics in a 2-meter square
             solar sail model including axial load effects},
   Journal = {44th Aiaa/Asme/Asce/Ahs/Asc Structures, Structural Dynamics,
             and Materials Conference},
   Year = {2003},
   Month = {December},
   Abstract = {This paper presents a parameter study of the effect of boom
             axial loading on the global dynamics of a 2-meter solar sail
             scale model. The experimental model used is meant for
             building expertise in finite element analysis and
             experimental execution, not as a predecessor to any planned
             flight mission or particular design concept. The results
             here are to demonstrate the ability to predict and measure
             structural dynamics and mode shapes in the presence of axial
             loading. © 2003 by the American Institute of Aeronautics
             and Astronautics, Inc. All rights reserved.},
   Key = {fds282345}
}

@article{fds282389,
   Author = {Holland, DB and Virgin, LN and Belvin, WK},
   Title = {Investigation of structural dynamics in a 2-meter square
             solar sail model including axial load effects},
   Journal = {Collection of Technical Papers Aiaa/Asme/Asce/Ahs/Asc
             Structures, Structural Dynamics and Materials
             Conference},
   Volume = {5},
   Pages = {3192-3198},
   Year = {2003},
   Month = {August},
   Abstract = {This paper presents a parameter study of the effect of boom
             axial loading on the global dynamics of a 2-meter solar sail
             scale model. The experimental model used is meant for
             building expertise in finite element analysis and
             experimental execution, not as a predecessor to any planned
             flight mission or particular design concept. The results
             here are to demonstrate the ability to predict and measure
             structural dynamics and mode shapes in the presence of axial
             loading.},
   Key = {fds282389}
}

@article{03147424081,
   Author = {Virgin, LN and Davis, RB},
   Title = {Vibration isolation using buckled struts
             [3]},
   Journal = {Journal of Sound and Vibration},
   Volume = {260},
   Number = {5},
   Pages = {965-973},
   Publisher = {Elsevier BV},
   Year = {2003},
   Month = {March},
   url = {http://dx.doi.org/10.1016/S0022-460X(02)01177-X},
   Keywords = {Struts;Buckling;Natural frequencies;Springs
             (components);Deflection (structures);Stiffness;Damping;},
   Abstract = {Post-buckled struts were used as spring components in a
             vibration isolation system. Vibration isolation is concerned
             with the minimization of the force or motion transmitted to
             a device from a source of vibration. The approach was shown
             to have promise in isolating very sensitive systems subject
             to very high frequency excitation.},
   Doi = {10.1016/S0022-460X(02)01177-X},
   Key = {03147424081}
}

@article{7588245,
   Author = {Nichols, JM and Todd, MD and Seaver, M and Virgin,
             LN},
   Title = {Use of chaotic excitation and attractor property analysis in
             structural health monitoring.},
   Journal = {Physical Review. E, Statistical, Nonlinear, and Soft Matter
             Physics},
   Volume = {67},
   Number = {1 Pt 2},
   Pages = {016209},
   Year = {2003},
   Month = {January},
   ISSN = {1539-3755},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000181018000044&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Keywords = {chaos;dynamics;error analysis;Lyapunov methods;monitoring;prediction
             theory;structural engineering;},
   Abstract = {This work explores the utility of attractor-based approaches
             in the field of vibration-based structural health
             monitoring. The technique utilizes the unique properties of
             chaotic signals by driving the structure directly with the
             output of a chaotic oscillator. Using the Kaplan-Yorke
             conjecture, the Lyapunov exponents of the driving signal may
             be tuned to the dominant eigenvalues of the structure, thus
             controlling the dimension of the structural response. Data
             are collected at various stages of structural degradation
             and a simple nonlinear model, constructed from the undamaged
             data, is used to make predictions for the damaged response
             data. Prediction error is then introduced as a "feature" for
             classifying the magnitude of the damage. Results are
             presented for an experimental cantilevered beam instrumented
             with fiber-optic strain sensors.},
   Doi = {10.1103/physreve.67.016209},
   Key = {7588245}
}

@article{03207471106,
   Author = {Nichols, JM and Virgin, LN},
   Title = {System identification through chaotic interrogation},
   Journal = {Mechanical Systems and Signal Processing},
   Volume = {17},
   Number = {4},
   Pages = {871-881},
   Publisher = {Elsevier BV},
   Year = {2003},
   Month = {January},
   url = {http://dx.doi.org/10.1006/mssp.2001.1471},
   Keywords = {Damping;Oscillators (mechanical);Chaos theory;Eigenvalues
             and eigenfunctions;Lyapunov methods;Mathematical
             models;},
   Abstract = {We introduce a method by which the coefficient of viscous
             damping for a linear ndof system may be estimated. The
             technique utilises the unique properties of chaos by driving
             the system with the output of a non-linear oscillator. By
             tuning the Lyapunov exponents of the driving signal to the
             eigenvalues of the linear structure, the dimension of the
             output is effectively controlled. Estimates of the complete
             Lyapunov spectrum may then be used to extract the real part
             of the dominant eigenvalue, and hence the damping, for the
             system. Results are presented for a 2-dof spring-mass-damper
             driven with the output of the chaotic Lorenz oscillator. The
             effects of additive noise are also considered.},
   Doi = {10.1006/mssp.2001.1471},
   Key = {03207471106}
}

@article{7830267,
   Author = {Virgin, LN and Nichols, JM and Trickey, ST},
   Title = {A note on the response spectrum map},
   Journal = {International Journal of Bifurcation and
             Chaos},
   Volume = {13},
   Number = {5},
   Pages = {1337-1341},
   Publisher = {World Scientific Pub Co Pte Lt},
   Year = {2003},
   Month = {January},
   url = {http://dx.doi.org/10.1142/S0218127403007278},
   Keywords = {bifurcation;harmonic oscillators;hysteresis;nonlinear
             dynamical systems;},
   Abstract = {A study was performed on the response spectrum map. A plot
             of frequency, or spectral, content versus a system parameter
             was a useful alternative to bifurcation diagrams in
             nonlinear dynamics. The spectrum map was based on the data
             taken from two experimental mechanical systems in which
             hysteresis was featured.},
   Doi = {10.1142/S0218127403007278},
   Key = {7830267}
}

@article{03367624747,
   Author = {Nichols, JM and Virgin, LN and Todd, MD and Nichols,
             JD},
   Title = {On the use of attractor dimension as a feature in structural
             health monitoring},
   Journal = {Mechanical Systems and Signal Processing},
   Volume = {17},
   Number = {6},
   Pages = {1305-1320},
   Publisher = {Elsevier BV},
   Year = {2003},
   Month = {January},
   url = {http://dx.doi.org/10.1006/mssp.2002.1521},
   Keywords = {Health;Vibration control;Cantilever beams;Correlation
             methods;},
   Abstract = {Recent works in the vibration-based structural health
             monitoring community have emphasised the use of correlation
             dimension as a discriminating statistic in separating a
             damaged from undamaged response. This paper explores the
             utility of attractor dimension as a 'feature' and offers
             some comparisons between different metrics reflecting
             dimension. This focus is on evaluating the performance of
             two different measures of dimension as damage indicators in
             a structural health monitoring context. Results indicate
             that the correlation dimension is probably a poor choice of
             statistic for the purpose of signal discrimination. Other
             measures of dimension may be used for the same purposes with
             a higher degree of statistical reliability. The question of
             competing methodologies is placed in a hypothesis testing
             framework and answered with experimental data taken from a
             cantilivered beam. © 2003 Elsevier Science Ltd. All rights
             reserved.},
   Doi = {10.1006/mssp.2002.1521},
   Key = {03367624747}
}

@article{fds336174,
   Author = {Nichols, JM and Todd, MD and Seaver, M and Virgin,
             LN},
   Title = {Use of chaotic excitation and attractor property analysis in
             structural health monitoring},
   Journal = {Physical Review E Statistical, Nonlinear, and Soft Matter
             Physics},
   Volume = {67},
   Number = {1 2},
   Pages = {162091-162098},
   Year = {2003},
   Month = {January},
   Abstract = {The utility of attractor based approaches in the field of
             vibration based structural health monitoring (SHM) was
             discussed. The technique utilized the properties of chaotic
             signals by driving the structure directly with the output of
             a chaotic oscillator. Data was collected at various stages
             of structural degradation and a simple nonlinear model was
             constructed from the undamaged data.},
   Key = {fds336174}
}

@article{7836634,
   Author = {Nichols, J.M. and Virgin, L.N.},
   Title = {System identification through chaotic interrogation},
   Journal = {Mech. Syst. Signal Process. (UK)},
   Volume = {17},
   Number = {4},
   Pages = {871 - 81},
   Year = {2003},
   url = {http://dx.doi.org/10.1006/mssp.2001.1471},
   Keywords = {chaos;damping;eigenvalues and eigenfunctions;identification;interference
             (signal);linear systems;Lyapunov methods;oscillators;spectral
             analysis;},
   Abstract = {We introduce a method by which the coefficient of viscous
             damping for a linear ndof system may be estimated. The
             technique utilises the unique properties of chaos by driving
             the system with the output of a nonlinear oscillator. By
             tuning the Lyapunov exponents of the driving signal to the
             eigenvalues of the linear structure, the dimension of the
             output is effectively controlled. Estimates of the complete
             Lyapunov spectrum may then be used to extract the real part
             of the dominant eigenvalue, and hence the damping, for the
             system. Results are presented for a 2-dof spring-mass-damper
             driven with the output of the chaotic Lorenz oscillator. The
             effects of additive noise are also considered},
   Key = {7836634}
}

@article{03167440053,
   Author = {Nichols, JM and Trickey, ST and Todd, MD and Virgin,
             LN},
   Title = {Structural health monitoring through chaotic
             interrogation},
   Journal = {Meccanica},
   Volume = {38},
   Number = {2},
   Pages = {239-250},
   Year = {2003},
   url = {http://dx.doi.org/10.1023/A:1022898403359},
   Keywords = {Vibrations (mechanical);Moisture;Cantilever beams;Chaos
             theory;Finite element method;Time series
             analysis;},
   Abstract = {The field of vibration based structural health monitoring
             involves extracting a 'feature' which robustly quantifies
             damage induced changes to the structure in the presence of
             ambient variation, that is, changes in ambient temperature,
             varying moisture levels, etc. In this paper, we present an
             attractor-based feature derived from the field of nonlinear
             time-series analysis. Emphasis is placed on the use of chaos
             for the purposes of system interrogation. The structure is
             excited with the output of a chaotic oscillator providing a
             deterministic (low-dimensional) input. Use is made of the
             Kaplan-Yorke conjecture in order to 'tune' the Lyapunov
             exponents of the driving signal so that varying degrees of
             damage in the structure will alter the state space
             properties of the response attractor. The average local
             attractor variance ratio (ALAVR) is suggested as one
             possible means of quantifying the state space changes.
             Finite element results are presented for a thin aluminum
             cantilever beam subject to increasing damage, as specified
             by weld line separation, at the clamped end. Comparisons of
             the ALAVR to two modal features are evaluated through the
             use of a performance metric.},
   Doi = {10.1023/A:1022898403359},
   Key = {03167440053}
}

@article{7427802,
   Author = {Trickley, ST and Virgin, LN and Dowell, EH},
   Title = {The stability of limit-cycle oscillations in a nonlinear
             aeroelastic system},
   Journal = {Proceedings. Mathematical, Physical, and Engineering
             Sciences},
   Volume = {458},
   Number = {2025},
   Pages = {2203-2226},
   Publisher = {The Royal Society},
   Year = {2002},
   Month = {September},
   ISSN = {1364-5021},
   url = {http://dx.doi.org/10.1098/rspa.2002.0965},
   Keywords = {elasticity;limit cycles;nonlinear dynamical
             systems;oscillations;},
   Abstract = {The effects of a freeplay structural nonlinearity on an
             aeroelastic system are studied experimentally. Particular
             attention is paid to the stability of a periodic nonlinear
             aeroelastic response, known as limit-cycle oscillations
             (LCOs). The major thrust of this research lies in the
             application of relatively recently developed techniques from
             nonlinear dynamics and signal processing to the realm of
             experimental aeroelasticity. Innovations from the field of
             nonlinear dynamics include time-delay embedded coordinates
             to reconstruct system dynamics, a Poincaré section to
             assess the periodic nature of a response and to prescribe an
             operating point about which a linear description of the
             dynamics can be approximated, stochastic perturbations to
             assess the stability and robustness of responses, and a
             basin of attraction measure to assess initial condition
             dependence. A novel system-identification approach is used
             to generate a linear approximation of the experimental
             system dynamics about the LCO. This technique makes use of a
             rotating slotted cylinder gust generator and incorporates a
             least-squares fit of the resulting transient dynamics. An
             extension to this method is then developed based on the
             outcome of relatively large disturbances to the flow and
             hence airfoil, to obtain global stability.},
   Doi = {10.1098/rspa.2002.0965},
   Key = {7427802}
}

@article{02467203690,
   Author = {Virgin, LN and Plaut, RH},
   Title = {Use of frequency data to predict secondary
             bifurcation},
   Journal = {Journal of Sound and Vibration},
   Volume = {251},
   Number = {5},
   Pages = {919-926},
   Publisher = {Elsevier BV},
   Year = {2002},
   Month = {April},
   ISSN = {0022-460X},
   url = {http://dx.doi.org/10.1006/jsvi.2001.3906},
   Keywords = {Bifurcation (mathematics);Buckling;Vibration
             measurement;Degrees of freedom (mechanics);Nonlinear
             equations;Mathematical models;Stiffness;},
   Doi = {10.1006/jsvi.2001.3906},
   Key = {02467203690}
}

@article{fds282384,
   Author = {Holland, DB and Virgin, LN and Tinker, ML and Slade,
             KN},
   Title = {Geometric scaling properties of inflatable structures for
             use in space solar power generation},
   Journal = {Collection of Technical Papers Aiaa/Asme/Asce/Ahs/Asc
             Structures, Structural Dynamics and Materials
             Conference},
   Volume = {1},
   Pages = {507-516},
   Year = {2002},
   Month = {January},
   Abstract = {Investigation of the geometric scaling properties of
             polyimide film inflatable booms is described. These
             structures have considerable potential for use in space with
             solar concentrators, solar sails, and space solar power
             systems including solar arrays. Multiple cylindrical test
             articles were fabricated, utilizing two different
             thicknesses of Kapton polyimide film and seven aspect
             (slenderness) ratios. Numerous static bending and axial
             buckling experiments were conducted and compared to computer
             simulations using the MSC/NASTRAN program. Both beam element
             models and shell element models were developed for several
             inflatable struts and compared to experimental test results.
             Several problems encountered during the construction,
             experimentation, and finite element analyses are described.
             These included creating the proper experimental setup for
             static testing and establishing the optimum finite element
             analysis process for the analytical models. Many of these
             problems were overcome in the course of the research. Using
             the results from both experimental and analytical aspects of
             the research effort, guidelines for appropriate analysis
             techniques and experimental test article design were
             determined. These can be used to approximately determine
             properties of large-scale structures, which can not be
             tested in laboratory experiments.},
   Key = {fds282384}
}

@article{fds282386,
   Author = {Todd, M and Seaver, M and Trickey, S and Nichols, J and Virgin,
             L},
   Title = {The use of a high-performance fiber optic measurement system
             in structural damage assessment},
   Journal = {Smart Structures and Materials 2005: Active Materials:
             Behavior and Mechanics},
   Volume = {4753 I},
   Pages = {167-173},
   Year = {2002},
   Month = {January},
   Abstract = {We have developed and tested a fiber optic system that
             relies on Fiber Bragg Gratings (FBGs) as strain gages for
             structural monitoring. FBGs reflect a narrow (< 0.2 nm) band
             of light whose center wavelength changes as the fiber is
             stretched or compressed. We interrogate multiple FBGs
             distributed along one strand of optical fiber with a
             scanning Fabry-Perot filter for selecting individual
             reflection wavelengths, an unbalanced Mach-Zehnder
             interferometer to detect wavelength shifts, and a 3×3 fiber
             optic coupler which converts the wavelength shifts into
             phase changes. This work will describe the system in detail,
             present key performance metrics, and demonstrate the use of
             the system in detection of boundary clamp damage in a
             chaotically excited beam. The features chosen in the damage
             assessment problem are based on subtle geometric changes
             which occur on the system attractor changes as the beam is
             damaged.},
   Key = {fds282386}
}

@article{fds282387,
   Author = {Todd, M and Trickey, S and Seaver, M and Nichols, J and Virgin,
             L},
   Title = {Structural damage assessment using chaotic dynamic
             interrogation},
   Journal = {Asme International Mechanical Engineering Congress and
             Exposition, Proceedings},
   Pages = {613-620},
   Publisher = {ASME},
   Year = {2002},
   Month = {January},
   url = {http://dx.doi.org/10.1115/IMECE2002-32026},
   Abstract = {This work considers a new technique for damage detection in
             vibration-based structural health monitoring. The technique
             involves exciting a structure with a low-dimensional chaotic
             input, reconstructing the attractor, and analyzing certain
             properties of the attractor for the subtle changes which may
             occur due to damage. Recourse is made to the Kaplan-Yorke
             conjecture for motivating the technique. The technique is
             then demonstrated in the laboratory on a beam subject to
             boundary clamp damage controlled by means of a special
             elastic clamp. The measurements are made with a special
             fiber optic strain measurement system whose key performance
             features are described. Copyright © 2002 by
             ASME.},
   Doi = {10.1115/IMECE2002-32026},
   Key = {fds282387}
}

@article{fds282385,
   Author = {Todd, M and Trickey, S and Seaver, M and Nichols, J and Virgin,
             L},
   Title = {Structural damage assessment using chaotic dynamic
             interrogation},
   Journal = {American Society of Mechanical Engineers, Dynamic Systems
             and Control Division (Publication) Dsc},
   Volume = {71},
   Pages = {613-620},
   Year = {2002},
   url = {http://dx.doi.org/10.1115/IMECE2002-32026},
   Abstract = {This work considers a new technique for damage detection in
             vibration-based structural health monitoring. The technique
             involves exciting a structure with a low-dimensional chaotic
             input, reconstructing the attractor, and analyzing certain
             properties of the attractor for the subtle changes which may
             occur due to damage. Recourse is made to the Kaplan-Yorke
             conjecture for motivating the technique. The technique is
             then demonstrated in the laboratory on a beam subject to
             boundary clamp damage controlled by means of a special
             elastic clamp. The measurements are made with a special
             fiber optic strain measurement system whose key performance
             features are described.},
   Doi = {10.1115/IMECE2002-32026},
   Key = {fds282385}
}

@article{fds282383,
   Author = {Slade, KN and Virgin, LN and Tinker, ML},
   Title = {Mode splitting in an inflated polyimide cylinder with
             circumferential asymmetry},
   Journal = {19th Aiaa Applied Aerodynamics Conference},
   Volume = {3},
   Pages = {1720-1728},
   Year = {2001},
   Month = {December},
   Abstract = {In the past, a good deal of the research on the feasibility
             of inflatable structures for space applications has focused
             on the behavior of inflated cylinders. In many cases,
             especially in theoretical and numerical studies, the
             cylinder has been assumed to be uniform across its
             circumference. In the case of many thin-film structures,
             this assumption does not hold. These structures often
             contain at least one seam that produces localized changes in
             film thickness and stiffness. Experimental evidence of the
             effect of this seam in the form of mode splitting and the
             accompanying divergence of repeated eigenvalues was seen
             during modal testing of a polyimide cylinder at NASA
             Marshall Space Flight Center (MSFC). This paper will examine
             the effect of asymmetry through the inspection of
             experimental data and the use of finite element methods. ©
             2001 by the American Institute of Aeronautics and
             Astronautics, Inc.},
   Key = {fds282383}
}

@article{fds282413,
   Author = {Virgin, LN and Nichols, JM and Simmons, WN and Plaut,
             RH},
   Title = {On the response of a shaken cable-suspended
             mass},
   Journal = {Proceedings of the Asme Design Engineering Technical
             Conference},
   Volume = {6 B},
   Pages = {2109-2113},
   Year = {2001},
   Month = {December},
   Abstract = {A small mass is suspended by two cables which are attached
             at angles to a rigid frame. The frame is shaken harmonically
             in the horizontal direction, causing the mass to respond
             typically in an erratic manner as the cables alternately
             become taut and slack. Since the cables are assumed to be
             inextensional, they provide an effective impulsive force to
             the mass as they become taut, causing an elastic rebound
             (which is modeled using a coefficient of restitution) [Plaut
             and Farmer, 2000]. The mass is assumed to be a point mass,
             and motion takes place within a vertical plane. One of the
             practical motivations for this work is the potential for
             using moored buoyant devices in an attempt to mitigate wave
             energy. Simulations capture the unpredictable dynamic
             response of the mass, despite the relatively simplistic
             nature of the modeling. Special care is taken to accurately
             model the sudden transition when a cable instantaneously
             becomes taut. In the general case, the motion has chaotic
             characteristics and Poincare sampling provides a useful
             diagnostic tool [Virgin, 2000]. The experimental results
             also show the complex nature of the behavior. The motion of
             the center of mass is obtained using a video camera and the
             IMAQ image processing package within LabVDEW. The results
             agree qualitatively with simulation.},
   Key = {fds282413}
}

@article{fds282417,
   Author = {Virgin, LN and Aldemir, U and Gavin, HP and Nichols, JM and Plaut,
             RH},
   Title = {An investigation of a rocking-sliding block},
   Journal = {Proceedings of the Asme Design Engineering Technical
             Conference},
   Volume = {6 B},
   Pages = {1279-1283},
   Year = {2001},
   Month = {December},
   Abstract = {The short end of a rigid rectangular block with a 2:1 aspect
             ratio is placed on a flat horizontal surface. The surface
             exhibits a horizontal harmonic motion, and two-dimensional
             motions of the block are investigated numerically and
             experimentally. A variety of modes of behavior are possible,
             and, when viewed from the side, attention is focused on (a)
             rocking of the block about either bottom comer or (b)
             sliding while rocking about one of those comers. Different
             periodic or erratic rocking-sliding responses are observed,
             with overturning being one of the possible outcomes. This
             system has relevance to a number of practical applications,
             especially in the context of earthquake engineering. The
             experiment consists of two aluminum blocks separated by a
             heavy steel cylinder. It is mounted on a shake table that
             oscillates harmonically in the horizontal direction. Data
             are acquired using image video processing with a number of
             targets mounted on the block face. Two guides are used to
             ensure that the motion remains in the vertical plane.
             Reasonable qualitative agreement between simulations and
             experimental data is achieved, especially when viewed within
             the context of highly nonlinear systems and their inherent
             sensitivity. This work may be considered as an extension to
             our previous work (Fielder et al., 1997), with the addition
             of sliding being the major new ingredient.},
   Key = {fds282417}
}

@article{01496757901,
   Author = {Nichols, JM and Virgin, LN and Gavin, HP},
   Title = {Damping estimates from experimental non-linear
             time-series},
   Journal = {Journal of Sound and Vibration},
   Volume = {246},
   Number = {5},
   Pages = {815-827},
   Publisher = {Elsevier BV},
   Year = {2001},
   Month = {October},
   ISSN = {0022-460X},
   url = {http://dx.doi.org/10.1006/jsvi.2001.3653},
   Keywords = {Damping;Theorem proving;Lyapunov methods;Mathematical
             models;},
   Abstract = {This paper seeks to illustrate the utility of the Lyapunov
             spectrum in estimating the damping of an experimental
             non-linear system. A mechanical model of Duffing's equation
             operating in the chaotic regime is used to generate a single
             observable. Using standard techniques from non-linear
             time-series analysis, the complete Lyapunov spectrum is
             estimated. The sum of these exponents may, via the
             divergence theorem, be related directly to the coefficient
             of viscous damping. Estimations are performed in this manner
             for both a three- and four-dimensional response and results
             are compared to estimates taken from two linear-based
             techniques. The indication is that use of the Lyapunov
             spectrum to obtain quantitative damping estimates is a
             comparable alternative to methods requiring transient data
             or detailed knowledge of the dynamics. © 2001 Academic
             Press.},
   Doi = {10.1006/jsvi.2001.3653},
   Key = {01496757901}
}

@article{01516767017,
   Author = {Todd, MD and Nichols, JM and Pecora, LM and Virgin,
             LN},
   Title = {Vibration-based damage assessment utilizing state space
             geometry changes: local attractor variance
             ratio},
   Journal = {Smart Materials and Structures},
   Volume = {10},
   Number = {5},
   Pages = {1000-1008},
   Publisher = {IOP Publishing},
   Year = {2001},
   Month = {October},
   ISSN = {0964-1726},
   url = {http://dx.doi.org/10.1088/0964-1726/10/5/316},
   Keywords = {Structural analysis;Vibrations (mechanical);Degradation;Degrees
             of freedom (mechanics);State space methods;Geometry;Time
             series analysis;Lyapunov methods;Eigenvalues and
             eigenfunctions;},
   Abstract = {A novel feature extracted from a nonlinear time series is
             presented within the context of vibration-based damage
             detection in a system. An eight-degree-of-freedom
             spring-mass-damper 'structure' is considered with damage
             incurred by a stiffness degradation in one spring. The
             system is excited with a chaotic input, and by tuning the
             Lyapunov exponents of the chaotic excitation to the dominant
             eigenvalue of the structure the dimensionality of the entire
             system is effectively controlled. Both the input and output
             are viewed in state space as geometric objects, and the
             effect of the damage is shown to alter the geometric
             properties of the corresponding attractors at a local level,
             which may be captured in construction of the feature. The
             utility of the feature is compared with that of a number of
             modal-based features and shown to be superior in resolving
             capability and in robustness.},
   Doi = {10.1088/0964-1726/10/5/316},
   Key = {01516767017}
}

@article{fds282381,
   Author = {Nichols, JM and Todd, MD and Virgin, LN and Pecora,
             LM},
   Title = {Vibration-based damage assessment using local attractor
             variance},
   Journal = {Smart Structures and Materials 2005: Active Materials:
             Behavior and Mechanics},
   Volume = {4330},
   Number = {1},
   Pages = {128-136},
   Publisher = {SPIE},
   Year = {2001},
   Month = {July},
   url = {http://dx.doi.org/10.1117/12.434112},
   Abstract = {Recently proposed methodologies in the field of
             vibration-based structural health monitoring have focused on
             the incorporation of statistical-based analysis. The
             structure in question is dynamically excited, some feature
             is identified for extraction from a measured data set, and
             that feature is classified as coming from a damaged or
             undamaged structure by means of some statistical approach.
             Perhaps the most important aspect of this new paradigm is
             the selection of a "feature" which accurately details the
             appearance, and possibly the location and scope, of the
             damage. In this paper we propose a feature derived from the
             field of nonlinear time-series analysis. Specifically,
             system response is classified according to the geometry of
             its dynamical attractor. Emphasis is placed on the use of
             chaos for the purposes of system interrogation. The
             deterministic nature of chaos ensures that the dynamics are
             restricted to finite, often low-dimensional, attractors. By
             analyzing the ratio of local variance of the driving
             attractor to that of the response attractor, subtle
             geometric changes, and hence damage, are identified. Results
             are presented for a linear 8-D.O.F system subject to chaotic
             forcing. Comparisons are then drawn with some of the more
             familiar modal methods. The indication is that this
             particular statistic represents one of a potentially large
             class of features which may prove useful in the field of
             structural health monitoring. © 2001 SPIE - The
             International Society for Optical Engineering.},
   Doi = {10.1117/12.434112},
   Key = {fds282381}
}

@article{01256545317,
   Author = {Donescu, P and Virgin, LN},
   Title = {An implicit boundary element solution with consistent
             linearization for free surface flows and non-linear
             fluid-structure interaction of floating bodies},
   Journal = {International Journal for Numerical Methods in
             Engineering},
   Volume = {51},
   Number = {4},
   Pages = {379-412},
   Publisher = {WILEY},
   Year = {2001},
   Month = {June},
   ISSN = {0029-5981},
   url = {http://dx.doi.org/10.1002/nme.141},
   Keywords = {Boundary element method;Integration;Linearization;Theorem
             proving;},
   Abstract = {In this work, a new comprehensive method has been developed
             which enables the solution of large, non-linear motions of
             rigid bodies in a fluid with a free surface. The application
             of the modern Eulerian-Lagrangian approach has been
             translated into an implicit time-integration formulation, a
             development which enables the use of larger time steps
             (where accuracy requirements allow it). Novel features of
             this project include: (1) an implicit formulation of the
             rigid-body motion in a fluid with a free surface valid for
             both two or three dimensions and several moving bodies; (2)
             a complete formulation and solution of the initial
             conditions; (3) a fully consistent (exact) linearization for
             free surface flows valid for any boundary elements such that
             optimal convergence properties are obtained when using a
             Newton-Raphson solver. The proposed framework has been
             completed with details on implementation issues referring
             mainly to the computation of the complete initial conditions
             and the consistent linearization of the formulation for free
             surface flows. The second part of the paper demonstrates the
             mathematical and numerical formulation through numerical
             results simulating large free surface flows and non-linear
             fluid structure interaction. The implicit formulation using
             a fully consistent linearization based on the boundary
             element method and the generalized trapezoidal rule has been
             applied to the solution of free surface flows for the
             evolution of a triangular wave, the generation of tsunamis
             and the propagation of a wave up to overturning.
             Fluid-structure interaction examples include the free and
             forced motion of a circular cylinder and the sway, heave and
             roll motion of a U-shaped body in a tank with a flap wave
             generator. The presented examples demonstrate the
             applicability and performance of the implicit scheme with
             consistent linearization. Copyright © 2001 John Wiley and
             Sons. Ltd.},
   Doi = {10.1002/nme.141},
   Key = {01256545317}
}

@article{fds282344,
   Author = {Slade, KN and Virgin, LN and Tinker, ML},
   Title = {Mode splitting in an inflated polyimide cylinder with
             circumferential asymmetry},
   Journal = {Collection of Technical Papers Aiaa/Asme/Asce/Ahs/Asc
             Structures, Structural Dynamics and Materials
             Conference},
   Volume = {3},
   Pages = {1720-1728},
   Year = {2001},
   Month = {January},
   Abstract = {In the past, a good deal of the research on the feasibility
             of inflatable structures for space applications has focused
             on the behavior of inflated cylinders. In many cases,
             especially in theoretical and numerical studies, the
             cylinder has been assumed to be uniform across its
             circumference. In the case of many thin-film structures,
             this assumption does not hold. These structures often
             contain at least one seam that produces localized changes in
             film thickness and stiffness. Experimental evidence of the
             effect of this seam in the form of mode splitting and the
             accompanying divergence of repeated eigenvalues was seen
             during modal testing of a polyimide cylinder at NASA
             Marshall Space Flight Center (MSFC). This paper will examine
             the effect of asymmetry through the inspection of
             experimental data and the use of finite element
             methods.},
   Key = {fds282344}
}

@article{fds282382,
   Author = {Todd, MD and Nichols, JM and Pecora, LM and Virgin,
             LN},
   Title = {Novel nonlinear feature identification in vibration-based
             damage detection using local attractor variance},
   Journal = {Proceedings of the International Modal Analysis Conference
             Imac},
   Volume = {1},
   Pages = {438-444},
   Year = {2001},
   Month = {January},
   Abstract = {Recent research in the broad scope of structural health
             monitoring has introduced a somewhat new paradigm within the
             context of vibration-based damage detection. The
             incorporation of statistical-based analysis has shown great
             promise in more accurately assessing the appearance, the
             location, and the scope (Levels I-III) of damage in
             structures from measured global vibration properties. One of
             the most important and least-developed aspects of the newer
             paradigm is the problem of "feature extraction", or
             identifying the most appropriate measurements, whether
             direct or indirect, for sensitively assessing damage. In
             this paper, we propose a feature extracted from a nonlinear
             time series involving attractor variance and test it on an
             eight-degree-of-freedom structure subject to a linear damage
             model.},
   Key = {fds282382}
}

@article{01416676689,
   Author = {Begley, CJ and Virgin, LN},
   Title = {On the OGY control of an impact-friction
             oscillator},
   Journal = {Journal of Vibration and Control},
   Volume = {7},
   Number = {6},
   Pages = {923-931},
   Publisher = {SAGE Publications},
   Year = {2001},
   Month = {January},
   url = {http://dx.doi.org/10.1177/107754630100700609},
   Keywords = {Friction;Vibrations (mechanical);Damping;Stiffness;Chaos
             theory;Degrees of freedom (mechanics);Computer
             simulation;},
   Abstract = {An earlier paper by the same authors examined the dynamic
             behavior of an impact-friction oscillator. It was shown that
             a variety of highly complex behavior was possible including
             chaos, and the results of numerical simulation were verified
             experimentally. Because friction is so common in mechanical
             applications and has a relatively profound effect on
             behavior, it is logical to consider whether friction forces
             can be used to advantage in such engineering systems. The
             Ott-Grebogi-Yorke (OGY) method is used here to control the
             impact oscillator using friction force as the control
             parameter.},
   Doi = {10.1177/107754630100700609},
   Key = {01416676689}
}

@article{02046837353,
   Author = {Nichols, JM and Virgin, LN},
   Title = {Practical evaluation of invariant measures for the chaotic
             response of a two-frequency excited mechanical
             oscillator},
   Journal = {Nonlinear Dynamics},
   Volume = {26},
   Number = {1},
   Pages = {67-86},
   Year = {2001},
   ISSN = {0924-090X},
   url = {http://dx.doi.org/10.1023/A:1012923517945},
   Keywords = {Chaos theory;Dynamic response;Lyapunov methods;Approximation
             theory;},
   Abstract = {This paper presents results which characterize the chaotic
             response of a low-dimensional mechanical oscillator. An
             experimental system based on a cart rolling on a two-well
             potential surface has been shown to closely approximate a
             modified form of Duffing's equation. Two-frequency forcing
             is applied, providing a useful means of varying the
             dimension of the response. Computation of correlation
             dimension and Lyapunov spectra are performed on both
             experimental and numerical data in order to assess the
             utility of these measures in a practical setting. A specific
             focus is the distinction between subharmonic and
             quasi-periodic forcing, since this has a subtle, and
             interesting, effect on the subsequent dynamics. The results
             tend to highlight the statistical nature of the measures and
             the caution that should be used in their
             interpretation.},
   Doi = {10.1023/A:1012923517945},
   Key = {02046837353}
}

@article{fds282419,
   Author = {Trickey, ST and Virgin, LN and Dowell, EH},
   Title = {Characterizing stability of responses in a nonlinear
             aeroelastic system},
   Journal = {41st Structures, Structural Dynamics, and Materials
             Conference and Exhibit},
   Volume = {1},
   Number = {I},
   Pages = {57-62},
   Year = {2000},
   Month = {December},
   Abstract = {A method for investigating the degree of stability of
             nonlinear limit cycle oscillations (LCO) observed in an
             aeroelastic system is presented. The system considered is a
             typical section airfoil model with a free-play nonlinear-ity
             in the control surface stiffness. Stability information of
             the LCO is obtained by fitting a map to an ensemble of
             perturbation induced transient data and then observing the
             properties of the map as a function of flow speed. Stability
             analysis of the linear subdomains only can suggest
             approximate locations of global system features such as LCO
             onset and flutter. Whereas the proposed method allows for
             the nonlinearity and thus can indicate impending stability
             transitions with much greater accuracy. © 1999 by S. T.
             Trickey, L. N. Virgin, and E. H. Dowell.},
   Key = {fds282419}
}

@article{fds282343,
   Author = {Trickey, ST and Virgin, LN and Dowell, EH},
   Title = {Characterizing stability of responses in a nonlinear
             aeroelastic system},
   Journal = {Collection of Technical Papers Aiaa/Asme/Asce/Ahs/Asc
             Structures, Structural Dynamics and Materials
             Conference},
   Volume = {1},
   Number = {I},
   Pages = {57-62},
   Year = {2000},
   Month = {January},
   Abstract = {A method for investigating the degree of stability of
             nonlinear limit cycle oscillations (LCO) observed in an
             aeroelastic system is presented. The system considered is a
             typical section airfoil model with a free-play nonlinearity
             in the control surface stiffness. Stability information of
             the LCO is obtained by fitting a map to an ensemble of
             perturbation induced transient data and then observing the
             properties of the map as a function of flow speed. Stability
             analysis of the linear subdomains only can suggest
             approximate locations of global system features such as LCO
             onset and flutter. Whereas the proposed method allows for
             the nonlinearity and thus can indicate impending stability
             transitions with much greater accuracy.},
   Key = {fds282343}
}

@article{04057863914,
   Author = {Virgin, LN and Dowell, EH and Conner, MD},
   Title = {On the evolution of deterministic non-periodic behavior of
             an airfoil},
   Journal = {International Journal of Non Linear Mechanics},
   Volume = {34},
   Number = {3},
   Pages = {499-514},
   Publisher = {Elsevier BV},
   Year = {1999},
   Month = {January},
   ISSN = {0020-7462},
   url = {http://dx.doi.org/10.1016/S0020-7462(98)00038-9},
   Abstract = {This paper describes some interesting transitional behavior
             in the limit cycle response of a typical section airfoil
             with a loosely connected flap subject to a fluid flow. The
             freeplay non-linearity associated with the flap connection
             has considerable practical importance since wear and
             maintenance problems inevitably accompany moving mechanical
             parts. Piecewise linear systems have been studied within the
             non-linear dynamics community for some time. However,
             application to a relatively complicated, fluid-structure
             interaction problem such as this shows the ubiquity of a
             number of characteristically non-linear features. Special
             attention is focused on almost-or quasi-periodic behavior,
             and the correpsonding stability transitions. Brief reference
             is made to some prior experimental work which suggests the
             extent to which these responses can be realized in wind
             tunnel testing © 1998 Elsevier Science Ltd. All rights
             reserved.},
   Doi = {10.1016/S0020-7462(98)00038-9},
   Key = {04057863914}
}

@article{99104840091,
   Author = {Virgin, LN and Begley, CJ},
   Title = {Grazing bifurcations and basins of attraction in an
             impact-friction oscillator},
   Journal = {Physica D: Nonlinear Phenomena},
   Volume = {130},
   Number = {1-2},
   Pages = {43-57},
   Publisher = {Elsevier BV},
   Year = {1999},
   ISSN = {0167-2789},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000080569700004&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Abstract = {This paper describes some interesting global dynamic
             behavior in the response of a double-sided,
             harmonically-forced, impact oscillator including the
             influence of Coulomb damping. The system under study is
             modeled as piecewise linear in both its force-deflection and
             force-velocity characteristics. Grazing bifurcations caused
             by this latter effect are a new feature. The paper has two
             distinct but related foci. First, the study of basins of
             attraction provides information regarding the complete
             solution set for the system, given a specific set of
             parameters. Second, grazing bifurcations represent the
             primary source of sudden change in qualitative behavior as a
             system parameter is varied. The numerical technique of
             cell-to-cell mapping provides a useful insight into the
             relation between these two. Thus, both local and global
             issues are addressed - indeed it is the interplay of
             periodic attractors and their basins of attraction that
             dominates bifurcational behavior. ©1999 Elsevier Science
             B.V. All rights reserved.},
   Doi = {10.1016/S0167-2789(99)00016-0},
   Key = {99104840091}
}

@article{6125765,
   Author = {Trickey, ST and Virgin, LN},
   Title = {Bottlenecking phenomenon near a saddle-node remnant in a
             Duffing oscillator},
   Journal = {Physics Letters A},
   Volume = {248},
   Number = {2-4},
   Pages = {185-190},
   Publisher = {Elsevier BV},
   Year = {1998},
   Month = {November},
   url = {http://dx.doi.org/10.1016/S0375-9601(98)00665-3},
   Keywords = {bifurcation;chaos;circuit oscillations;nonlinear dynamical
             systems;nonlinear network analysis;numerical
             analysis;stochastic processes;},
   Abstract = {The bottlenecking phenomenon near a saddle-node remnant or
             ghost is discussed for an electronic circuit modeling
             Duffing's equation. Numerical simulation and a useful
             experimental perturbation method, stochastic interrogation,
             are used to confirm the analytic inverse square root scaling
             law associated with saddle-node bifurcations. © 1998
             Elsevier Science B.V.},
   Doi = {10.1016/S0375-9601(98)00665-3},
   Key = {6125765}
}

@article{04057864334,
   Author = {Hu, HY and Dowell, EH and Virgin, LN},
   Title = {Stability estimation of high dimensional vibrating systems
             under state delay feedback control},
   Journal = {Journal of Sound and Vibration},
   Volume = {214},
   Number = {3},
   Pages = {497-511},
   Publisher = {Elsevier BV},
   Year = {1998},
   Month = {July},
   url = {http://dx.doi.org/10.1006/jsvi.1998.1548},
   Abstract = {The paper presents a method of assessing the stability of
             high dimensional vibrating systems under state feedback
             control with a short time delay. It is first proved that if
             the time delay is sufficiently short, an n
             -degree-of-freedom system with feedback delay maintains 2n
             eigenvalues near those of the corresponding system without
             feedback delay. A perturbation approach is then proposed to
             determine the first order variation of an arbitrary
             eigenvalue and corresponding eigenvector of the system with
             feedback delay by solving a set of linear algebraic
             equations only. The computation in this approach can be
             simplified to a matrix multiplication provided that the
             product of the time delay and the modulus of the eigenvalue
             is much less than 1. Furthermore, the approach is directly
             related to the Newton-Raphson iteration in the continuation
             of eigenvalues for long time delay. The efficacy of the
             approach is demonstrated via a number of case studies on two
             feedback delay systems of two degrees of freedom and ten
             degrees of freedom respectively. © 1998 Academic
             Press.},
   Doi = {10.1006/jsvi.1998.1548},
   Key = {04057864334}
}

@article{04057861837,
   Author = {Begley, CJ and Virgin, LN},
   Title = {Impact response and the influence of friction},
   Journal = {Journal of Sound and Vibration},
   Volume = {211},
   Number = {5},
   Pages = {801-818},
   Publisher = {Elsevier BV},
   Year = {1998},
   Month = {April},
   ISSN = {0022-460X},
   url = {http://dx.doi.org/10.1006/jsvi.1997.1389},
   Abstract = {Non-smooth stiffness and damping characteristics are
             commonly encountered in mechanical systems. The specific
             physical contacts considered in this paper are impact and
             friction. Although these individual effects have been the
             subject of quite intensive research it is their interaction
             and influence on the dynamic behavior of a mechanical
             oscillatory system that is the subject of the current work.
             Dynamical systems theory is used as a conceptual framework
             and comparisons are made between numerical and experimental
             results over a relatively wide range of parameters. © 1998
             Academic Press Limited.},
   Doi = {10.1006/jsvi.1997.1389},
   Key = {04057861837}
}

@article{04057859894,
   Author = {Tang, D and Dowell, EH and Virgin, LN},
   Title = {Limit cycle behavior of an airfoil with a control
             surface},
   Journal = {Journal of Fluids and Structures},
   Volume = {12},
   Number = {7},
   Pages = {839-858},
   Publisher = {Elsevier BV},
   Year = {1998},
   Month = {January},
   url = {http://dx.doi.org/10.1006/jfls.1998.0174},
   Abstract = {A three-degree-of-freedom aeroelastic model with freeplay is
             modeled theoretically using a small number of aerodynamic
             eigenmodes (i.e. a reduced order model) based upon Peters'
             finite-state model for two-dimensional aerodynamic flow. The
             limit cycle behavior and the sensitivity to initial
             conditions for the onset of limit cycle oscillations are
             discussed. A simple and interesting physical explanation for
             this behavior is presented based on harmonic balance or
             describing function calculations that have been confirmed by
             numerical time simulations. The theoretical results are also
             in good agreement with experiment and a universal scaling
             law for the dependence of limit cycle oscillations and
             bifurcation parameters on freeplay is elucidated. © 1998
             Academic Press.},
   Doi = {10.1006/jfls.1998.0174},
   Key = {04057859894}
}

@article{98064268503,
   Author = {Hu, H and Dowell, EH and Virgin, LN},
   Title = {Resonances of a Harmonically Forced Duffing Oscillator with
             Time Delay State Feedback},
   Journal = {Nonlinear Dynamics},
   Volume = {15},
   Number = {4},
   Pages = {311-327},
   Year = {1998},
   url = {http://dx.doi.org/10.1023/A:1008278526811},
   Keywords = {Resonance;Oscillations;Feedback control;Approximation
             theory;Damping;Vibration control;Numerical
             analysis;},
   Abstract = {The paper presents analytical and numerical studies of the
             primary resonance and the 1/3 subharmonic resonance of a
             harmonically forced Duffing oscillator under state feedback
             control with a time delay. By using the method of multiple
             scales, the first order approximations of the resonances are
             derived and the effect of time delay on the resonances is
             analyzed. The concept of an equivalent damping related to
             the delay feedback is proposed and the appropriate choice of
             the feedback gains and the time delay is discussed from the
             viewpoint of vibration control. In order to numerically
             solve the problem of history dependence prior to the start
             of excitation, the concepts of the Poincaré section and
             fixed points are generalized. Then, a modified shooting
             scheme associated with the path following technique is
             proposed to locate the periodic motion of the delayed
             system. The numerical results show the efficacy of the first
             order approximations of the resonances.},
   Key = {98064268503}
}

@article{6038245,
   Author = {Virgin, LN and Todd, MD and Begley, CJ and Trickey, ST and Dowell,
             EH},
   Title = {Basins of attraction in experimental nonlinear
             oscillators},
   Journal = {International Journal of Bifurcation and Chaos in Applied
             Sciences and Engineering},
   Volume = {8},
   Number = {3},
   Pages = {521-533},
   Publisher = {World Scientific Pub Co Pte Lt},
   Year = {1998},
   url = {http://dx.doi.org/10.1142/S0218127498000334},
   Keywords = {bifurcation;chaos;nonlinear dynamical systems;oscillations;},
   Abstract = {This paper addresses two relatively simple but fundamental
             questions in nonlinear oscillations: Given an arbitrary
             initial condition where will the trajectory go, and how long
             will it take to get there? These related questions are
             addressed from an experimental perspective where generating
             global transient behavior has received relatively little
             attention, despite the fact that a global view of transient
             behavior provides a much more complete description of the
             dynamics of a system than a traditional concentration on
             steady-state behavior. Three different physical systems are
             studied, each of which exhibits a specific behavior heavily
             influenced by transient global effects.},
   Doi = {10.1142/S0218127498000334},
   Key = {6038245}
}

@article{5594547,
   Author = {Todd, MD and Virgin, LN},
   Title = {An experimental impact oscillator},
   Journal = {Chaos, Solitons & Fractals},
   Volume = {8},
   Number = {4},
   Pages = {699-714},
   Publisher = {Elsevier BV},
   Year = {1997},
   Month = {April},
   ISSN = {0960-0779},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1997WZ30900015&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Keywords = {chaos;impact (mechanical);object-oriented
             programming;oscillations;physics computing;},
   Abstract = {The present work considers the impacting behavior of a
             piecewise linear experimental system, a previous version of
             which has successfully displayed a wide variety of
             non-linear, including chaotic, behavior in other previous
             experiments [1-3]; making use of the 'ball rolling on a
             hill' concept, a cart is constrained to roll along an
             'energy well' track, shaped in the form of a parabola such
             that the governing equations of motion of the cart are
             almost linear. In contrast to previous studies, where the
             impact condition was fixed (usually at equilibrium), the
             rigid barrier is placed at varying positions along the track
             in this study to provide a displacement constraint that
             gives rise to a discontinuity in the restoring force on the
             cart (provided solely by gravity in the non-impacting
             region). Varying the position of the impact can
             significantly change the overall behavior of the system, and
             this experimental study will concentrate on behavior where
             the impact point is varied among three different positions
             along the parabolic track, one chosen at a position less
             than equilibrium, one chosen at equilibrium, and one chosen
             greater than equilibrium; wide and varied responses are
             observed for these cases. Data were collected with the
             LabVIEW object-oriented, programmable interface, about which
             a few salient features are also discussed. © 1997 Elsevier
             Science Ltd.},
   Doi = {10.1016/s0960-0779(96)00112-9},
   Key = {5594547}
}

@article{fds282378,
   Author = {Begley, CJ and Virgin, LN},
   Title = {A detailed study of the low-frequency periodic beliavior of
             a dry friction oscillator},
   Journal = {Journal of Dynamic Systems, Measurement, and
             Control},
   Volume = {119},
   Number = {3},
   Pages = {491-497},
   Publisher = {ASME International},
   Year = {1997},
   Month = {January},
   url = {http://dx.doi.org/10.1115/1.2801284},
   Abstract = {This work examines the periodic stopping motion present in
             the low-frequency response of a dry friction oscillator,
             excited harmonically through a base spring. Piecewise linear
             solution methods are used to compare two simple friction
             models, to consider the effects of viscous damping, and.to
             illustrate stability considerations. Seeding phenomena,
             particularly at degenerate frequency ratios, are noted.
             Finally, experimental results provide a means to assess the
             effectiveness of the simple friction models in predicting
             observed motion. © 1997 ASME.},
   Doi = {10.1115/1.2801284},
   Key = {fds282378}
}

@article{5710772,
   Author = {Slade, KN and Virgin, LN and Bayly, PV},
   Title = {Extracting information from interimpact intervals in a
             mechanical oscillator},
   Journal = {Physical Review E Statistical, Nonlinear, and Soft Matter
             Physics},
   Volume = {55},
   Number = {3},
   Pages = {3705-3707},
   Year = {1997},
   Month = {January},
   url = {http://dx.doi.org/10.1103/PhysRevE.56.3705},
   Keywords = {classical mechanics;nonlinear dynamical systems;oscillations;pendulums;},
   Abstract = {Monitoring all the state variables in dynamic experiments
             may be difficult or even impossible. It is also desirable to
             reduce the coupling between the system under study and the
             measuring device to as low a level as possible. To these
             ends, we investigated the use of interimpact interval as a
             discrete state variable. It is well established that
             topological information can be obtained from delay
             coordinate embedding and thus not all of the state
             variables, or even a continuous set of a single variable,
             need to be measured. In the case of impacting systems, the
             impacts can be viewed as discrete events that can then be
             used to reconstruct more general features of the behavior.
             The success of such reconstruction techniques will be
             assessed in this paper. © 1997 The American Physical
             Society.},
   Doi = {10.1103/PhysRevE.56.3705},
   Key = {5710772}
}

@article{97103855537,
   Author = {Fielder, WT and Virgin, LN and Plaut, RH},
   Title = {Experiments and simulation of overturning of an asymmetric
             rocking block on an oscillating foundation},
   Journal = {European Journal of Mechanics A/Solids},
   Volume = {16},
   Number = {5},
   Pages = {905-923},
   Year = {1997},
   Month = {January},
   Keywords = {Oscillations;Computer simulation;Mathematical models;Dynamic
             response;Sensitivity analysis;},
   Abstract = {This paper describes what happens when the base upon which a
             relatively slender rigid block rests is subjected to a
             horizontal harmonic acceleration. The force transmitted to
             the block may be sufficient to initiate rocking or even
             cause overturning. The number of times the block impacts the
             base before it overturns (if it does) may vary by a
             considerable amount. Transient rocking and overturning
             depend very sensitively on the forcing parameters (amplitude
             and frequency) and exhibit certain fractal characteristics.
             Some of the subtle phenomena obtained by numerical
             simulation are demonstrated by experiments in this
             investigation. Although the physical experiments described
             in this paper are relatively simple in terms of geometry,
             parameter ranges, and modeling assumptions, the emphasis
             throughout is on qualitative behavior. Despite these
             limitations, the inherent sensitivity of the dynamics poses
             some profound questions regarding the concept of
             experimental repeatability.},
   Key = {97103855537}
}

@article{5785161,
   Author = {Todd, MD and Virgin, LN},
   Title = {An experimental verification of basin metamorphoses in a
             nonlinear mechanical system},
   Journal = {International Journal of Bifurcation and
             Chaos},
   Volume = {7},
   Number = {6},
   Pages = {1337-1357},
   Publisher = {World Scientific Pub Co Pte Lt},
   Year = {1997},
   Month = {January},
   url = {http://dx.doi.org/10.1142/S0218127497001060},
   Keywords = {bifurcation;nonlinear dynamical systems;stochastic
             processes;},
   Abstract = {This paper describes bifurcations and the basin boundary
             metamorphoses that give rise to post-fold outcome
             indeterminacy from a primarily experimental perspective. A
             gravity-loaded cart-and-track system is constrained to mimic
             the twin-well, single-degree-of-freedom Duffing oscillator.
             Of primary interest is the study of how motion, initially
             contained within a single well, "spills over" into the
             adjacent well. Although this system is globally bounded, it
             retains the same generic features of the single-well
             canonical escape equation. Using time-embedded coordinates,
             the technique of stochastic interrogation is used to
             generate the initial condition maps at three different
             forcing levels corresponding to three different regimes of
             post-fold outcomes. These three regions are characterized,
             respectively, by smooth basin boundaries with safe jumps to
             resonance, fractal basin boundaries with jumps that may or
             may not restabilize on to the resonant attractor, and eroded
             basins with unsafe jumps leading to escape from the local
             well. This experiment successfully replicates much of the
             subtle global behavior observed in numerical
             simulations.},
   Doi = {10.1142/S0218127497001060},
   Key = {5785161}
}

@article{04057842250,
   Author = {Conner, MD and Tang, DM and Dowell, EH and Virgin,
             LN},
   Title = {Nonlinear behavior of a typical airfoil section with control
             surface freeplay: A numerical and experimental
             study},
   Journal = {Journal of Fluids and Structures},
   Volume = {11},
   Number = {1},
   Pages = {89-109},
   Publisher = {Elsevier BV},
   Year = {1997},
   Month = {January},
   url = {http://dx.doi.org/10.1006/jfls.1996.0068},
   Abstract = {A three degree-of-freedom aeroelastic typical section with
             control surface freeplay is modeled theoretically as a
             system of piecewise linear state-space models. The system
             response is determined by time marching of the governing
             equations using a standard Runge-Kutta algorithm in
             conjunction with Hénon's method for integrating a system of
             equations to a prescribed surface of phase space section.
             Hénon's method is used to locate the "switching points"
             accurately and efficiently as the system moves from one
             linear region into another. An experimental model which
             closely approximates the three degree-of-freedom typical
             section in two-dimensional, incompressible flow has been
             created to validate the theoretical model. Consideration is
             given to modeling realistically the structural damping
             present in the experimental system. The effect of the
             freeplay on the system response is examined numerically and
             experimentally. The development of the state-space model
             offers a low-order, computationally efficient means of
             modeling fully the freeplay nonlinearity and may offer
             advantages in future research which will investigate the
             effects of freeplay on the control of flutter in the typical
             section. © 1997 Academic Press Limited.},
   Doi = {10.1006/jfls.1996.0068},
   Key = {04057842250}
}

@article{5582165,
   Author = {Murphy, KD and Virgin, LN},
   Title = {The effect of thermal prestress on the free vibration
             characteristics of clamped rectangular plates: Theory and
             experiment},
   Journal = {Journal of Vibration and Acoustics},
   Volume = {119},
   Number = {2},
   Pages = {243-249},
   Publisher = {ASME International},
   Year = {1997},
   Month = {January},
   url = {http://dx.doi.org/10.1115/1.2889710},
   Keywords = {buckling;thermal stresses;vibrations;},
   Abstract = {In a combined theoretical and experimental approach, the
             free vibration characteristics of a uniformly heated, fully
             clamped (out-of-plane), rectangular plate are considered.
             Specifically, this work focuses on the behavior of the small
             amplitude natural frequencies as the temperature is
             increased from the ambient. The effects of initial geometric
             imperfections, modal coupling, imperfect clamping (in-plane)
             and post-buckling are addressed. Comparisons between theory
             and experiment show excellent agreement. © 1997 by
             ASME.},
   Doi = {10.1115/1.2889710},
   Key = {5582165}
}

@article{fds319935,
   Author = {Todd, MD and Virgin, LN},
   Title = {An experimental impact oscillator},
   Journal = {Chaos, Solitons & Fractals},
   Volume = {8},
   Number = {4 SPEC. ISS.},
   Pages = {699-714},
   Year = {1997},
   Month = {January},
   Abstract = {The present work considers the impacting behavior of a
             piecewise linear experimental system, a previous version of
             which has successfully displayed a wide variety of
             non-linear, including chaotic, behavior in other previous
             experiments [1-3]; making use of the 'ball rolling on a
             hill' concept, a cart is constrained to roll along an
             'energy well' track, shaped in the form of a parabola such
             that the governing equations of motion of the cart are
             almost linear. In contrast to previous studies, where the
             impact condition was fixed (usually at equilibrium), the
             rigid barrier is placed at varying positions along the track
             in this study to provide a displacement constraint that
             gives rise to a discontinuity in the restoring force on the
             cart (provided solely by gravity in the non-impacting
             region). Varying the position of the impact can
             significantly change the overall behavior of the system, and
             this experimental study will concentrate on behavior where
             the impact point is varied among three different positions
             along the parabolic track, one chosen at a position less
             than equilibrium, one chosen at equilibrium, and one chosen
             greater than equilibrium; wide and varied responses are
             observed for these cases. Data were collected with the
             LabVIEW object-oriented, programmable interface, about which
             a few salient features are also discussed. © 1997 Elsevier
             Science Ltd.},
   Key = {fds319935}
}

@article{97053645389,
   Author = {Murphy, K.D. and Virgin, L.N. and Rizzi,
             S.A.},
   Title = {Effect of thermal prestress on the free vibration
             characteristics of clamped rectangular plates: Theory and
             experiment},
   Journal = {Journal of Vibration and Acoustics, Transactions of the
             ASME},
   Volume = {119},
   Number = {2},
   Pages = {243 - 249},
   Year = {1997},
   Keywords = {Prestressing;Thermal effects;Natural frequencies;Vibrations
             (mechanical);Buckling;Defects;Mathematical
             models;Eigenvalues and eigenfunctions;Equations of
             motion;},
   Abstract = {In a combined theoretical and experimental approach, the
             free vibration characteristics of a uniformly heated, fully
             clamped (out-of-plane), rectangular plate are considered.
             Specifically, this work focuses on the behavior of the small
             amplitude natural frequencies as the temperature is
             increased from the ambient. The effects of initial geometric
             imperfections, modal coupling, imperfect clamping (in-plane)
             and post-buckling are addressed. Comparisons between theory
             and experiment show excellent agreement.},
   Key = {97053645389}
}

@article{fds282375,
   Author = {Donescu, P and Virgin, LN},
   Title = {Free surface flow computation using a fully consistent
             method},
   Journal = {American Society of Mechanical Engineers, Fluids Engineering
             Division (Publication) Fed},
   Volume = {238},
   Pages = {421-426},
   Year = {1996},
   Month = {December},
   Abstract = {Free surface flows described by nonlinear equations due to
             nonlinear boundary conditions written for unknown boundary
             position are solved using a new implicit, fully consistent
             method. The proposed algorithm is tested for a couple of
             hydrodynamic free surface problems studying both the
             evolution of an initial disturbance and the creation of
             waves by wave makers and proves to be accurate,
             computationally efficient and extendible towards the study
             of floating vessels behavior in waves.},
   Key = {fds282375}
}

@article{fds282376,
   Author = {Slade, KN and Virgin, LN},
   Title = {Monitoring the behavior of an experimental impacting
             system},
   Journal = {American Society of Mechanical Engineers, Design Engineering
             Division (Publication) De},
   Volume = {90},
   Pages = {75-84},
   Year = {1996},
   Month = {December},
   Abstract = {Since monitoring all the state variables in dynamic
             experiments may be difficult or even impossible, and since
             it is desirable to reduce the coupling between the system
             under study and the measuring device to as low a level as
             possible, it is useful to assess novel data acquisition
             techniques. Furthermore, it is well established that
             topological information can be obtained from delay
             coordinate embedding, and thus, not all of the state
             variables, or even a continuous set of a single variable,
             need to be measured. In the case of impacting systems, the
             impacts can be viewed as discrete events which can then be
             used to reconstruct more general features of the behavior.
             The success of such reconstruction techniques will be
             assessed in this paper.},
   Key = {fds282376}
}

@article{96110407089,
   Author = {Murphy, KD and Virgin, LN and Rizzi, SA},
   Title = {Characterizing the dynamic response of a thermally loaded,
             acoustically excited plate},
   Journal = {Journal of Sound and Vibration},
   Volume = {196},
   Number = {5},
   Pages = {635-658},
   Publisher = {Elsevier BV},
   Year = {1996},
   Month = {October},
   url = {http://dx.doi.org/10.1006/jsvi.1996.0506},
   Keywords = {Plates (structural components);Acoustic wave effects;Thermal
             load;Fatigue of materials;Buckling;Structural
             analysis;Mathematical models;Chaos theory;Lyapunov
             methods;Dynamic response;},
   Abstract = {In this work the dynamic response is considered of a
             homogeneous, fully clamped rectangular plate subject to
             spatially uniform thermal loads and narrow-band acoustic
             excitation. In both the pre-and post-buckled regimes, the
             small amplitude, linear response is confirmed. However, the
             primary focus is on the large amplitude, non-linear,
             snap-through response, because of the obvious implications
             for fatigue in aircraft components. A theoretical model is
             developed which uses nine spatial modes and incorporates
             initial imperfections and non-ideal boundary conditions.
             Because of the higher order nature of this model, it is
             inherently more complicated than a one-mode buckled beam
             equation (Duffing's equation). An experimental system was
             developed to complement the theoretical results, and also to
             measure certain system parameters for the model which are
             not available theoretically. Several analysis techniques are
             used to characterize the response. These include time
             series, power spectra and autocorrelation functions. In
             addition, the fractal dimension and Lyapunov exponents for
             the response are computed to address the issue of spatial
             dimension and temporal complexity (chaos), respectively.
             Comparisons between theory and experiment are made and show
             considerable agreement. However, these comparisons also
             serve to point out difficulties in computing the fractal
             dimension and Lyapunov exponents from experimental data. ©
             1996 Academic Press Limited.},
   Doi = {10.1006/jsvi.1996.0506},
   Key = {96110407089}
}

@article{96083291581,
   Author = {Todd, MD and Virgin, LN},
   Title = {Natural frequency considerations of an impact
             oscillator},
   Journal = {Journal of Sound and Vibration},
   Volume = {194},
   Number = {3},
   Pages = {452-460},
   Publisher = {Elsevier BV},
   Year = {1996},
   Month = {July},
   url = {http://dx.doi.org/10.1006/jsvi.1996.0370},
   Keywords = {Natural frequencies;Constraint theory;Calculations;Equations
             of motion;Dynamics;Lagrange multipliers;Vibrations
             (mechanical);},
   Abstract = {This paper studies an experimental linear oscillator with
             one-sided displacement constraint. Due to the mobility of
             the constraint, the natural frequency of the system changes
             as the impact point changes, and the analytical calculations
             are performed to describe this dependence for pure elastic
             rebound and for a bilinear oscillator. Bilinear results show
             that a general decrease in the natural frequency is seen for
             all constraint locations when compared to elastic rebound
             results, which is expected since the mass spends a non-zero
             amount of time in the stiffer region. A series solution is
             partially obtained for the corresponding non-linear
             experimental system. The experimental results correlated
             very well with analytical calculations based on a pure
             elastic rebound.},
   Doi = {10.1006/jsvi.1996.0370},
   Key = {96083291581}
}

@article{96063227023,
   Author = {Donescu, P and Virgin, LN and Wu, JJ},
   Title = {Periodic solutions of an unsymmetric oscillator including a
             comprehensive study of their stability characteristics},
   Journal = {Journal of Sound and Vibration},
   Volume = {192},
   Number = {5},
   Pages = {959-976},
   Publisher = {Elsevier BV},
   Year = {1996},
   Month = {May},
   url = {http://dx.doi.org/10.1006/jsvi.1996.0228},
   Keywords = {Numerical methods;Stability;Harmonic generation;Harmonic
             analysis;Approximation theory;Stability criteria;Bifurcation
             (mathematics);Calculations;Integration;Efficiency;},
   Abstract = {The periodic solutions of a non-linear oscillator with
             unsymmetric restoring force and harmonic excitation are
             studied by means of harmonic balance using an arbitrary
             number of modes in the assumed solution. Comparisons between
             the approximate solution for two modes are made with respect
             to both one mode and numerical solutions. Different
             stability criteria have been used in a comparative analysis
             which shows that higher order criteria not only give more
             accurate results but also respect the correct sequence of
             flips and folds without a significant increase in
             computational cost. © 1996 Academic Press
             Limited.},
   Doi = {10.1006/jsvi.1996.0228},
   Key = {96063227023}
}

@article{96053168898,
   Author = {Virgin, LN and Fielder, WT and Plaut, RH},
   Title = {Transient motion and overturning of a rocking block on a
             seesawing foundation},
   Journal = {Journal of Sound and Vibration},
   Volume = {191},
   Number = {1},
   Pages = {177-187},
   Publisher = {Elsevier BV},
   Year = {1996},
   Month = {March},
   url = {http://dx.doi.org/10.1006/jsvi.1996.0114},
   Keywords = {Foundations;Earthquakes;Dynamic response;Soil structure
             interactions;Failure (mechanical);Structural
             analysis;Mathematical models;},
   Abstract = {A slender, rigid, rectangular block resting on a rigid, flat
             foundation is subjected to a seesawing excitation. The
             foundation rotates back and forth about a pivot point
             located under the center of gravity of the block, causing
             the block to rock and overturn. The seesawing motion leads
             to some interesting phenomena, including the possible
             increase in energy at impact. As for the case of a
             translating foundation, the transient response of the block
             is extremely sensitive to the excitation parameters, and
             fractal behavior is exhibited.},
   Doi = {10.1006/jsvi.1996.0114},
   Key = {96053168898}
}

@article{fds282418,
   Author = {Conner, MD and Virgin, LN and Dowell, EH},
   Title = {Accurate numerical integration of state-space models for
             aeroelastic systems with free play},
   Journal = {Aiaa Journal},
   Volume = {34},
   Number = {10},
   Pages = {2202-2205},
   Publisher = {American Institute of Aeronautics and Astronautics
             (AIAA)},
   Year = {1996},
   Month = {January},
   url = {http://dx.doi.org/10.2514/3.13377},
   Doi = {10.2514/3.13377},
   Key = {fds282418}
}

@article{96073231603,
   Author = {Conner, MD and Donescu, P and Virgin, LN},
   Title = {On the global convergence characteristics of numerically
             evaluated jacobian matrices: Technical note},
   Journal = {Nonlinear Dynamics},
   Volume = {10},
   Number = {2},
   Pages = {165-174},
   Publisher = {Springer Nature America, Inc},
   Year = {1996},
   Month = {January},
   url = {http://dx.doi.org/10.1007/BF00045455},
   Keywords = {Convergence of numerical methods;Oscillators
             (electronic);Numerical methods;Dynamics;Bifurcation
             (mathematics);Mathematical techniques;},
   Abstract = {Since locating all the fixed points of a nonlinear
             oscillator involves the numerical solution of simultaneous
             equations, it is useful to observe some of the global
             convergence characteristics of these techniques.
             Specifically, the popular Newton or quasi-Newton approaches
             require numerical evaluation of the Jacobian matrix of the
             Poincarè map. This note focuses attention on the domains of
             attraction for a number of fixed point techniques applied to
             a single nonlinear oscillator with a single set of
             parameters. Clearly, there are many issues here, including
             proximity to bifurcations, order of the dynamical system,
             temporal convergence characteristics, i.e. CPU time, and so
             on, but it is instructive to observe a snapshot of the
             basins of attraction, the boundaries of which path-following
             routines seek to avoid when a parameter is changed. © 1996
             Kluwer Academic Publishers.},
   Doi = {10.1007/BF00045455},
   Key = {96073231603}
}

@article{96053196930,
   Author = {Donescu, P and Virgin, LN},
   Title = {Efficient determination of higher-order periodic solutions
             using n-mode harmonic balance},
   Journal = {Ima Journal of Applied Mathematics},
   Volume = {56},
   Number = {1},
   Pages = {21-32},
   Publisher = {Oxford University Press (OUP)},
   Year = {1996},
   Month = {January},
   url = {http://dx.doi.org/10.1093/imamat/56.1.21},
   Keywords = {Differential equations;Harmonic analysis;Numerical
             methods;Bifurcation (mathematics);Nonlinear
             equations;Numerical analysis;},
   Abstract = {This paper presents a systematic procedure to explicitly
             determine the algebraic equations arising from the method of
             harmonic balance with an arbitrary number of modes in the
             assumed solutions. The technique can be used for a wide
             variety of nonlinear oscillators (including systems of
             ordinary differential equations). The method is illustrated
             in the case of second-order differential equations with
             nonlinear restoring force. Although numerical methods have
             been employed to solve the resulting systems of algebraic
             equations, the general approach is analytic. As such, this
             study confirms independently (i.e. nonsimulation) the
             period-doubling cascade of an escape equation including the
             bifurcation universal scaling laws.},
   Doi = {10.1093/imamat/56.1.21},
   Key = {96053196930}
}

@article{96053197214,
   Author = {Todd, MD and Virgin, LN and Gottwald, JA},
   Title = {The nonstationary transition through resonance},
   Journal = {Nonlinear Dynamics},
   Volume = {10},
   Number = {1},
   Pages = {31-48},
   Publisher = {Springer Nature},
   Year = {1996},
   Month = {January},
   url = {http://dx.doi.org/10.1007/BF00114797},
   Keywords = {Resonance;Dynamics;Bifurcation (mathematics);Vibrations
             (mechanical);Mathematical models;Nonlinear systems;Rotating
             machinery;},
   Abstract = {This paper considers the resonant behavior of a mechanical
             oscillator during a linear frequency sweep. Both numerical
             and experimental results are presented. The experimental
             system consisting of a track in the shape of a potential
             energy surfaces has been used to highlight other types of
             nonlinear behavior and is here adapted so that the forcing
             frequency can be evolved continuously in time. The classic
             linear oscillator (with a parabolic potential well) is used
             as an introduction to illustrate basic features of the
             experiment and its response. Then, a track with a double
             well is used to assess nonstationary frequency effects on
             certain nonlinear characteristics, specifically amplitude
             jumps and flip bifurcations. © 1996 Kluwer Academic
             Publishers.},
   Doi = {10.1007/BF00114797},
   Key = {96053197214}
}

@article{96043120198,
   Author = {Plaut, RH and Fielder, WT and Virgin, LN},
   Title = {Fractal Behavior of an Asymmetric Rigid Block Overturning
             Due to Harmonic Motion of a Tilted Foundation},
   Journal = {Chaos, Solitons & Fractals},
   Volume = {7},
   Number = {2},
   Pages = {177-196},
   Publisher = {Elsevier BV},
   Year = {1996},
   Month = {January},
   url = {http://dx.doi.org/10.1016/0960-0779(95)00059-3},
   Abstract = {The motion of a slender rigid block with a flat or concave
             base resting on a rigid and flat foundation is analyzed. The
             block may be symmetric or asymmetric, and the foundation may
             be horizontal or tilted. The foundation oscillates
             harmonically for a finite period of time, and the block
             exhibits planar motion: it may rotate about either of its
             bottom corners, it may rock from one corner to the other,
             and it may overturn. Sliding and bouncing are not
             considered. Energy is lost during the impact when the point
             of rotation switches from one corner to the other. The
             number of impacts prior to overturning is computed, and
             results for horizontal foundation acceleration are plotted
             in the plane of excitation amplitude versus excitation
             frequency. The boundaries separating regions associated with
             different numbers of impacts, and in particular the boundary
             between overturning and nonoverturning regions, are
             fractal.},
   Doi = {10.1016/0960-0779(95)00059-3},
   Key = {96043120198}
}

@article{97013487572,
   Author = {Murphy, KD and Virgin, LN and Rizzi, SA},
   Title = {Experimental snap-through boundaries for acoustically
             excited, thermally buckled plates},
   Journal = {Experimental Mechanics},
   Volume = {36},
   Number = {4},
   Pages = {312-317},
   Publisher = {Springer Nature},
   Year = {1996},
   Month = {January},
   url = {http://dx.doi.org/10.1007/BF02328572},
   Keywords = {Vibrations (mechanical);Loads (forces);Pressure
             effects;Acoustic waves;Acoustic intensity;Frequency domain
             analysis;},
   Abstract = {This paper presents some recent experimental results on the
             dynamic snap-through behavior of a clamped, rectangular
             plate subject to thermal loading and intense acoustic
             excitation. The likelihood of snap-through oscillations is
             characterized in terms of boundaries separating regions of
             snap-through and no snap-through in the parameter space. Two
             scenarios are considered. First, using tonal inputs, the
             regions of snap-through are mapped in the sound pressure
             level - input frequency domain ((SPL, ω) plane). Second,
             random acoustic inputs are used, and the effect of varying
             the overall sound pressure level and frequency bandwidth are
             investigated ((SPL, ωcenter+ ω̄) plane). Several
             nonlinear characteristics are evident and
             discussed.},
   Doi = {10.1007/BF02328572},
   Key = {97013487572}
}

@article{5349936,
   Author = {Todd, M.D. and Virgin, L.N.},
   Title = {Natural frequency considerations of an impact
             oscillator},
   Journal = {J. Sound Vib. (UK)},
   Volume = {194},
   Number = {3},
   Pages = {452 - 60},
   Year = {1996},
   url = {http://dx.doi.org/10.1006/jsvi.1996.0370},
   Keywords = {classical mechanics;impact (mechanical);oscillations;},
   Abstract = {We present some general analytical calculations for
             determining how the natural frequency of a linear oscillator
             with a one-sided displacement constraint varies with the
             positioning of the constraint. An experimental system
             consisting of a cart rolling along a parabolic potential
             surface (track) is used for experimental verification; a
             movable barrier can be placed at a prescribed location on
             the track to impose the displacement constraint},
   Key = {5349936}
}

@article{fds282373,
   Author = {Murphy, KD and Virgin, LN and Rizzi, SA},
   Title = {Experimental study of the forced response of pre- and
             post-critical plates},
   Journal = {American Society of Mechanical Engineers, Design Engineering
             Division (Publication) De},
   Volume = {84},
   Number = {3 Pt A/1},
   Pages = {695-701},
   Year = {1995},
   Month = {December},
   Abstract = {Experimental results are presented which characterize the
             dynamic response of homogeneous, fully clamped, rectangular
             plates to narrow band acoustic excitation and uniform
             thermal loads. Using time series, pseudo-phase projections,
             power spectra and auto-correlation functions, small
             amplitude vibrations are considered about both the pre- and
             postcritical states. These techniques are then employed to
             investigate the snap-through response. The results for
             snap-through suggest that the motion is temporally complex
             and a Lyapunov exponent calculation confirms that the motion
             is chaotic. Finally, a snap-through boundary is mapped in
             the (ω, SPL) parameter space separating the regions of
             snap-through and no snap-through.},
   Key = {fds282373}
}

@article{fds282374,
   Author = {Fielder, WT and Virgin, LN and Plaut, RH},
   Title = {Experiments on a rocking block},
   Journal = {American Society of Mechanical Engineers, Design Engineering
             Division (Publication) De},
   Volume = {84},
   Number = {3 Pt A/1},
   Pages = {781-786},
   Year = {1995},
   Month = {December},
   Abstract = {A rigid, slender, rectangular block is an apparently simple
             example of a stability problem. In a static sense, the
             upright position remains stable providing the restoring
             moment due to gravity is sufficient to offset any applied
             overturning moment. Rotated about either corner, the block
             will overturn if a critical angle is exceeded. However, if
             the (quiescent) block is subjected to a horizontal (dynamic)
             base excitation, and assuming that no sliding, bouncing, or
             out-of-plane motion occurs, a typical block may either: (i)
             remain stationary relative to the base, (ii) rock, or (iii)
             overturn. The conditions under which overturning occurs are
             of particular interest here, i.e., the boundary between
             categories (ii) and (iii) above. Combinations of forcing
             parameters, i.e., magnitude and frequency of the sinusoidal
             excitation, are categorized according to whether, and how
             quickly, overturning occurs. The transition when the block
             changes from rotation about one corner to the other, the
             energy loss at impact, and large-angle geometric effects are
             the sources of nonlinearity in this problem. Based on
             numerical integration, and taking great care to accurately
             model the impact condition, it is shown that transient
             rocking prior to overturning exhibits an extreme sensitivity
             and dependence on certain system parameters. A number of
             counter-intuitive features are observed. Some elementary
             experiments conducted on a relatively slender, rigid block
             placed on a shake table confirm some of the simulation
             results, but also point out the modeling difficulties
             encountered in such inherently sensitive
             systems.},
   Key = {fds282374}
}

@article{5141631,
   Author = {Plaut, RH and Murphy, KD and Virgin, LN},
   Title = {CURVE AND SURFACE VEERING FOR A BRACED COLUMN},
   Journal = {Journal of Sound and Vibration},
   Volume = {187},
   Number = {5},
   Pages = {879-885},
   Publisher = {Elsevier BV},
   Year = {1995},
   Month = {November},
   ISSN = {0022-460X},
   url = {http://dx.doi.org/10.1006/jsvi.1995.0570},
   Keywords = {buckling;vibrations;},
   Abstract = {Curve veering arises naturally in a wide variety of
             eigenvalue problems in structural mechanics, such as
             vibration of beams, rotors, plates and shells, and buckling
             of columns and plates. Previous work on curve veering is
             extended with the consideration of more than one eigenvalue
             parameter. Both vibrations and buckling are included in a
             problem of a pinned column with a brace that is at or near
             the center. An exact solution of the continuous problem is
             obtained. For a fixed position of the brace, the parameters
             are the vibration frequencies, the buckling loads, and the
             stiffness of the brace. Curve veering is observed in the
             planes formed by fixing the value of one of these parameters
             and letting the other two vary, and surface veering is
             studied in the space of the three parameters},
   Doi = {10.1006/jsvi.1995.0570},
   Key = {5141631}
}

@article{5116119,
   Author = {Gottwald, JA and Virgin, LN and Dowell, EH},
   Title = {Routes to escape from an energy well},
   Journal = {Journal of Sound and Vibration},
   Volume = {187},
   Number = {1},
   Pages = {133-144},
   Publisher = {Elsevier BV},
   Year = {1995},
   Month = {October},
   ISSN = {0022-460X},
   url = {http://dx.doi.org/10.1006/jsvi.1995.0506},
   Keywords = {nonlinear differential equations;nonlinear dynamical
             systems;},
   Abstract = {Dynamical systems characterized by the possibility of escape
             from a local potential energy well occur in a great many
             physical problems, including a rigid-arm pendulum passing
             over its inverted equilibrium position, snap-through
             buckling in arch and shell structures, and capsizing of
             ships. This is a thoroughly non-linear problem and has
             received substantial recent attention, especially using
             techniques based on numerical simulation. The current paper
             confirms much of these earlier findings using a mechanical
             experiment which mimics the behavior of a typical
             “escape” non-linear ordinary differential equation. ©
             1995 by Academic Press, Inc.},
   Doi = {10.1006/jsvi.1995.0506},
   Key = {5116119}
}

@article{fds282372,
   Author = {Fielder, WT and Virgin, LN and Plaut, RH},
   Title = {Overturning of a rigid block under horizontal base
             excitation},
   Journal = {Proceedings of Engineering Mechanics},
   Volume = {1},
   Pages = {195-198},
   Year = {1995},
   Month = {January},
   Abstract = {Overturning conditions for a rigid, rectangular block on a
             rigid, horizontal, vibrating base are investigated. The base
             moves with a simple-harmonic horizontal acceleration over a
             finite period of time, and the block can rotate about either
             of its bottom corners. Energy is lost during the impact when
             the point of rotation switches from one corner to the other.
             The motion of the block is investigated for various
             combinations of excitation amplitude and frequency. When
             overturning occurs, the number of prior impacts is computed.
             The overturning boundary in the parameter plane exhibits a
             fractal behavior.},
   Key = {fds282372}
}

@article{95122949877,
   Author = {Begley, CJ and Virgin, LN},
   Title = {A comparison of piecewise linear and continuous
             approximating models},
   Journal = {Mechanics Research Communications},
   Volume = {22},
   Number = {6},
   Pages = {527-532},
   Publisher = {Elsevier BV},
   Year = {1995},
   Month = {January},
   ISSN = {0093-6413},
   url = {http://dx.doi.org/10.1016/0093-6413(95)00057-7},
   Doi = {10.1016/0093-6413(95)00057-7},
   Key = {95122949877}
}

@article{5096112,
   Author = {Virgin, LN and Walsh, TF and Knight, JD},
   Title = {Nonlinear behavior of a magnetic bearing
             system},
   Journal = {Journal of Engineering for Gas Turbines and
             Power},
   Volume = {117},
   Number = {3},
   Pages = {582-588},
   Publisher = {ASME International},
   Year = {1995},
   Month = {January},
   url = {http://dx.doi.org/10.1115/1.2814135},
   Keywords = {bifurcation;feedback;machine bearings;magnetic
             devices;magnetic variables control;stability;transient
             response;},
   Abstract = {This paper describes the results of a study into the dynamic
             behavior of a magnetic bearing system. The research focuses
             attention on the influence of nonlinearities on the forced
             response of a two-degree-of-freedom rotating mass suspended
             by magnetic bearings and subject to rotating unbalance and
             feedback control. Geometric coupling between the degrees of
             freedom leads to a pair of nonlinear ordinary differential
             equations, which are then solved using both numerical
             simulation and approximate analytical techniques. The system
             exhibits a variety of interesting and somewhat unexpected
             phenomena including various amplitude driven bifurcational
             events, sensitivity to initial conditions, and the complete
             loss of stability associated with the escape from the
             potential well in which the system can be thought to be
             oscillating. An approximate criterion to avoid this last
             possibility is developed based on concepts of limiting the
             response of the system. The present paper may be considered
             as an extension to an earlier study by the same authors,
             which described the practical context of the work, free
             vibration, control aspects, and derivation of the
             mathematical model. © 1995 by ASME.},
   Doi = {10.1115/1.2814135},
   Key = {5096112}
}

@article{95122947293,
   Author = {Gottwald, J.A. and Virgin, L.N. and Dowell,
             E.H.},
   Title = {Routes to escape from an energy well},
   Journal = {Journal of Sound and Vibration},
   Volume = {187},
   Number = {1},
   Pages = {133 -},
   Year = {1995},
   url = {http://dx.doi.org/10.1006/jsvi.1995.0506},
   Key = {95122947293}
}

@article{4760034,
   Author = {Bayly, PV and Virgin, LN},
   Title = {Practical considerations in the control of
             chaos.},
   Journal = {Physical Review E Statistical, Nonlinear, and Soft Matter
             Physics},
   Volume = {50},
   Number = {1},
   Pages = {604-607},
   Publisher = {American Physical Society (APS)},
   Year = {1994},
   Month = {July},
   ISSN = {1063-651X},
   url = {http://dx.doi.org/10.1103/PhysRevE.50.604},
   Keywords = {chaos;feedback;stability;},
   Abstract = {Unstable periodic orbits in certain chaotic systems may be
             stabilized via small perturbations of a control parameter.
             Stabilization using linear feedback has been achieved in
             both simulations and physical experiments. Not all chaotic
             systems can be controlled easily or well, and the
             effectiveness of proposed control algorithms depends
             strongly on mathematical properties of the chaotic behavior.
             Practical considerations are discussed that affect the
             robustness of local linear control strategies, with emphasis
             on the range of feedback gains which can stabilize the
             linearized map. © 1994 The American Physical
             Society.},
   Doi = {10.1103/physreve.50.604},
   Key = {4760034}
}

@article{94061321479,
   Author = {Murphy, KD and Bayly, PV and Virgin, LN and Gottwald,
             JA},
   Title = {Measuring the stability of periodic attractors using
             perturbation-induced transients: Applications to two
             non-linear oscillators},
   Journal = {Journal of Sound and Vibration},
   Volume = {172},
   Number = {1},
   Pages = {85-102},
   Publisher = {Elsevier BV},
   Year = {1994},
   Month = {April},
   url = {http://dx.doi.org/10.1006/jsvi.1994.1160},
   Keywords = {Perturbation techniques;Control systems;Oscillators
             (mechanical);Conformal mapping;Vibrations
             (mechanical);Approximation theory;Matrix algebra;Degrees of
             freedom (mechanics);},
   Abstract = {In this paper a combined analytical, numerical and
             experimental approach is used to study the behavior of
             small, perturbation-induced transients superimposed on a
             periodic steady state. The behavior of these transients is
             monitored in terms of characteristic multipliers as a
             control parameter is changed and instability is approached.
             Two non-linear mechanical oscillators are used which
             exemplify the application of these concepts to physical
             systems. © 1994 Academic Press Limited.},
   Doi = {10.1006/jsvi.1994.1160},
   Key = {94061321479}
}

@article{94061310928,
   Author = {Virgin, LN and Murphy, KD},
   Title = {On the Behavior of Characteristic Multipliers Through a
             Period-Doubling Sequence},
   Journal = {Journal of Sound and Vibration},
   Volume = {169},
   Number = {5},
   Pages = {699-703},
   Publisher = {Elsevier BV},
   Year = {1994},
   Month = {February},
   ISSN = {0022-460X},
   url = {http://dx.doi.org/10.1006/jsvi.1994.1042},
   Keywords = {System stability;Mathematical models;Dynamics;},
   Abstract = {Initial work along these lines by the present authors has
             focused attention on how these ideas can be used to infer
             and predict the loss of stability of an n = 1 solution.
             Here, the algorithm is applied through a series of
             period-doubling bifurcations, but certain practical
             limitations operate [2]. These include problems associated
             with the length of transient decay and magnitude of the
             perturbation used. This brief note shows that it is possible
             to track the stability of increasingly high order
             subharmonic oscillations through a period-doubling sequence
             using a careful numerical approach. It is also shown that
             the passage through this sequence results in the scaling of
             successive CM radii if the forcing amplitude is used as the
             control parameter.},
   Doi = {10.1006/jsvi.1994.1042},
   Key = {94061310928}
}

@article{94021208568,
   Author = {Virgin, LN and Erickson, BK},
   Title = {A new approach to the overturning stability of floating
             structures},
   Journal = {Ocean Engineering},
   Volume = {21},
   Number = {1},
   Pages = {67-80},
   Publisher = {Elsevier BV},
   Year = {1994},
   Month = {January},
   ISSN = {0029-8018},
   url = {http://dx.doi.org/10.1016/0029-8018(94)90030-2},
   Keywords = {System stability;Vibrations (mechanical);Computer
             simulation;},
   Abstract = {The increasingly widespread use of floating offshore
             production facilities has led to a need for a better
             understanding and accurate prediction of dynamic behavior.
             The approach described in this paper uses an approximate
             criterion for safe, forced, roll oscillations of a typical
             semi-submersible based on a stability margin. This stability
             margin is developed from a comparison between the total
             energy of the steady-state oscillating system and the total
             energy required to cause instability in the corresponding
             unforced, undamped system. The accuracy and utility of the
             new approach is assessed by comparing the loss of stability
             of numerical simulations with the approximate criterion. ©
             1994.},
   Doi = {10.1016/0029-8018(94)90030-2},
   Key = {94021208568}
}

@article{fds311305,
   Author = {Virgin, LN and Walsh, TF and Knight, JD},
   Title = {Nonlinear behavior of a magnetic bearing
             system},
   Journal = {Proceedings of the Asme Turbo Expo},
   Volume = {5},
   Pages = {1-7},
   Publisher = {ASME},
   Year = {1994},
   Month = {January},
   url = {http://dx.doi.org/10.1115/94-GT-341},
   Abstract = {Copyright © 1994 by ASME. This paper describes the results
             of a study into the dynamic behavior of a magnetic bearing
             system. The research focuses attention on the influence of
             nonlinearities on the forced response of a
             two-degree-of-freedom rotating mass suspended by magnetic
             bearings and subject to rotating unbalance and feedback
             control. Geometric coupling between the degrees of freedom
             leads to a pair of nonlinear ordinary differential equations
             which are then solved using both numerical simulation and
             approximate analytical techniques. The system exhibits a
             variety of interesting and somewhat unexpected phenomena
             including various amplitude driven bifurcational events,
             sensitivity to initial conditions and the complete loss of
             stability associated with the escape from the potential well
             in which the system can be thought to be oscillating. An
             approximate criterion to avoid this last possibility is
             developed based on concepts of limiting the response of the
             system. The present paper may be considered as an extension
             to an earlier study by the same authors which described the
             practical context of the work, free vibration, control
             aspects and derivation of the mathematical
             model.},
   Doi = {10.1115/94-GT-341},
   Key = {fds311305}
}

@article{4671712,
   Author = {Murphy, K.D. and Bayly, P.V. and Virgin, L.N. and Gottwald,
             J.A.},
   Title = {Measuring the stability of periodic attractors using
             perturbation-induced transients: applications to two
             non-linear oscillators},
   Journal = {J. Sound Vib. (UK)},
   Volume = {172},
   Number = {1},
   Pages = {85 - 102},
   Year = {1994},
   url = {http://dx.doi.org/10.1006/jsvi.1994.1160},
   Keywords = {bifurcation;nonlinear dynamical systems;vibrations;},
   Abstract = {In this paper a combined analytical, numerical and
             experimental approach is used to study the behavior of
             small, perturbation-induced transients superimposed on a
             periodic steady state. The behavior of these transients is
             monitored in terms of characteristic multipliers as a
             control parameter is changed and instability is approached.
             Two non-linear mechanical oscillators are used which
             exemplify the application of these concepts to physical
             systems},
   Key = {4671712}
}

@article{94041254901,
   Author = {Virgin, LN and Plaut, RH},
   Title = {Effect Of Axial Load On Forced Vibrations Of
             Beams},
   Journal = {Journal of Sound and Vibration},
   Volume = {168},
   Number = {3},
   Pages = {395-405},
   Publisher = {Elsevier BV},
   Year = {1993},
   Month = {December},
   url = {http://dx.doi.org/10.1006/jsvi.1993.1382},
   Keywords = {Particle beams;Tensile testing;Load testing;Elasticity;Force
             measurement;},
   Abstract = {The steady state linear response of beams subjected to a
             distributed, harmonically varying, transverse force is
             considered. A static axial load, either tensile or
             compressive, is also applied to the beam, and damping is
             included in the analysis. Four standard sets of boundary
             conditions are treated. The influence of the axial load on
             the response is investigated, with attention focused on the
             maximum amplitude of the central deflection over all
             possible forcing frequencies. Approximate formulas are
             proposed for the effect of axial load on this maximum
             response and on the corresponding forcing frequency. The
             first of these formulas is then compared to a similar
             approximation for the central deflection when the transverse
             force is static rather than harmonic. © 1993 Academic
             Press. All rights reserved.},
   Doi = {10.1006/jsvi.1993.1382},
   Key = {94041254901}
}

@article{fds282425,
   Author = {Donescu, P and Virgin, LN},
   Title = {Nonlinear coupled heave and roll oscillations of a ship in
             beam seas},
   Journal = {American Society of Mechanical Engineers, Dynamic Systems
             and Control Division (Publication) Dsc},
   Volume = {51},
   Pages = {21-28},
   Year = {1993},
   Month = {December},
   Abstract = {The coupled (heave and roll) oscillations of a ship in
             transverse sinusoidal waves are considered. Extensive
             simulation studies show that resonance conditions may lead
             to large amplitude roll angles with the possibility of
             capsize. In contrast to much of the recent research in this
             area nonlinear effects, fluid-structure interaction and
             geometry of a realistic vessel are included in the analysis.
             The ship hull is described by a set of realistic transverse
             sections and fluid influence coefficients are computed using
             three-dimensional linear interpolation from tables taking
             into account the instantaneous waterplane and the frequency
             of the waves. The fundamental forcing parameters of this
             problem are the wave height and wave frequency. As expected,
             large response amplitudes occur for large wave height and
             proximity of the fundamental frequency of the waves to a
             natural frequency of the vessel. However, nonlinear effects
             have a strong influence on these results. Several initial
             conditions of the system were chosen and therefore transient
             effects are an integral part of this study. Combinations of
             wave parameters leading to either steady-state motion or
             capsize are mapped out as 'safe' and 'unsafe' conditions
             respectively.},
   Key = {fds282425}
}

@article{fds282427,
   Author = {Reynolds, RR and Dowell, EH and Tang, D and Virgin,
             LN},
   Title = {Nonlinear behavior of low aspect ratio panels in subsonic
             flow: a preliminary study},
   Journal = {American Society of Mechanical Engineers, Aerospace Division
             (Publication) Ad},
   Volume = {33},
   Pages = {9-12},
   Year = {1993},
   Month = {December},
   Abstract = {We describe an experimental investigation into the nonlinear
             behavior of thin elastic panels in subsonic flow. Specially,
             an apparatus is detailed that supports a low aspect ratio
             panel by clamping it along the spanwise edges while leaving
             its leading and trailing edges free. Preliminary results are
             given for a 0.016 inch thick panel with an aspect ratio of
             2.72. A pronounced, leading-edge divergence phenomenon was
             observed at nonzero angles of attack.},
   Key = {fds282427}
}

@article{94071345457,
   Author = {Reynolds, RR and Virgin, LN and Dowell, EH},
   Title = {High-dimensional chaos can lead to weak turbulence},
   Journal = {Nonlinear Dynamics},
   Volume = {4},
   Number = {6},
   Pages = {531-546},
   Publisher = {Springer Nature},
   Year = {1993},
   Month = {December},
   url = {http://dx.doi.org/10.1007/BF00162231},
   Keywords = {Aerodynamics;Elasticity;Turbulence;Supersonic
             flow;},
   Abstract = {One of the outstanding unresolved questions of nonlinear
             dynamics is the relationship between chaos and turbulence.
             This is a deep and difficult question, not the least reason
             being that the definitions of "chaos" and "turbulence" are
             not universally agreed upon. Here we define chaos as the
             time history of a single descriptor of a deterministic
             dynamical system which undergoes a loss of temporal
             correlation with a change in some system parameter and that
             displays sensitivity to initial conditions. Turbulence is
             defined as the time history of the spatial distribution of a
             deterministic dynamical system which undergoes a loss of
             temporal and (subsequently) spatial correlation with a
             change in some system parameter(s). By analogy and numerical
             simulation it is argued that turbulence can be a consequence
             of multi-mode interaction of individually chaotic modes. The
             physical system used here is a fluttering panel in a
             supersonic airstream. am = modal amplitude coefficients D =
             panel stiffness (=Eh212(1-v2)) E = modulus of elasticity of
             panel material h = panel thickness k = dimensional
             foundation stiffness K = nondimensional foundation stiffness
             (=kL4/Dh) L = length of panel in direction of flow M = Mach
             number N = number of modes in series expansion of panel
             deflection Nfv/pa = dimensional applied inplane load Δp =
             dimensional static pressure differential across panel P =
             nondimensional static pressure differential across panel
             (=ΔpL4/Dh) q = dimensional dynamic pressure (=ρχU2/2) Rv
             = nondimensional inplane load (=Nfxpaa2/D) t = dimensional
             time T = period over which correlation is averaged U =
             dimensional flow velocity w = dimensional panel deflection W
             = nondimensional panel deflection (deflection/h) x =
             dimensional coordinate along panel α = inplane spring
             stiffness parameter λ = nondimensional dynamic pressure of
             flow over panel ( {Mathematical expression}) μ = mass ratio
             (ρχL/ρmh)) ν = Poisson's ratio ξ = nondimensional
             location along panel (x/L) Δξ = separation between points
             used in correlation function ξu = nondimensional
             correlation length ψ = correlation function © 1993 Kluwer
             Academic Publishers.},
   Doi = {10.1007/BF00162231},
   Key = {94071345457}
}

@article{93111131733,
   Author = {Bayly, PV and Virgin, LN},
   Title = {On the stability of forced radial oscillations of an
             experimental spring pendulum},
   Journal = {American Society of Mechanical Engineers, Design Engineering
             Division (Publication) De},
   Volume = {56},
   Pages = {229-236},
   Address = {Albuquerque, NM, USA},
   Year = {1993},
   Month = {December},
   Keywords = {Oscillations;Stability;Springs (components);Degrees of
             freedom (mechanics);Resonance;Equations of motion;Nonlinear
             equations;Mathematical models;Control nonlinearities;Parameter
             estimation;Motion control;},
   Abstract = {The elastic pendulum is a 2-degree-of-freedom, non-linear
             device in which the pendulum bob may slide up and down the
             pendulum arm subject to the restoring force of a linear
             spring. In this study, radial motion (motion along the arm)
             is excited directly. Responses to this excitation include
             purely radial oscillations as well as swinging motion due to
             a 2:1 internal resonance. Changes in the behavior of the
             nonlinear spring pendulum occur when, under the control of a
             parameter, radial oscillations become unstable and are
             replaced by radial plus swinging motion. This bifurcation is
             explored analytically, numerically and experimentally, using
             the basic ideas of Floquet theory. Poincare sampling is used
             to reduce the problem of describing the stability of a limit
             cycle to the easier task of defining the stability of the
             fixed point of a Poincare map.},
   Key = {93111131733}
}

@article{4583180,
   Author = {Bayly, PV and Virgin, LN},
   Title = {An Empirical Study of the Stability of Periodic Motion in
             the Forced Spring-Pendulum},
   Journal = {Proceedings. Mathematical, Physical, and Engineering
             Sciences},
   Volume = {443},
   Number = {1918},
   Pages = {391-408},
   Publisher = {The Royal Society},
   Year = {1993},
   Month = {November},
   ISSN = {1364-5021},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1993MG24500008&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Keywords = {bifurcation;mechanical stability;nonlinear dynamical
             systems;numerical analysis;pendulums;perturbation
             theory;resonance;},
   Abstract = {The elastic pendulum is a two-degree-of-freedom, nonlinear
             device in which the primary mass slides up and down the
             pendulum arm subject to the restoring force of a linear
             spring. In this study, radial motion (motion along the arm)
             is excited directly. Responses to this excitation include
             purely radial motion as well as swinging motion due to a 2:1
             internal resonance. Changes in the behaviour of the
             nonlinear spring-pendulum occur when, under the control of a
             parameter, one response becomes unstable and is replaced by
             another. These bifurcations are explored analytically,
             numerically and experimentally, using the basic ideas of
             Floquet theory. Poincare sampling is used to reduce the
             problem of describing the stability of a limit cycle to the
             easier task of defining the stability of the fixed point of
             a Poincare map. Empirical estimates of characteristic
             multipliers in four-dimensional state space are obtained by
             examining transient behaviour after perturbations; the
             Karhunen-Loeve decomposition is used to identify dominant
             local modes in these transients},
   Doi = {10.1098/rspa.1993.0152},
   Key = {4583180}
}

@article{93091085944,
   Author = {Bayly, PV and Virgin, LN},
   Title = {An experimental study of an impacting pendulum},
   Journal = {Journal of Sound and Vibration},
   Volume = {164},
   Number = {2},
   Pages = {364-374},
   Publisher = {Elsevier BV},
   Year = {1993},
   Month = {June},
   url = {http://dx.doi.org/10.1006/jsvi.1993.1220},
   Keywords = {Equations of motion;Dynamic response;Damping;Frequency
             response;Mathematical models;Correlation methods;Chaos
             theory;},
   Abstract = {This letter catalogues a number of periodic and chaotic
             responses exhibited by a periodically excited impacting
             pendulum. Numerical simulation of the underlying equation of
             motion shows excellent correlation with experimental
             results. A number of specific techniques are developed to
             capture and characterize this type of non-linear behavior. A
             similar spectrum of responses could be expected under the
             variation of an alternative parameter such as forcing
             amplitude or damping. Many physical systems possess
             stiffness discontinuities, and under the action of periodic
             external excitation these complicated responses tend to be
             the rule rather than the exception.},
   Doi = {10.1006/jsvi.1993.1220},
   Key = {93091085944}
}

@article{93121755474,
   Author = {Virgin, LN},
   Title = {Dynamic characteristics of deteriorating engineering
             structures},
   Journal = {Applied Mechanics Reviews},
   Volume = {46},
   Number = {5},
   Pages = {220-226},
   Publisher = {ASME International},
   Year = {1993},
   Month = {January},
   url = {http://dx.doi.org/10.1115/1.3120341},
   Abstract = {The monitoring of energy production and distribution systems
             with a view to predicting their future performance and
             service life is a difficult but increasingly important
             exercise. Specific interest here concerns the behavior of
             aging offshore oil and gas structures. The maintenance and
             safety of these systems is a major challenge considering
             their generally deteriorating nature and harsh operating
             environment. The dynamic response of a structural component
             or structure can be used to assess properties such as mass,
             stiffness and damping. If periodic assessment is conducted
             then any changes, specifically deterioration, during the
             lifetime of a structure can be monitored using vibration
             measurement methods. This information can then be used to
             predict the useful life of the structure given a constant
             rate of deterioration or provide the basis for remedial
             action to be taken to strengthen the structure. The
             prevention of catastrophic failure is included in this
             scenario. Suggestions for possible research directions are
             made with regard to nonlinear behavior. © 1993 American
             Society of Mechanical Engineers.},
   Doi = {10.1115/1.3120341},
   Key = {93121755474}
}

@article{4475992,
   Author = {Bayly, P.V. and Virgin, L.N.},
   Title = {An experimental study of an impacting pendulum},
   Journal = {J. Sound Vib. (UK)},
   Volume = {164},
   Number = {2},
   Pages = {364 - 74},
   Year = {1993},
   url = {http://dx.doi.org/10.1006/jsvi.1993.1220},
   Keywords = {chaos;pendulums;},
   Abstract = {The authors describe the agreement obtained between
             simulations and experiments on the periodically forced,
             fully nonlinear impacting pendulum. The amplitude rotation
             is not restricted to small angles. A number of methods of
             characterizing periodic and chaotic behavior are
             illustrated},
   Key = {4475992}
}

@article{4416139,
   Author = {BAYLY, PHILIPV and VIRGIN, LAWRANCEN},
   Title = {EXPERIMENTAL EVIDENCE OF DIFFUSIVE DYNAMICS AND “RANDOM
             WALKING” IN A SIMPLE DETERMINISTIC MECHANICAL SYSTEM: THE
             SHAKEN PENDULUM},
   Journal = {International Journal of Bifurcation and
             Chaos},
   Volume = {02},
   Number = {04},
   Pages = {983-988},
   Publisher = {World Scientific Pub Co Pte Lt},
   Year = {1992},
   Month = {December},
   url = {http://dx.doi.org/10.1142/s0218127492000586},
   Keywords = {Brownian motion;chaos;diffusion;dynamics;pendulums;random
             processes;time series;},
   Abstract = {<jats:p> An experimental model of a simple pendulum,
             harmonically shaken, displays chaotic dynamics. Moreover, in
             strongly excited chaotic regimes the time series of total
             angular displacement, which is rarely examined, wanders
             unboundedly, displaying a power spectrum which falls off as
             1/f<jats:sup>α</jats:sup> over several decades. This
             behavior corresponds to deterministic diffusion, which has
             been found in simulations of nonlinear maps with periodic
             translational symmetry. The displacement time series
             obtained by sampling the pendulum displacement once per
             cycle is self-affine and quantitatively similar to Brownian
             motion. </jats:p>},
   Doi = {10.1142/s0218127492000586},
   Key = {4416139}
}

@article{4306878,
   Author = {Gottwald, JA and Virgin, LN and Dowell, EH},
   Title = {Experimental mimicry of Duffing's equation},
   Journal = {Journal of Sound and Vibration},
   Volume = {158},
   Number = {3},
   Pages = {447-467},
   Publisher = {Elsevier BV},
   Year = {1992},
   Month = {November},
   ISSN = {0022-460X},
   url = {http://dx.doi.org/10.1016/0022-460X(92)90419-X},
   Keywords = {chaos;hysteresis;nonlinear dynamical systems;oscillations;partial
             differential equations;},
   Abstract = {Extensive analytical and numerical investigations have
             focused on Duffing's equation. However, experimental work,
             in a mechanics context, has been limited to studying systems
             the stiffness characteristics of which can be approximated
             by a non-linear (cubic) restoring force; e.g., a buckled
             beam excited transversely or a rigid pendulum undergoing
             moderately large amplitude motion. This work describes a
             novel experimental approach whereby a particle/rigid body is
             contrived to mimic the behavior of Duffing's equation. This
             is a direct extension of the concept of a ball rolling on a
             double-well potential energy surface. Both free and forced
             oscillations are considered, illustrating familiar
             non-linear dynamics features including competing steady
             state attractors, hysteresis, sensitivity to initial
             conditions, subharmonic oscillations and chaos. ©
             1992.},
   Doi = {10.1016/0022-460X(92)90419-X},
   Key = {4306878}
}

@article{fds282424,
   Author = {Virgin, LN and Plaut, RH and Cheng, CC},
   Title = {Prediction of escape from a potential well under harmonic
             excitation},
   Journal = {International Journal of Non Linear Mechanics},
   Volume = {27},
   Number = {3},
   Pages = {357-365},
   Publisher = {Elsevier BV},
   Year = {1992},
   Month = {January},
   ISSN = {0020-7462},
   url = {http://dx.doi.org/10.1016/0020-7462(92)90005-R},
   Abstract = {Non-linear dynamical systems are considered which are
             conservative except for the presence of viscous damping. The
             systems are initially at rest in a potential well. Harmonic
             excitation is applied, and approximate conditions for escape
             from the potential well are sought. A method is described
             which uses the harmonic-balance technique to obtain an
             approximate motion, and then compares the maximum energy
             during that motion with the potential barrier. Numerical
             results are presented for three one-degree-of-freedom
             systems and a system with two-degrees-of-freedom. The
             approximate critical forcing amplitudes are plotted as a
             function of the forcing frequency, and the results are
             compared to those obtained by numerical integration of the
             equations of motion. © 1992.},
   Doi = {10.1016/0020-7462(92)90005-R},
   Key = {fds282424}
}

@article{fds282423,
   Author = {Bayly, PV and Virgin, LN},
   Title = {Chaotic rattling of a piecewise nonlinear
             oscillator},
   Journal = {American Society of Mechanical Engineers
             (Paper)},
   Pages = {1-6},
   Year = {1991},
   Month = {December},
   Abstract = {Loosely connected sructures may rattle: free play due to
             design tolerances, wear, or manufacturing error causes
             drastic force discontinuities (impacts) in periodically
             driven mechanisms. Previous investigators have examined
             impact oscillators described by linear equations in the
             non-impact regions, and have shown the existence of periodic
             limit cycles and chaotic motion. Experiments have confirmed
             the nature of their results. However, many useful systems,
             such as robot arms or linkages, include strongly nonlinear
             effects away from the impact condition. In order to study
             the effect of nonlinearity between impacts the linear
             restoring force of a rattling model is replaced with a
             sinusoidal, or pendulum-type, restoring force. A modified
             time grid is used to locate and model impacts accurately in
             numerical simulations, and a number of alternative Poincare
             maps are used to describe the complex motion exhibited by
             such innocent-looking systems.},
   Key = {fds282423}
}

@article{91060223082,
   Author = {Virgin, LN and Cartee, LA},
   Title = {A note on the escape from a potential well},
   Journal = {International Journal of Non Linear Mechanics},
   Volume = {26},
   Number = {3-4},
   Pages = {449-452},
   Publisher = {Elsevier BV},
   Year = {1991},
   Month = {January},
   ISSN = {0020-7462},
   url = {http://dx.doi.org/10.1016/0020-7462(91)90074-4},
   Keywords = {Vibrations--Analysis;Stresses--Analysis;Mathematical
             Models;Computers--Applications;},
   Abstract = {This brief note compares analytical results pertaining to
             the escape from a potential well. The system studied is the
             classical Duffing's equation with positive linear and
             negative cubic stiffness terms, i.e. a softening spring
             characteristic. Under gradually increasing periodic forcing,
             close to resonance, solutions may escape from the potential
             in which the system is oscillating. Comparison is made
             between the method of multiple scales and the harmonic
             balance method, and their stability characteristics
             investigated using Floquet theory and the Routh-Hurwitz
             criterion. This type of equation is familiar as an
             approximation to the motion of a pendulum, and similar types
             of equations have more recently been used to model the roll
             response of floating vessels in regular waves. ©
             1991.},
   Doi = {10.1016/0020-7462(91)90074-4},
   Key = {91060223082}
}

@article{91020143387,
   Author = {Plaut, RH and Virgin, LN},
   Title = {Use of frequency data to predict buckling},
   Journal = {Journal of Engineering Mechanics},
   Volume = {116},
   Number = {10},
   Pages = {2330-2335},
   Publisher = {American Society of Civil Engineers (ASCE)},
   Year = {1990},
   Month = {January},
   url = {http://dx.doi.org/10.1061/(ASCE)0733-9399(1990)116:10(2330)},
   Keywords = {Vibrations;},
   Abstract = {The use of measured vibration frequencies to determine
             approximate values of buckling loads nondestructively has
             been discussed in a number of papers. For example, Singer
             (1982, 1983) and his colleagues carried out experiments on
             cylindrical shells and used measured frequencies at low load
             levels to predict buckling loads. In most cases, the
             predicted values were higher than the actual buckling loads.
             It would be advantageous if one could also determine a lower
             bound for the buckling load so that a safe range for loading
             could be established. The objective of this paper is to
             examine Singer's procedure and suggest how one can estimate
             lower and upper bounds on the buckling load, as well as
             predict its value. A simple example with an analytical
             solution is utilized to derive typical load-frequency curves
             for buckling at a limit point (case I) and a bifurcation
             point (case II). Buckling occurs when the fundamental (i.e.,
             lowest) vibration frequency decreases to zero, and the
             prediction methods involve extrapolation from some measured
             frequencies to zero frequency.},
   Doi = {10.1061/(ASCE)0733-9399(1990)116:10(2330)},
   Key = {91020143387}
}

@article{90100524142,
   Author = {Virgin, LN and Bishop, SR},
   Title = {Catchment Regions of Multiple Dynamic Responses in Nonlinear
             Problems of Offshore Mechanics},
   Journal = {Journal of Offshore Mechanics and Arctic
             Engineering},
   Volume = {112},
   Number = {2},
   Pages = {127-133},
   Publisher = {ASME International},
   Year = {1990},
   Month = {January},
   url = {http://dx.doi.org/10.1115/1.2919846},
   Keywords = {Structural Analysis - Dynamic Response;Equations of
             Motion;Mathematical Techniques - Differential
             Equations;Mathematical Models;},
   Abstract = {Consideration of nonlinear effects in the dynamic analysis
             of offshore structures leads to complex phenomena even for
             relatively simple deterministic mathematical models.
             Nonlinearity in the stiffness or restoring force of a
             structure can be conveniently incorporated into a
             differential equation of motion, which can then be solved
             either analytically, using perturbation techniques, or
             numerically for various parameter ranges and forcing
             conditions. A particular feature of nonlinear dynamics is
             the appearance of multiple, competing steady-state
             oscillations which depend crucially on initial conditions.
             These coexisting stable solutions can be thought of as
             attractors for transient motion. A central question is
             therefore: How does the final long-term behavior of a
             dynamical system depend on the starting conditions? This
             paper concentrates on the computation of the domains of
             attraction or catchment regions using numerical techniques
             based on Poincare mapping ideas. The three specific examples
             illustrated are the roll motion of a ship, the oscillations
             of an articulated column and the surge response of a moored
             semi-submersible. This work may be considered an extension
             of previous work by the same authors. © 1990 by
             ASME.},
   Doi = {10.1115/1.2919846},
   Key = {90100524142}
}

@article{3925885,
   Author = {Dowell, EH and Virgin, LN},
   Title = {On spatial chaos, asymptotic modal analysis, and
             turbulence},
   Journal = {Journal of Applied Mechanics},
   Volume = {57},
   Number = {4},
   Pages = {1094-1097},
   Publisher = {ASME International},
   Year = {1990},
   Month = {January},
   ISSN = {0021-8936},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1990ER42300051&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Keywords = {chaos;classical mechanics of continuous media;turbulence;},
   Abstract = {In low-dimensional systems exhibiting chaos the response is
             temporally random (uncorrelated), but spatially
             deterministic (correlated). A mechanism has been identified
             by which the response of a continuum system may be both
             temporally and spatially uncorrelated, i.e. `turbulent'. The
             explanation of the mechanism is based upon recent work in
             chaos of low-to-moderate dimensional systems and also
             asymptotic modal analysis of high-dimensional systems. The
             conjectured mechanism and explanation has been confirmed by
             numerical experiments for a nonlinear system previously
             studied in the literature},
   Doi = {10.1115/1.2897637},
   Key = {3925885}
}

@article{90040152659,
   Author = {Virgin, LN},
   Title = {Approximate criterion for capsize based on deterministic
             dynamics},
   Journal = {Dynamics and Stability of Systems},
   Volume = {4},
   Number = {1},
   Pages = {55-70},
   Publisher = {Informa UK Limited},
   Year = {1989},
   url = {http://dx.doi.org/10.1080/02681118908806062},
   Keywords = {Naval Architecture--Calculations;Hydrodynamics--Fluid
             Structure Interaction;},
   Abstract = {An approach to studying the critical forcing parameters of
             an oscillator with a softening spring characteristic is
             developed. The harmonic response of the system is limited
             within a region of the phase plane, the boundary of which
             corresponds to a level of constant total energy for the
             underlying conservative system. This approach may be a
             useful conceptual aid in the understanding of the difficult
             problem of roll motion leading to capsize of a floating
             vessel.},
   Doi = {10.1080/02681118908806062},
   Key = {90040152659}
}

@article{89010254231,
   Author = {Virgin, LN},
   Title = {On the harmonic response of an oscillator with unsymmetric
             restoring force},
   Journal = {Journal of Sound and Vibration},
   Volume = {126},
   Number = {1},
   Pages = {157-165},
   Publisher = {Elsevier BV},
   Year = {1988},
   Month = {October},
   ISSN = {0022-460X},
   url = {http://dx.doi.org/10.1016/0022-460X(88)90405-1},
   Keywords = {Mathematical Techniques - Harmonic Analysis;},
   Abstract = {The approximate fundamental response of a driven mechanical
             oscillator with a quadratic stiffness characteristic is
             studied by using the method of harmonic balance.The accuracy
             of the periodic solutions based on first approximation
             theory, and their stability, are compared with exact results
             obtained from direct time integration. ©
             1988.},
   Doi = {10.1016/0022-460X(88)90405-1},
   Key = {89010254231}
}

@article{3113980,
   Author = {Thompson, JMT and Virgin, LN},
   Title = {Spatial chaos and localization phenomena in nonlinear
             elasticity},
   Journal = {Physics Letters A},
   Volume = {126},
   Number = {8-9},
   Pages = {491-496},
   Publisher = {Elsevier BV},
   Year = {1988},
   Month = {January},
   ISSN = {0375-9601},
   url = {http://dx.doi.org/10.1016/0375-9601(88)90045-X},
   Keywords = {buckling;chaos;elasticity;},
   Abstract = {Classical static-dynamic analogies are invoked to
             demonstrate spatial chaos and localization of deformations
             in the elastica of a post-buckled strut. Some conjectures
             are then made relating homoclinic events in the dynamic
             analogy of a strut on a nonlinear elastic foundation to the
             spatial localization of the buckling pattern. ©
             1988.},
   Doi = {10.1016/0375-9601(88)90045-X},
   Key = {3113980}
}

@article{fds282421,
   Author = {Virgin, LN and Bishop, SR},
   Title = {CATCHMENT REGIONS OF MULTIPLE DYNAMIC RESPONSES IN NONLINEAR
             PROBLEMS OF OFFSHORE MECHANICS.},
   Journal = {Proceedings of the International Offshore Mechanics and
             Arctic Engineering Symposium},
   Volume = {2},
   Pages = {15-22},
   Year = {1988},
   Month = {January},
   Abstract = {Consideration of nonlinear effects in the dynamic analysis
             of offshore structures leads to complex phenomena even for
             relatively simple deterministic mathematical models.
             Nonlinearity in the stiffness or restoring force of a
             structure can be conveniently incorporated into a
             differential equation of motion which can then be solved
             either analytically, using perturbation techniques, or
             numerically for various parameter ranges and forcing
             conditions. A particular feature of nonlinear dynamics is
             the appearance of multiple, competing steady-state
             oscillations which depend crucially on initial conditions.
             This paper concentrates on the computation of the domains of
             attraction or catchment regions using numerical techniques
             based on Poincare mapping ideas. The three specific examples
             illustrated are the roll motion of a ship, the oscillations
             of an articulated column and the surge response of a moored
             semi-submersible.},
   Key = {fds282421}
}

@article{fds282422,
   Author = {Virgin, LN and Bishop, SR},
   Title = {Catchment regions of multiple dynamic responses in nonlinear
             problems of offshore mechanics.},
   Journal = {In: Omae 1988 Houston, Proc. 7th Int. Conf. on Offshore
             Mechanics and Arctic Engineering, (Houston, U.S.A.: Feb. 7
             12, 1988),},
   Volume = {II, New York, U.S.A., Am. Soc. Mech. Eng},
   Pages = {15-22},
   Year = {1988},
   Month = {January},
   Abstract = {This paper concentrates on the computation of the domains of
             attraction or catchment regions using numerical techniques
             based on Poincare mapping ideas. The three specific examples
             illustrated are the roll motion of a ship, the oscillations
             of an articulated column and the surge response of a moored
             semisubmersible.},
   Key = {fds282422}
}

@article{89030234631,
   Author = {Bishop, SR and Virgin, LN and Leung, DLM},
   Title = {On the computation of domains of attraction during the
             dynamic modelling of oscillating systems},
   Journal = {Applied Mathematical Modelling},
   Volume = {12},
   Number = {5},
   Pages = {503-516},
   Publisher = {Elsevier BV},
   Year = {1988},
   Month = {January},
   ISSN = {0307-904X},
   url = {http://dx.doi.org/10.1016/0307-904X(88)90088-1},
   Keywords = {Structural Analysis--Dynamic Response;Mathematical
             Techniques--Differential Equations;},
   Abstract = {A particular feature of nonlinear differential equations is
             that they may have competing steady-state solutions. This
             paper describes some multiple dynamic responses typically
             found when modelling nonlinear systems with particular
             reference to the catchment regions which illustrate
             sensitivity to initial conditions. The form of dynamic
             behavior persisting after the decay of transient motion due
             to damping depends on the starting conditions in terms of
             initial displacement and velocity of the system. Methods of
             obtaining domains of attraction to particular stable
             solutions are described with reference to simple equations
             incorporating nonlinear resonance phenomena together with
             examples of coexisting subharmonic oscillations in offshore
             mechanics. © 1988.},
   Doi = {10.1016/0307-904X(88)90088-1},
   Key = {89030234631}
}

@article{88040053888,
   Author = {Virgin, LN and Bishop, SR},
   Title = {Complex dynamics and chaotic responses in the time domain
             simulations of a floating structure},
   Journal = {Ocean Engineering},
   Volume = {15},
   Number = {1},
   Pages = {71-90},
   Publisher = {Elsevier BV},
   Year = {1988},
   Month = {January},
   ISSN = {0029-8018},
   url = {http://dx.doi.org/10.1016/0029-8018(88)90020-0},
   Keywords = {MATHEMATICAL TECHNIQUES - Time Domain Analysis;MATHEMATICAL
             MODELS;SEMISUBMERSIBLES;OFFSHORE STRUCTURES;},
   Abstract = {The motion of a moored semi-submersible is modelled using a
             semi-empirical nonlinear ordinary differential equation.
             Time domain simulations, guided by the qualitative theory of
             dynamical systems, illustrate the extremely complex nature
             of typical responses in regular seas. The importance of
             nonlinearities is emphasised together with the implications
             for floating structures in general. © 1988.},
   Doi = {10.1016/0029-8018(88)90020-0},
   Key = {88040053888}
}

@article{fds327858,
   Author = {Bishop, SR and Virgin, LN},
   Title = {The onset of chaotic motions of a moored
             semi-submersible},
   Journal = {Journal of Offshore Mechanics and Arctic
             Engineering},
   Volume = {110},
   Number = {3},
   Pages = {205-209},
   Publisher = {ASME International},
   Year = {1988},
   Month = {January},
   url = {http://dx.doi.org/10.1115/1.3257052},
   Abstract = {This paper describes a combined numerical and geometric
             approach to study the dynamic behavior of a moored
             semi-submersible based on solutions of the nonlinear
             differential equation used to model the system. Complex
             features including competing steady states, subharmonic
             resonances and chaos are shown to be typical responses in
             regular seas. A qualitative overview is used to classify the
             computer data generated from direct time simulation with the
             aim of illustrating the inadequacies and limitations of a
             linear or a purely analytical approach. © 1988 by
             ASME.},
   Doi = {10.1115/1.3257052},
   Key = {fds327858}
}

@article{88110157590,
   Author = {Bishop, SR and Virgin, LN},
   Title = {The onset of chaotic motions of a moored
             semi-submersible.},
   Journal = {In: Proc. Asme Sixth (1987) Int. Offshore Mechanics and
             Arctic Engineering Symp., (Houston, U.S.A.: Mar. 1 6,
             1987)},
   Volume = {II, J.S. Chung; S. Berg; S.K. Chakrabart},
   Number = {3},
   Pages = {205-209},
   Year = {1988},
   Keywords = {DYNAMICS - Mathematical Models;MATHEMATICAL TECHNIQUES -
             Differential Equations;},
   Abstract = {This paper describes a combined numerical and geometric
             approach to study the dynamic behaviour of a moored
             semi-submersible based on solutions of the non-linear
             differential equation used to model the system. Complex
             features including competing steady states, subharmonic
             resonances and chaos are shown to be typical responses in
             regular seas. A qualitative overview was used to classify
             the computer data generated from direct time simulation with
             the aim of illustrating the inadequacies and limitations of
             a linear or a purely analytical approach.
             (A)},
   Key = {88110157590}
}

@article{87080119978,
   Author = {Virgin, LN},
   Title = {The nonlinear rolling response of a vessel including chaotic
             motions leading to capsize in regular seas},
   Journal = {Applied Ocean Research},
   Volume = {9},
   Number = {2},
   Pages = {89-95},
   Publisher = {Elsevier BV},
   Year = {1987},
   Month = {January},
   ISSN = {0141-1187},
   url = {http://dx.doi.org/10.1016/0141-1187(87)90011-3},
   Keywords = {HYDRODYNAMICS - Fluid Structure Interaction;STATISTICAL
             METHODS;},
   Abstract = {The rolling motion of a ship has been successfully modelled
             using a semi-empirical nonlinear differential equation by a
             number of researchers. Experimental data has been used to
             model nonlinear damping and righting lever characteristics
             and comparison with observed behaviour has been reasonably
             good. The present article describes a numerical,
             phenomenological approach to analyse this type of behaviour.
             The stability of the periodic motion, and in particular the
             possibility of capsize, is explored with reference to
             qualitative prediction techniques. The appearance of chaotic
             motions in regular beam seas is a new feature which should
             be of interest to designers. The inability of traditional
             quantitative methods, such as the perturbation technique, to
             detect chaos is a further justification for using numerical
             simulation guided by dynamical systems theory. ©
             1987.},
   Doi = {10.1016/0141-1187(87)90011-3},
   Key = {87080119978}
}

@article{87120191926,
   Author = {Bishop, SR and Leung, LM and Virgin, LN},
   Title = {Predicting incipient jumps to resonance of compliant marine
             structures in an evolving sea-state},
   Journal = {Journal of Offshore Mechanics and Arctic
             Engineering},
   Volume = {109},
   Number = {3},
   Pages = {223-228},
   Publisher = {ASME International},
   Year = {1987},
   Month = {January},
   url = {http://dx.doi.org/10.1115/1.3257013},
   Keywords = {WATER WAVES;MATHEMATICAL TECHNIQUES - Differential
             Equations;MATHEMATICAL MODELS;},
   Abstract = {When monitoring the wave-driven motions of a compliant
             offshore facility, be it an articulated mooring tower or a
             vessel, the engineer would like to be able to predict, in
             real time, any incipient jump to resonance that might be
             imminent due to the slowly evolving sea-state. We explore in
             this paper a study of some new possible prediction
             techniques for both a jump to a main fundamental resonance
             leading to capsize and a flip bifurcation to a subharmonic
             resonance. Stroboscopic Poincare mapping techniques based on
             discrete time sampling are used to give information about
             the approach to instability. The first application of these
             techniques is in the prediction of the jump in resonance and
             consequent capsize at a cyclic fold in the roll response of
             a vessel in regular beam seas. Secondly, the techniques are
             shown to work extremely well in a variety of computational
             situations when applied to the simulation of an articulated
             mooring tower during the approach to the potentially
             dangerous oscillations produced by the onset of subharmonic
             resonance at a flip bifurcation, in both regular and
             irregular ocean waves. © 1987 by ASME.},
   Doi = {10.1115/1.3257013},
   Key = {87120191926}
}

@article{fds319936,
   Author = {Bishop, SR and Virgin, LN},
   Title = {ONSET OF CHAOTIC MOTIONS OF A MOORED SEMI-SUBMERSIBLE.},
   Journal = {Proceedings of the International Offshore Mechanics and
             Arctic Engineering Symposium},
   Volume = {2},
   Pages = {319-323},
   Year = {1987},
   Month = {January},
   Abstract = {This paper describes a combined numerical and geometric
             approach to study the dynamic behaviour of a moored
             semi-submersible based on solutions of the nonlinear
             differential equation used to model the system. Complex
             features including competing steady-states, subharmonic
             resonances and chaos are shown to be typical responses in
             regular seas. A qualitative overview is used to classify the
             computer data generated from direct time simulation with the
             aim of illustrating the inadequacies and limitations of a
             linear or a purely analytical approach.},
   Key = {fds319936}
}

@article{88030034995,
   Author = {Virgin, LN},
   Title = {FREE VIBRATIONS OF IMPERFECT CANTILEVER BARS UNDER
             SELF-WEIGHT LOADING.},
   Journal = {Proceedings of the Institution of Mechanical Engineers. Part
             C. Mechanical Engineering Science},
   Volume = {201},
   Number = {C5},
   Pages = {345-347},
   Publisher = {SAGE Publications},
   Year = {1987},
   url = {http://dx.doi.org/10.1243/PIME_PROC_1987_201_133_02},
   Keywords = {MATHEMATICAL TECHNIQUES - Harmonic Analysis;BEAMS AND
             GIRDERS - Deflection;},
   Abstract = {This brief study examines the relationship between the
             natural frequency of small oscillations and the length of
             vertical cantilever struts in a gravitational field. The
             analysis uses a Rayleigh approach and includes post-buckled
             equilibrium states and emphasizes the influence of initial
             imperfections. Further terms may be added to improve the
             accuracy of the analysis although this work is primarily
             restricted to regions where the first mode is
             dominant.},
   Doi = {10.1243/PIME_PROC_1987_201_133_02},
   Key = {88030034995}
}

@article{2801472,
   Author = {Virgin, LN},
   Title = {Parametric studies of the dynamic evolution through a
             fold},
   Journal = {Journal of Sound and Vibration},
   Volume = {110},
   Number = {1},
   Pages = {99-109},
   Year = {1986},
   Month = {October},
   ISSN = {0022-460X},
   url = {http://dx.doi.org/10.1016/S0022-460X(86)80077-3},
   Keywords = {vibrating bodies;},
   Abstract = {A brief study is presented of the dynamic behaviour of a
             system approaching a fold (also known in the literature as a
             limit point or saddle-node bifurcation). A study of the
             transient dynamics shows that it is possible to predict the
             incipient loss of stability of equilibrium by using an
             appropriate frequency relationship. The relative advantages
             of an ω2 and an ω4 predictor, respectively, are fully
             explored for damped and undamped systems. Digital
             computations are used to explore the range of validity of
             the predictions and a simple laboratory study of the
             snap-through buckling of an elastic cantilevered column
             provides an experimental verification. © 1986 Academic
             Press Inc. (London) Limited.},
   Doi = {10.1016/S0022-460X(86)80077-3},
   Key = {2801472}
}

@article{86110177521,
   Author = {Thompson, JMT and Virgin, LN},
   Title = {Predicting a jump to resonance using transient maps and
             beats},
   Journal = {International Journal of Non Linear Mechanics},
   Volume = {21},
   Number = {3},
   Pages = {205-216},
   Publisher = {Elsevier BV},
   Year = {1986},
   Month = {January},
   ISSN = {0020-7462},
   url = {http://dx.doi.org/10.1016/0020-7462(86)90004-1},
   Keywords = {MATHEMATICAL TECHNIQUES - Differential Equations;},
   Abstract = {In this paper it is shown how the transient frequencies can
             be used to predict an incipient jump to resonance of a
             lightly damped non-linear oscillator. The appropriate
             frequency ω can be determined from the rotation number of a
             Poincaré map, or measured directly from the beats
             superimposed on the steady state oscillation. The relative
             advantages of using an ω2 or an ω4 predictor are explored
             in digital computations and in an experimental study of a
             vibrating beam. © 1986.},
   Doi = {10.1016/0020-7462(86)90004-1},
   Key = {86110177521}
}

@article{86050062413,
   Author = {Virgin, LN},
   Title = {Postbuckling dynamics of struts as related to their loading
             devices},
   Journal = {Engineering Structures},
   Volume = {8},
   Number = {2},
   Pages = {127-133},
   Publisher = {Elsevier BV},
   Year = {1986},
   Month = {January},
   ISSN = {0141-0296},
   url = {http://dx.doi.org/10.1016/0141-0296(86)90028-3},
   Keywords = {STRUCTURAL ANALYSIS - Dynamic Response;},
   Abstract = {This paper examines the linear dynamics of axially
             compressed pin-ended 'perfect' inextensional struts.
             Relationships are established between the natural
             frequencies of small oscillations about any equilibrium
             configuration (unbuckled and postbuckled) and axial
             compression for systems characterized by a stable-symmetric
             point of bifurcation. The general result that the initial
             slope of the postbuckling frequency squared curve is half
             the prebuckling value is shown to hold for both dead and
             semi-rigid loading, provided the appropriate control
             parameter is used. For the latter, this control is an end
             displacement rather than the actual load experienced by the
             structure: use of the load may of course be desirable, but
             the universal slope is then lost. © 1986.},
   Doi = {10.1016/0141-0296(86)90028-3},
   Key = {86050062413}
}

@article{85110161991,
   Author = {Virgin, LN},
   Title = {The dynamics of symmetric post-buckling},
   Journal = {International Journal of Mechanical Sciences},
   Volume = {27},
   Number = {4},
   Pages = {235-248},
   Publisher = {Elsevier BV},
   Year = {1985},
   Month = {January},
   ISSN = {0020-7403},
   url = {http://dx.doi.org/10.1016/0020-7403(85)90082-7},
   Keywords = {VIBRATIONS;},
   Abstract = {This work examines the relationship between natural
             frequency and compressive load for a conservative elastic
             mechanical system characterised by symmetric buckling.
             Application of some general theory shows that for a perfect
             system, exhibiting a stable-symmetric point of bifurcation,
             the initial post-buckling curve of compressive load against
             the square of the natural frequency is linear and has a
             slope of - 1 2 that of the pre-buckling curve. Simple link
             models and discretised continuous systems are analysed to
             illustrate the results of the general theory. These models
             are also used to show that the initial post-buckling curve
             is independent of axial inertia. The influence of initial
             imperfections is then considered and compared with
             experimental evidence. © 1985.},
   Doi = {10.1016/0020-7403(85)90082-7},
   Key = {85110161991}
}


%% Papers Accepted   
@article{fds218648,
   Author = {Y. Chandra and I. Stanciulescu and L.N. Virgin and R. Wiebe and T.G.
             Eason and S.M. Spottswood},
   Title = {Characterizing dynamic transitions associated with
             snap-through: A continuous model’},
   Journal = {Journal of Sound and Vibration},
   Year = {2013},
   Key = {fds218648}
}


%% Papers Submitted   
@article{fds214558,
   Author = {T. Witelski and L.N. Virgin and C. George},
   Title = {A double impact pendulum system},
   Year = {2013},
   Key = {fds214558}
}

@article{fds194713,
   Author = {B. Phungpaingam and L. N. Virgin and S. Chucheepsakul},
   Title = {Snap-through phenomenon and self-contact of spatial elastica
             subjected to mid-torque},
   Year = {2011},
   Key = {fds194713}
}