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@article{fds369383,
Author = {Virgin, LN and Harvey, PS},
Title = {A lateral–torsional buckling demonstration model using 3D
printing},
Journal = {Engineering Structures},
Volume = {280},
Year = {2023},
Month = {April},
url = {http://dx.doi.org/10.1016/j.engstruct.2023.115682},
Abstract = {It is well-established that beams of relatively narrow
cross-section have a tendency to buckle laterally when
loaded. This type of lateral–torsional instability, which
has considerable practical importance in a variety of
thin-walled structures, is a classical buckling situation in
which the critical load is related, among other things, to
characteristic features of the cross-section. In this short
paper, 3D-printing is exploited to provide a parametric
study based on a fixed cantilever geometry in which a number
of standard cross-sectional forms are compared in terms of
their effect on this kind of buckling behavior.},
Doi = {10.1016/j.engstruct.2023.115682},
Key = {fds369383}
}
@article{fds369731,
Author = {Cooley, SA and Yang, H and Virgin, LN},
Title = {3D-printing and cylinder buckling: challenges and
opportunities.},
Journal = {Philosophical Transactions. Series A, Mathematical,
Physical, and Engineering Sciences},
Volume = {381},
Number = {2244},
Pages = {20220035},
Year = {2023},
Month = {April},
url = {http://dx.doi.org/10.1098/rsta.2022.0035},
Abstract = {Cylinder buckling is notoriously sensitive to small
geometric imperfections. This is an underlying motivation
for the use of knock-down factors in the design process,
especially in circumstances in which minimum weight is a key
design goal, an approach well-established at NASA, for
example. Not only does this provide challenges in the
practical design of this commonly occurring structural
load-bearing configuration, but also in the carefully
controlled laboratory setting. The recent development of
3D-printing (additive manufacturing) provides an appealing
experimental platform for conducting relatively
high-fidelity experiments on the buckling of cylinders.
However, in addition to geometric precision, there are a
number of shortcomings with this approach, and this article
seeks to describe the challenges and opportunities
associated with the use of 3D-printing in cylinder buckling
in general, and probing the robustness of equilibrium
configurations in particular. This article is part of the
theme issue 'Probing and dynamics of shock sensitive
shells'.},
Doi = {10.1098/rsta.2022.0035},
Key = {fds369731}
}
@article{fds368563,
Author = {Virgin, LN},
Title = {On the elastic snapping of structural elements},
Journal = {International Journal of Non Linear Mechanics},
Volume = {149},
Year = {2023},
Month = {March},
url = {http://dx.doi.org/10.1016/j.ijnonlinmec.2022.104329},
Abstract = {A bistable structural component possesses more than one
stable equilibrium configuration. In terms of the strain
energy stored in bending, this can be thought of as a system
with not only an initial equilibrium configuration
represented by an isolated minimum, but also a remote
minimum that might be accessed given a sufficient
disturbance. Whether the system is able to stay in this new
position, or revert back to the initial state when the
disturbance is removed is an important practical issue. This
distinction is largely determined by geometry. Continuous
elastic structures of the type produced using a 3D-printer
are necessarily of relatively high-order in a dimensional
sense, and most previous studies have used nonlinear finite
element analysis to determine parameter sensitivity.
However, there is a role to be played by discrete low-order
models in which the same type of essential qualitative
behavior can be captured, but where the parameter dependency
(in this case whether a system stays in its inverted,
snapped, configuration, or not) can be assessed more
directly than numerical simulation. This short note develops
a discrete model specifically designed to address this
issue, and presents the outcomes of some tests on 3D-printed
elements.},
Doi = {10.1016/j.ijnonlinmec.2022.104329},
Key = {fds368563}
}
@article{fds369106,
Author = {Cervi, C and Santillan, ST and Virgin, LN},
Title = {Interrogating the Configuration Space of Postbuckled
Beams},
Journal = {Journal of Engineering Mechanics},
Volume = {149},
Number = {3},
Year = {2023},
Month = {March},
url = {http://dx.doi.org/10.1061/JENMDT.EMENG-6839},
Abstract = {This paper considers the global configuration space of
postbuckled structures. Initially, a slender buckled beam is
considered. The boundary conditions are pinned at one end
and fully fixed at the other. The pin-end of the initially
flat beam is moved toward the other end by a small amount.
This causes the beam to buckle laterally (the beam is
axially inextensional) with a characteristic shape. Since
this is the outcome of a stable-symmetric pitchfork
bifurcation, the buckled shape possesses a near mirror-image
shape on the other side. Which of the two available
equilibrium configurations is taken up depends on the usual,
often small, symmetry-breaking effects commonly encountered
in axially loaded systems. Given fixed conditions to
maintain this initial buckled shape we then apply a moment
at the pinned end. The relation between the applied moment
and the change in shape is the primary focus of this study.
The extent of the buckling (end shortening) is varied, with
the magnitude of the moment, as a function of the angle,
providing considerable information about the potential
energy landscape in which the axially loaded system
operates. The applied moment can be thought of as a probing
mechanism whereby various equilibrium configurations are
revealed, together with information regarding their
stability and robustness. A similar approach is then used
where the structure consists of two nominally identical
beams attached at a right angle. In both cases, the opposite
end from the actuation is clamped. An experimental study is
conducted on 3D-printed specimens, and this is compared with
a finite element analysis using ANSYS, and a
large-deflection elastica analysis.},
Doi = {10.1061/JENMDT.EMENG-6839},
Key = {fds369106}
}
@article{fds360093,
Author = {Virgin, LN},
Title = {A shear center demonstration model using
3D-printing},
Journal = {International Journal of Mechanical Engineering
Education},
Volume = {50},
Number = {3},
Pages = {739-748},
Year = {2022},
Month = {July},
url = {http://dx.doi.org/10.1177/03064190211057429},
Abstract = {Locating the shear, or flexural, center of non-symmetric
cross-sectional beams is a key element in the teaching of
structural mechanics. That is, establishing the point on the
plane of the cross-section where an applied load, generating
a bending moment about a principal axis, results in
uni-directional deflection, and no twisting. For example, in
aerospace structures it is particularly important to assess
the propensity of an airfoil section profile to resist
bending and torsion under the action of aerodynamic forces.
Cross-sections made of thin-walls, whether of open or closed
form are of special practical importance and form the basis
of the material in this paper. The advent of 3D-printing
allows the development of tactile demonstration models based
on non-trivial geometry and direct observation.},
Doi = {10.1177/03064190211057429},
Key = {fds360093}
}
@article{fds363015,
Author = {Virgin, LN},
Title = {Interrogating the Lead-Up to a Critical Speed in
Rotordynamics},
Journal = {Journal of Vibration and Acoustics},
Volume = {144},
Number = {3},
Year = {2022},
Month = {June},
url = {http://dx.doi.org/10.1115/1.4053190},
Abstract = {This paper presents a new approach to predicting an
incipient critical speed in a rotating shaft. Based on the
classical governing equations of motion for an eccentric
mass on a flexible shaft (the Jeffcott rotor model), the
approach is centered on examining the behavior of small
perturbations or random disturbances to infer the approach
of a critical speed (resonance). Such disturbances, that may
be based on intentional probing, or simply the result of
naturally occurring fluctuations, cause small transients. It
is the changing nature of these transients (as characterized
by their associated eigenvalues) that is used to assess the
proximity to a critical speed. In this paper, the material
developed is based on analysis, but generating the data from
simulations or experiments will be the next step. The
approach is a kind of stress-test, conceptually not
dissimilar to structural health monitoring and damage
detection but here directed toward the lead-up to
resonance.},
Doi = {10.1115/1.4053190},
Key = {fds363015}
}
@article{fds358384,
Author = {Virgin, LN and Holland, DB},
Title = {Experiments on the symmetry-breaking effect of orientation
on a pair of connected cantilevers},
Journal = {Mechanical Systems and Signal Processing},
Volume = {164},
Year = {2022},
Month = {February},
url = {http://dx.doi.org/10.1016/j.ymssp.2021.108236},
Abstract = {It is well established that axial loads tend to influence
lateral stiffness and hence natural frequencies of slender
structural components. For very slender structures, the
axial loading can be caused by self-weight (in a
gravitational field), and these effects influence
equilibrium configurations and dynamic behavior. In some
applications, for example solar sails, attached cables
provide an additional complication. This paper will focus
attention on a specific form of double cantilever beam
system, i.e., two cantilevers sharing a common hub. Two
specific cases are considered, in which the two ends of the
cantilevers are connected by a cable under a given tensile
load. The key observation is the effect that orientation
(with respect to gravity) has on breaking the inherent
symmetry in the vibration modes shapes of the systems
studied. Although theoretical results are available for both
a single cantilever pulled by a cable attached to its tip,
together with results on the effect of gravity, the focus of
the current paper is on the natural frequencies and mode
shapes of two-beam systems from an experimental modal
analysis perspective.},
Doi = {10.1016/j.ymssp.2021.108236},
Key = {fds358384}
}
@article{fds358385,
Author = {Virgin, LN},
Title = {A note on lumped parameter modeling},
Journal = {Mechanics Research Communications},
Volume = {116},
Year = {2021},
Month = {September},
url = {http://dx.doi.org/10.1016/j.mechrescom.2021.103750},
Abstract = {This brief note examines the lumped dynamic modeling of two
simple structural systems: 3D-printed cantilevers, and
circular aluminum panels. In each case a set of stiffness
and natural frequency measurements are made based on simple
experiments, with a view to examining effective mass, and a
comparison is made with the basic theory.},
Doi = {10.1016/j.mechrescom.2021.103750},
Key = {fds358385}
}
@article{fds355640,
Author = {Virgin, L},
Title = {Simultaneous buckling, contact, and load-carrying
capacity},
Journal = {Journal of Engineering Mechanics},
Volume = {147},
Number = {5},
Year = {2021},
Month = {May},
url = {http://dx.doi.org/10.1061/(ASCE)EM.1943-7889.0001926},
Abstract = {This paper considers the case of a relatively large number
of parallel columns that buckle simultaneously. The close
proximity between columns results in the possibility of
contact between adjacent columns as buckling proceeds, and
this brings with it some interesting observations on
load-carrying capacity. Some experimental results verify the
theoretical development based on the versatility of
high-fidelity 3D printing, but also highlights the
difficulty of applying purely axial loading. The sensitive
nature of initial geometric imperfections (slight lack of
straightness) and load eccentricity strongly influence
postbuckled contact, load-carrying capacity, and, as the
number of columns is increased, a statistically based
evaluation of anticipated behavior is explored and
ultimately found to be unrealistic.},
Doi = {10.1061/(ASCE)EM.1943-7889.0001926},
Key = {fds355640}
}
@article{fds353895,
Author = {Virgin, LN and Plaut, RH},
Title = {Large deflections of folded cantilever: Experiments and
elastica analysis},
Journal = {International Journal of Non Linear Mechanics},
Volume = {129},
Year = {2021},
Month = {March},
url = {http://dx.doi.org/10.1016/j.ijnonlinmec.2020.103641},
Abstract = {Folded cantilevers have been utilized in MEMS devices,
particularly for suspension. The structures consist of a
horizontal beam segment fixed at its left end, a short
downward connector (joint) at the right end, and a lower
horizontal segment under the upper one. Here, the left end
of the lower segment is free and a downward concentrated
load is applied there. Experiments are conducted on five
folded cantilevers with different lengths of the lower
segment. An elastica analysis is performed, allowing for
large deflections and rotations. The self-weight of the
segments is included in the analysis. The effects of the end
load and the relative lengths of the segments are
investigated. The experimental results compare well to those
from the theory.},
Doi = {10.1016/j.ijnonlinmec.2020.103641},
Key = {fds353895}
}
@article{fds353342,
Author = {Guan, Y and Virgin, LN},
Title = {A Pyramidal Lattice Frame: Pathways to Inversion},
Journal = {International Journal of Structural Stability and
Dynamics},
Volume = {21},
Number = {2},
Year = {2021},
Month = {February},
url = {http://dx.doi.org/10.1142/S0219455421500206},
Abstract = {This paper considers the load-deflection behavior of a
pyramid-like, shallow lattice structure. It consists of four
beams that join at a central apex and when subject to a
lateral load, it exhibits a propensity to snap-through: A
classical buckling phenomenon. Whether this structural
inversion occurs, and the routes by which it happens,
depends sensitively on geometry. Given the often sudden
nature of the instability, the behavior is also examined
within a dynamics context. The outcome of numerical
simulations are favorably compared with experimental data
extracted from the testing of three-dimensional (3D)-printed
specimens. The key contributions of this paper are that
despite the continuous nature of the physical system, its
behavior (transient and equilibria) can be adequately
described using a discrete model, and the paper also
illustrates the utility of 3D-printing in an accessible
research context.},
Doi = {10.1142/S0219455421500206},
Key = {fds353342}
}
@article{fds352681,
Author = {Xu, Y and Virgin, LN and Wiebe, R},
Title = {Inferring unstable equilibrium configurations from observed
dynamics},
Journal = {Conference Proceedings of the Society for Experimental
Mechanics Series},
Pages = {199-201},
Year = {2021},
Month = {January},
ISBN = {9783030476250},
url = {http://dx.doi.org/10.1007/978-3-030-47626-7_29},
Abstract = {Unstable equilibria play an important organizing role in
nonlinear dynamic systems in a global sense. However, it is
difficult to measure them directly in a physical experiment.
In this study, a digital image correlation (DIC) system is
used to capture the transient behavior of a post-buckled
beam in which trajectories are generated by repeated
impacts. The dynamic data collected by the DIC system, with
relatively high temporal and spatial resolution, is used
estimate equilibrium configurations of the post-buckled
beam, including a detection of the presence of unstable
equilibria. The results show good agreement with the
equilibrium configurations obtained from two-mode models for
the beam.},
Doi = {10.1007/978-3-030-47626-7_29},
Key = {fds352681}
}
@article{fds352682,
Author = {Xu, Y and Virgin, LN},
Title = {Force probing to access potential energy},
Journal = {Conference Proceedings of the Society for Experimental
Mechanics Series},
Pages = {55-57},
Year = {2021},
Month = {January},
ISBN = {9783030476250},
url = {http://dx.doi.org/10.1007/978-3-030-47626-7_9},
Abstract = {Perhaps the two most common forms of potential energy are
those associated with gravitational and elastic forces. In
an experimental setting, if we can measure the force
required to maintain equilibrium, then the extraction of
potential energy is relatively straightforward, since the
force is the negative vector gradient of the potential. In
this paper we apply this approach to a small mass that is
placed on various shapes under the action of
gravity.},
Doi = {10.1007/978-3-030-47626-7_9},
Key = {fds352682}
}
@article{fds352683,
Author = {Ehrhardt, D and Virgin, LN and Spottswood, SM},
Title = {Experiments on probing the configuration space of
post-buckled panels},
Journal = {Journal of Applied Mechanics},
Volume = {87},
Number = {12},
Year = {2020},
Month = {December},
url = {http://dx.doi.org/10.1115/1.4048197},
Abstract = {This paper describes a primarily experimental study in which
a nonlinear structural component (a slender, mechanically
buckled panel) is subject to probing. That is, equilibrium
configurations are explored when a specific location on the
panel is subject to the application of a (variable)
displacement constraint and characterized by a corresponding
probe force. This probe force (in this study located at the
center of the rectangular panels) is measured using a load
cell and the resulting shape(s), taken up by the panel,
measured using digital image correlation (DIC). Although the
probe is only applied at a single location, this arrangement
supplies considerable information about the changing
equilibrium landscape including revealing co-existing
equilibrium configurations using large perturbations and
associated hysteresis phenomena. In addition, monitoring the
probing force, and specifically when it drops to zero,
provides a window into "free" equilibria that would
otherwise be unstable and unobservable. Finally, it is shown
that the probed equilibrium configurations provide the
"landscape" within which any dynamically induced
trajectories evolve including snap-through oscillations.
copy; 2020 by ASME.},
Doi = {10.1115/1.4048197},
Key = {fds352683}
}
@article{fds353896,
Author = {Virgin, LN},
Title = {Comparative structural stiffness: Exploiting
3D-printing},
Journal = {American Journal of Physics},
Volume = {88},
Number = {12},
Pages = {1049-1058},
Year = {2020},
Month = {December},
url = {http://dx.doi.org/10.1119/10.0001756},
Abstract = {The teaching of structural stiffness is one of the keystones
of the undergraduate curriculum in mechanics and the
strength of materials. Standard linear theory, going back to
Hooke's law, has proven to be very successful in predicting
the performance of elastic structures under load. Many
courses in basic mechanics have a conventional laboratory
component often involving a universal testing machine and
extensometer. However, the advent of 3D printing presents an
appealing pedagogical opportunity mid-way between theory and
a formal lab experience. The material contained in this
paper focuses on using the 3D printing of relatively simple,
flexible cantilever structures. The relatively high
resolution of modern 3D printers facilitates the production
of slender (elastically deformable) structures, and thus
provides an opportunity to exploit geometric parametric
variations to enhance a practical understanding of
fundamental mechanics concepts such as stiffness. This
approach has proved successful in initial inclusion in both
the classroom via demonstration models, as well as in the
lab in which elementary facilities can be utilized to
acquire data. The boundary conditions associated with a
cantilever, and the application of a point force are
especially simple to produce in practice, and provide an
effective tactile demonstration of the influence of
geometrical changes on the relation between force and
deflection, i.e., stiffness.},
Doi = {10.1119/10.0001756},
Key = {fds353896}
}
@article{fds352336,
Author = {Guan, Y and Virgin, LN},
Title = {Stability and Bifurcation in Discrete Mechanical Systems: An
Experimental and Analytical Study},
Journal = {International Journal of Bifurcation and
Chaos},
Volume = {30},
Number = {9},
Year = {2020},
Month = {July},
url = {http://dx.doi.org/10.1142/S0218127420300244},
Abstract = {The curse of dimensionality looms over many studies in
science and engineering. Low-order systems provide
conceptual clarity but often fail to reveal the extent of
possible complexity, whereas high-order systems present a
host of daunting challenges to the analyst, not least the
classification and visualization of typical behavior. In
this paper, we detail the behavior of systems that fall
somewhere between a classification of low- and high-order.
We present both theoretical and experimental investigations
into the nonlinear behavior of a couple of mechanical
systems with three mechanical/structural degrees-of-freedom
(DOF), with a special focus on bifurcation and multiple
equilibria. Useful insight is provided by observation of
transient trajectories as they meander about and between
equilibria, especially revealing the influence of unstable
equilibria, not normally accessible in an experimental
context. For instance, the influences of index-1 saddles are
mainly detected in three aspects: determining the systems
capability to snap-through by generating accessible
snap-though tubes, attracting nearby trajectories
temporarily oscillating around it, and separating adjacent
trajectories. Iso-potentials are 3D-printed to present the
energy landscape. For these systems, the 3D configuration
space allows considerable complexity, but is also somewhat
amenable to geometric interpretation. By varying a
mass/stiffness ratio as a control parameter, bifurcation
structures and morphing potential energy landscapes
exhibiting up to 11 equilibria are obtained. Finally,
analytical and experimental studies reveal that parametric
excitations can stabilize some unstable equilibria under the
right amplitudes and frequencies.},
Doi = {10.1142/S0218127420300244},
Key = {fds352336}
}
@article{fds353343,
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 = {2020},
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 = {fds353343}
}
@article{fds348094,
Author = {Thompson, JMT and Virgin, LN},
Title = {Instabilities of nonconservative fluid-loaded
systems},
Journal = {International Journal of Bifurcation and
Chaos},
Volume = {29},
Number = {14},
Year = {2019},
Month = {December},
url = {http://dx.doi.org/10.1142/S0218127419300398},
Abstract = {Nonlinear bifurcations and instabilities of autonomous
nonconservative systems, mainly involving the fluid loading
of a solid or structure, are reviewed and described in this
accessible, pictorial overview. In contrast to the earlier
papers in this series (focusing on the instability of
elastic deformable systems, and low-order
periodically-forced mechanical systems), we focus on a
handful of case studies in which the loss of stability is
primarily driven by nonconservative forces, i.e.
path-dependent forces not associated with a potential. Many
systems involving fluid-structure interaction can lose
stability under changing conditions in which there is a net
flow of energy from the fluid to the structure, sometimes
resulting in growing oscillatory behavior. Again, the
generic manifestations of instability typically occur within
the framework of bifurcation theory. Progression is from
simple local bifurcations to more complex global events, and
all are related to instructive and intriguing applications.
Hopf bifurcations are presented in the context of the
galloping and flutter of cables and pipes. Next, Neimark
bifurcations appear in aircraft applications involving the
free-play fluttering of aerofoils and the wing rock of the
Harrier jump-jet. Turning to ships in wind and waves, a
homoclinic saddle connection governs the surging and
surf-riding of a vessel in stern seas, while an omega flow
explosion can compromise the course-keeping of a passenger
ferry in a side wind. Recent work on the dynamic
step-buckling of a spherical shell illustrates the role of a
center manifold, and the paper ends with a careful study of
dissipation-generated instabilities, drawing on the
historical struggles to understand the evolution of spinning
liquid planets.},
Doi = {10.1142/S0218127419300398},
Key = {fds348094}
}
@article{fds357353,
Author = {Xu, Y and Virgin, LN},
Title = {Probing the force field to identify potential
energy},
Journal = {Journal of Applied Mechanics},
Volume = {86},
Number = {10},
Year = {2019},
Month = {October},
url = {http://dx.doi.org/10.1115/1.4044305},
Abstract = {A small ball resting on a curve in a gravitational field
offers a simple and compelling example of potential energy.
The force required to move the ball, or to maintain it in a
given position on a slope, is the negative of the vector
gradient of the potential field: The steeper the curve, the
greater the force required to push the ball up the hill (or
keep it from rolling down). We thus observe the turning
points (horizontal tangency) of the potential energy shape
as positions of equilibrium (in which case the "restoring
force"drops to zero). In this paper, we appeal directly to
this type of system using both one- A nd twodimensional
shapes: Curves and surfaces. The shapes are produced to a
desired mathematical form generally using additive
manufacturing, and we use a combination of load cells to
measure the forces acting on a small steel ball-bearing
subject to gravity. The measured forces, as a function of
location, are then subject to integration to recover the
potential energy function. The utility of this approach, in
addition to pedagogical clarity, concerns extension and
applications to more complex systems in which the potential
energy would not be typically known a priori, for example,
in nonlinear structural mechanics in which the potential
energy changes under the influence of a control parameter,
but there is the possibility of force probing the
configuration space. A brief example of applying this
approach to a simple elastic structure is
presented},
Doi = {10.1115/1.4044305},
Key = {fds357353}
}
@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 = {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 = {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 = {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 = {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}
}
@book{fds282327,
Author = {Virgin, LN},
Title = {Introduction to experimental nonlinear dynamics: A case
study in mechanical vibration},
Pages = {1-256},
Publisher = {Cambridge University Press},
Year = {2019},
Month = {January},
ISBN = {9780521662864},
url = {http://dx.doi.org/10.1017/9781139175227},
Abstract = {Nonlinear behavior can be found in such highly disparate
areas as population biology and aircraft wing flutter.
Largely because of this extensive reach, nonlinear dynamics
and chaos have become very active fields of study and
research. This book uses an extended case study - an
experiment in mechanical vibration - to introduce and
explore the subject of nonlinear behavior and chaos.
Beginning with a review of basic principles, the text then
describes a cart-on-a-track oscillator and shows what
happens when it is gradually subjected to greater
excitation, thereby encountering the full spectrum of
nonlinear behavior, from simple free decay to chaos.
Experimental mechanical vibration is the unifying theme as
the narrative evolves from a local, linear, largely
analytical foundation toward the rich and often
unpredictable world of nonlinearity. Advanced undergraduate
and graduate students, as well as practising engineers, will
find this book a lively, accessible introduction to the
complex world of nonlinear dynamics.},
Doi = {10.1017/9781139175227},
Key = {fds282327}
}
@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 = {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{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 = {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 = {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 = {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 = {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 = {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 = {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 = {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 = {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 = {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 = {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 = {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 = {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 = {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 = {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 = {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 = {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 = {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 = {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{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 = {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 = {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{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 = {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 = {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 = {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{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 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 = {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{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 = {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{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 = {August},
ISSN = {1758-8251},
url = {http://dx.doi.org/10.1142/S175882511550057X},
Abstract = {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{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 = {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{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 = {February},
ISSN = {0020-7683},
url = {http://dx.doi.org/10.1016/j.ijsolstr.2014.11.016},
Abstract = {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{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 = {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{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 = {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{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{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{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{fds214558,
Author = {T. Witelski and L.N. Virgin and C. George},
Title = {A double impact pendulum system},
Year = {2013},
Key = {fds214558}
}
@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}
}
@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}
}
@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}
}
@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}
}
@book{fds346276,
Author = {Virgin, L and Wagg, D},
Title = {Preface},
Volume = {536},
Year = {2012},
Month = {January},
Key = {fds346276}
}
@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{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{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{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 = {January},
ISSN = {2191-5644},
url = {http://dx.doi.org/10.1007/978-1-4419-9831-6_14},
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.},
Doi = {10.1007/978-1-4419-9831-6_14},
Key = {fds282402}
}
@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 = {January},
ISSN = {2191-5644},
url = {http://dx.doi.org/10.1007/978-1-4419-9719-7_4},
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.},
Doi = {10.1007/978-1-4419-9719-7_4},
Key = {fds282403}
}
@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}
}
@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{fds282429,
Author = {Srivastava, R and Panovsky, J and Kielb, R and Virgin, LN and Ekici,
K},
Title = {Non-linear flutter in fan stator vanes with time dependent
fixity},
Journal = {Asme Journal of Turbomachinery},
Volume = {134},
Number = {021009},
Pages = {1189-1199},
Publisher = {AMER SOC MECHANICAL ENGINEERS},
Year = {2011},
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{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{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{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{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{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{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{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{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}
}
@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 = {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}
}
@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 = {January},
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{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 = {January},
url = {http://dx.doi.org/10.2514/6.2007-2110},
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.},
Doi = {10.2514/6.2007-2110},
Key = {fds319934}
}
@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{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{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},
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{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{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{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 = {January},
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{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 = {January},
ISSN = {0273-4508},
url = {http://dx.doi.org/10.2514/6.2005-1969},
Doi = {10.2514/6.2005-1969},
Key = {fds282414}
}
@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{fds348095,
Author = {Todd, MD and Nichols, J and Seaver, M and Trickey, S and Virgin, L and Pecora, L and Carroll, T},
Title = {Development and application of chaotic attractor property
analysis for vibration-based structural damage
assessment},
Journal = {Aip Conference Proceedings},
Volume = {676},
Pages = {315-326},
Year = {2003},
Month = {August},
ISBN = {0735401454},
url = {http://dx.doi.org/10.1063/1.1612228},
Abstract = {Long-term, high-level performance demands on a variety of
structures and equipment have stimulated significant
research in the field of structural health monitoring. The
primary goals of this field are to provide information
regarding structural performance capability, damage
assessment, and even structural prognosis, all of which may
potentially reduce the ownership costs associated with the
maintenance and operation of the structure. Much of the
research has largely taken a vibration-based approach,
whereby the structural dynamic response to either ambient or
applied loading is analyzed for changes in certain
characteristic "features" that serve as appropriate damage
indicators. Many of the features proposed have involved
parameters derived from a modal analysis of the structure,
e.g., resonant frequencies, mode shapes, damping, strain
energy, flexibility, etc. In this work, we present features
taken from measured attractors of the structure. System
characterization (including damage detection) by means of
geometric invariants, such as attractor(s), is potentially a
powerful generic approach which does not rely on implicit
assumptions in an underlying model, e.g., linearity. The
structure is excited with a chaotic oscillator, and the
combined chaotic excitation dynamics and structural response
may be thought of as the "filtering" of chaotic data: the
structure acts as a "filter" through which the chaotic
signal is processed so that small changes to the structure
(ostensibly due to damage) will serve to alter the degree to
which the signal is filtered. We develop the attractor
property trajectory prediction error as a candidate feature
and evaluate its utility in detecting clamping force
degradation on a continuous metal beam.},
Doi = {10.1063/1.1612228},
Key = {fds348095}
}
@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},
Month = {April},
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{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{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 = {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{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 = {January},
url = {http://dx.doi.org/10.2514/6.2003-1746},
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.},
Doi = {10.2514/6.2003-1746},
Key = {fds282389}
}
@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{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{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{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},
url = {http://dx.doi.org/10.2514/6.2002-1264},
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.},
Doi = {10.2514/6.2002-1264},
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{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},
Month = {September},
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{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{fds282355,
Author = {VIRGIN, L and TRICKEY, S and DOWELL, E},
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{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{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{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{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{fds350907,
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},
Year = {2000},
Month = {January},
url = {http://dx.doi.org/10.2514/6.2000-1334},
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.},
Doi = {10.2514/6.2000-1334},
Key = {fds350907}
}
@book{fds71110,
Author = {L.N. Virgin},
Title = {Introduction to Experimental Nonlinear Dynamics},
Publisher = {Cambridge University Press},
Year = {2000},
Key = {fds71110}
}
@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{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},
Month = {January},
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.},
Doi = {10.1023/A:1008278526811},
Key = {98064268503}
}
@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{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{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{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{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},
url = {http://dx.doi.org/10.1016/s0960-0779(96)00112-9},
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 = {fds319935}
}
@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 = {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{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{5582165,
Author = {Murphy, KD and Virgin, LN and Rizzi, SA},
Title = {The effect of thermal prestress on the free vibration
characteristics of clamped rectangular plates: theory and
experiment},
Journal = {Trans. Asme. J. Vib. Acoust. (Usa)},
Volume = {119},
Number = {2},
Pages = {243-249},
Publisher = {ASME International},
Year = {1997},
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},
Doi = {10.1115/1.2889710},
Key = {5582165}
}
@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{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{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{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},
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.},
Doi = {10.1006/jsvi.1996.0506},
Key = {96110407089}
}
@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},
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+ω over-bar ) plane).
Several nonlinear characteristics are evident and
discussed.},
Doi = {10.1007/BF02328572},
Key = {97013487572}
}
@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{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{fds355886,
Author = {Murphy, KD and Virgin, LN and Rizzi, SA},
Title = {An experimental study of the forced response of pre- And
post-critical plates},
Journal = {Proceedings of the Asme Design Engineering Technical
Conference},
Volume = {3A-1995},
Pages = {695-701},
Year = {1995},
Month = {January},
ISBN = {9780791817186},
url = {http://dx.doi.org/10.115/DETC-1995-0310},
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
post-critical 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 (w, SPL) parameter space separating the regions of
snap-through and no snap-through.},
Doi = {10.115/DETC-1995-0310},
Key = {fds355886}
}
@article{fds355887,
Author = {Fielder, WT and Virgin, LN and Plaut, RH},
Title = {Experiments on a rocking block},
Journal = {Proceedings of the Asme Design Engineering Technical
Conference},
Volume = {3A-1995},
Pages = {781-786},
Year = {1995},
Month = {January},
ISBN = {9780791817186},
url = {http://dx.doi.org/10.115/DETC-1995-0319},
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 comer 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.},
Doi = {10.115/DETC-1995-0319},
Key = {fds355887}
}
@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{5141631,
Author = {Plaut, RH and Murphy, KD and Virgin, LN},
Title = {Curve and surface veering for a braced column},
Journal = {J. Sound Vib. (Uk)},
Volume = {187},
Number = {5},
Pages = {879-885},
Publisher = {Elsevier BV},
Year = {1995},
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{5096112,
Author = {Virgin, LN and Walsh, TF and Knight, JD},
Title = {Nonlinear behavior of a magnetic bearing
system},
Journal = {Trans. Asme, J. Eng. Gas Turbines Power (Usa)},
Volume = {117},
Number = {3},
Pages = {582-588},
Publisher = {ASME International},
Year = {1995},
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 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 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 = {10.1115/1.2814135},
Key = {5096112}
}
@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{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}
}
@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 = {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{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},
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.},
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},
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{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 of the Royal Society of London, Series A:
Mathematical and Physical 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 = {<jats:p>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. Poincaré 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 Poincaré 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.</jats:p>},
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{fds356007,
Author = {Bayly, PV and Virgin, LN},
Title = {On the stability of forced radial oscillations of an
experimental spring pendulum},
Journal = {Proceedings of the Asme Design Engineering Technical
Conference},
Volume = {Part F167972-5},
Pages = {229-236},
Year = {1993},
Month = {January},
ISBN = {9780791811733},
url = {http://dx.doi.org/10.1115/DETC1993-0110},
Abstract = {The elastic pendulum is a 2-degree-of-freedom, nonlinear
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.},
Doi = {10.1115/DETC1993-0110},
Key = {fds356007}
}
@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{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},
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.},
Doi = {10.1115/1.3120341},
Key = {93121755474}
}
@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{4416139,
Author = {Bayly, PV and Virgin, LN},
Title = {Experimental evidence of diffusive dynamics and `random
walking' in a simple deterministic mechanical system: the
shaken pendulum},
Journal = {Int. J. Bifurcation Chaos Appl. Sci. Eng.
(Singapore)},
Volume = {2},
Number = {4},
Pages = {983-988},
Publisher = {World Scientific Pub Co Pte Lt},
Year = {1992},
url = {http://dx.doi.org/10.1142/s0218127492000586},
Keywords = {Brownian motion;chaos;diffusion;dynamics;pendulums;random
processes;time series;},
Abstract = {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/fα
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},
Doi = {10.1142/s0218127492000586},
Key = {4416139}
}
@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{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{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 = {1987},
Month = {January},
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{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}
}
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