CNCS Center for Nonlinear and Complex Systems
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Lawrence N. Virgin, Professor of Mechanical Engineering and Materials Science and Civil and Environmental Engineering and CNCS: Center for nonlinear and complex systems

Lawrence N. Virgin

Professor Virgin's research is centered on studying the behavior of nonlinear dynamical systems. This work may be broadly divided into two components. First, investigation of the fundamental nature of nonlinear systems based on a mathematical description of their underlying equations of motion. Both analytical and numerical techniques are used with special attention focused on the loss of stability of dynamical systems.

The second area of interest is to apply recent results from nonlinear dynamical systems theory to problems of practical engineering importance. These include the nonlinear rolling motion of ships leading to capsize; buckling of axially-loaded structural components; aeroelastic flutter of aircraft panels at high supersonic speeds; vibration isolation based on nonlinear springs; energy harvesting; damage detection and structural health monitoring; and the dynamics of very flexible structures including solar sails and marine risers. Professor Virgin conducts mechanical experiments to complement these studies.

The flavor of much of this work is contained in the books:

Introduction to Experimental Nonlinear Dynamics, L.N. Virgin, Cambridge University Press, 2000.

Vibration of Axially Loaded Structures, L.N. Virgin, Cambridge University Press, 2007.

Contact Info:
Office Location:  3393 Fciemas, Duke Box 90300, Durham, NC 27708
Email Address: send me a message
Web Page:  http://nonlineardynamics.pratt.duke.edu/

Teaching (Fall 2017):

  • CEE 647.02, BUCKLING EGR STRUCTURES Synopsis
    Teer 211, MW 01:25 PM-02:40 PM
    (also cross-listed as ME 527.02)
Teaching (Spring 2018):

  • ME 490.03, SPECIAL TOPICS Synopsis
    Teer 215, MW 10:05 AM-11:20 AM
Education:

Ph.D.University of London (UK)1986
M.S.Cardiff University1982
B.S.University of Manchester (England)1981
Specialties:

Nonlinear Dynamics
Structural Engineering
Aerospace
Chaos, Dynamics
Chaos, Dynamics
Nonlinear Dynamics
Structural Engineering
Computational Mechanics
Vibration
Research Interests:

  • Experimental verification of low-order nonlinear dynamical behavior (including chaos) using mechanical models.
  • The interaction between dynamics and buckling including secondary bifurcation.
  • Time series analysis in the context of condition monitoring and damage detection.
  • Dynamic behavior of inflatable and lightwieght structures for space applications.
  • Nonlinear aeroelasticity of airfoils, wings and panels.
  • Parametric excitation of slender structural components including rotorblades and struts.
  • Rocking, sliding, bouncing and overturning of rigid blocks with applications in earthquake engineering and the nuclear industry.
  • Keywords:

    Adhesion • Algorithms • Buckling • Colloids • Computer Simulation • Diffusion • Dynamics • Elasticity • Fourier Analysis • Magnetics • Mathematical models • Mechanics • Microspheres • Miniaturization • Models, Statistical • Models, Theoretical • Nonlinear • Nonlinear Dynamics • Nonlinear oscillators • Optics and Photonics • Particle Size • Physics • Scattering, Radiation • Time Factors • Vibration

    Representative Publications   (More Publications)

    1. Wagg, D; Virgin, L, Exploiting Nonlinear Behavior in Structural Dynamics (2012), pp. 280 pages, Springer, ISBN 3709111862  [abs]
    2. Plaut, RH; Virgin, LN, Vibration and snap-through of bent elastica strips subjected to end rotations, Journal of Applied Mechanics, vol. 76 no. 041011 (2009), pp. 1-7, ISSN 0021-8936 [doi]  [abs]
    3. Davis, RB; Virgin, LN, Non-linear behavior in a discretely forced oscillator, International Journal of Non-Linear Mechanics, vol. 42 no. 5 (2007), pp. 744-753, ISSN 0020-7462 [doi]  [abs]
    4. Yellen, B; Virgin, LN, Non-linear dynamics of superparamagnetic beads in a traveling magnetic field wave, Physical Review E, vol. 80 no. 011402 (2009), pp. 011402, ISSN 1539-3755 [19658704], [doi]  [abs]
    5. Virgin, LN, Vibration of axially loaded structures (January, 2007), pp. 1-359, Cambridge University Press, ISBN 9780511619236 [doi]  [abs]
    6. Stanciulescu, I; Virgin, LN; Laursen, TA, Finite element analysis of a slender isogrid structure, Journal of Spacecraft and Rockets, vol. 44 (2007), pp. 529-537
    7. Chen, H; Virgin, LN, Finite element analysis of post-buckling dynamics in plates-Part I: An asymptotic approach, International Journal of Solids and Structures, vol. 43 no. 13 (2006), pp. 3983-4007, ISSN 0020-7683 [036], [doi]  [abs]
    8. Santillan, ST; Plaut, RH; Witelski, TP; Virgin, LN, Large oscillations of beams and columns including self-weight, International Journal of Non-Linear Mechanics, vol. 43 no. 8 (2008), pp. 761-771, ISSN 0020-7462 [doi]  [abs]
    9. L.N. Virgin, Introduction to Experimental Nonlinear Dynamics (2000), Cambridge University Press
    10. Virgin, LN; Santillan, ST; Plaut, RH, Vibration isolation using extreme geometric nonlinearity, Journal of Sound and Vibration, vol. 315 no. 3 (2008), pp. 721-731, ISSN 0022-460X [doi]  [abs]
    11. Santillan, S; Virgin, LN; Plaut, RH, Equilibria and vibration of a heavy pinched loop, Journal of Sound and Vibration, vol. 288 no. 1-2 (2005), pp. 81-90 [016], [doi]  [abs]
    12. Davis, RB; Virgin, LN; Brown, AM, Cylindrical shell submerged in bounded acoustic media: A modal approach, AIAA Journal, vol. 46 no. 3 (2008), pp. 752-763, ISSN 0001-1452 [doi]  [abs]
    13. Tahir, MA; Guo, L; Virgin, LN; Yellen, BB, Transport of superparamagnetic beads through a two-dimensional potential energy landscape, Physical Review E, vol. 84 no. 011403 (2011), pp. 011403, ISSN 1539-3755 [21867167], [doi]  [abs]
    14. Trickley, ST; Virgin, LN; Dowell, EH, The stability of limit-cycle oscillations in a nonlinear aeroelastic system, Proceedings of the Royal Society of London: Mathematical, Physical and Engineering Sciences, vol. 458 no. 2025 (2002), pp. 2203-2226, ISSN 1364-5021 [0965], [doi]  [abs]
    15. Holland, DB; Virgin, LN; Plaut, RH, Large deflections and vibration of a tapered cantilever pulled at its tip by a cable, Journal of Sound and Vibration, vol. 310 no. 1-2 (2008), pp. 433-441, ISSN 0022-460X [doi]  [abs]
    16. Todd, MD; Nichols, JM; Pecora, LM; Virgin, LN, Vibration-based damage assessment utilizing state space geometry changes: local attractor variance ratio, Smart Materials and Structures, vol. 10 no. 5 (2001), pp. 1000-1008, ISSN 0964-1726 [316], [doi]  [abs]
    17. Jeffers, AE; Plaut, RH; Virgin, LN, Vibration isolation using buckled or pre-bent columns-Part 2: Three-dimensional motions of horizontal rigid plate, Journal of Sound and Vibration, vol. 310 no. 1-2 (2008), pp. 421-432, ISSN 0022-460X [doi]  [abs]
    18. L.N. Virgin, S.T. Santillan and R.H. Plaut, Vibration isolation using extreme geometric nonlinearity, Journal of Sound and Vibration, vol. 315 (2008), pp. 721-731

    Research photographs

    Many of my research projects have an experimental component, some photos can be found in the following links showing:

    Some of my latest research involves solar sails for deep space exploration (sponsored by NASA):

    Numerical simulation has also played an important role in the development of dynamics: