Lawrie Virgin

Research Area(s): Structural Engineering
Chaos, Dynamics
Nonlinear Dynamics
Computational Mechanics

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 focussed on the loss of stability of dynamical systems. The recent discovery of chaos has stimulated much research in this area across the breadth of science and engineering.

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 via l.virgin@duke.edu or +1 919 660 5342 (office phone)
Visit via http://nonlineardynamics.pratt.duke.edu/ or 120 Engineering Bldg (office location)

Representative Publications (More Publications)

1. R.B. Davis and L.N. Virgin, Non-linear behavior in a discretely-forced oscillator, International Journal of Nonlinear Mechanics, vol. 42 (2007), ppt. 744-753
   
2. I. Stanciulescu, L.N. Virgin and T.A. Laursen, Finite element analysis of a slender isogrid structure, Journal of Spacecraft and Rockets, vol. 44 (2007), ppt. 529-537
   
3. H. Chen and L.N. Virgin, 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), ppt. 3983 - 4007 , [036] [abs]
   
4. S. Santillan, L.N. Virgin and R.H. Plaut, Equilibria and vibration of a heavy pinched loop, Journal of Sound and Vibration, vol. 288 no. 1-2 (2005), ppt. 81 - 90 , [016] [abs]
   
5. S.T. Trickey, L.N. Virgin and E.H. Dowell, The stability of limit-cycle oscillations in a nonlinear aeroelastic system, Proc. R. Soc. Lond. A, Math. Phys. Eng. Sci. (UK), vol. 458 no. 2025 (2002), ppt. 2203 - 26 , [0965] [abs]
   
6. M.D. Todd, J.M. Nichols, L.M. Pecora and L.N. Virgin, Vibration-based damage assessment utilizing state space geometry changes: local attractor variance ratio, Smart Materials and Structures, vol. 10 no. 5 (2001), ppt. 1000 - 1008 , [316] [abs]
   

Research photographs

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

• A cable-suspended mass
• A fiber-optic condition monitoring system
• An airfoil with a loose flap
• An experimental Duffing system
• A thermally buckled, acoustically excited papnel
• Inflatable beams for space attennas
• A rocking block
• A highly flexible structure
• A composite beam with bolted connection
• A hardening spring oscillator
• Vibration isolation

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

• The solar sail concept
• An experimental set-up

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

• Smooth basin boundaries
• Fractal basin boundaries