Papers Published
- Gottwald, J.A. and Virgin, L.N. and Dowell, E.H., Experimental mimicry of Duffing's equation,
J. Sound Vib. (UK), vol. 158 no. 3
(1992),
pp. 447 - 67 [0022-460X(92)90419-X] .
(last updated on 2007/04/10)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 nonlinear (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 nonlinear dynamics features including competing steady state attractors, hysteresis, sensitivity to initial conditions, subharmonic oscillations and chaosKeywords:
chaos;hysteresis;nonlinear dynamical systems;oscillations;partial differential equations;