- 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
pp. 447 - 67 [0022-460X(92)90419-X] .
(last updated on 2007/04/10)
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 chaos
chaos;hysteresis;nonlinear dynamical systems;oscillations;partial differential equations;