Experimental mimicry of Duffing's equation
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.
Gottwald, JA; Virgin, LN; Dowell, EH
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