Chaotic Response of a Slider Crank Mechanism

Abstract

A physical and corresponding theoretical model of a slider-crank mechanism is presented that approximates the single mode response of a continuous beam under a time periodic excitation in which the spatial distribution of the forcing is in the form of a half sine wave. The purpose of the model is to investigate the existence of chaos in systems having rigid members, as opposed to the highly flexible structures most often seen in chaotic demonstrations. The experimental construct displays complicated dynamical responses, including chaos, while the idealized theoretical model only supports the existence of a period one response. However, it is shown that the addition of an extremely small external perturbation will cause the response to demonstrate what appears to be a robustly chaotic response. A comparison of the Lyapunov exponents between this construct and the experimental model show close agreement.