Chaotic and Periodic Motions in a Vibro-Impacting System

Abstract

The present paper investigates the impact vibration in a single degree-of-freedom system having symmetric two-sided stops subjected to harmonic excitation. Periodic asymmetric two-impact/one-period motion, three-impact/one-period motion and symmetric four impact/one-period motion are determined analytically and numerically, and the corresponding stabilities are analyzed. Regions of stable periodic motion are given in the δ-Ω plane, where δ denotes the clearance between the mass and the stop at the rest and Ω denotes the frequency of harmonic excitation. Bifurcation diagrams relating the impact-velocity and a system parameter are also presented. Period-doubling bifurcations, fold bifurcations, grazing bifurcations and chaotic motion are obtained. The grazing bifurcation is peculiar to the vibro-impacting system. In addition, the invariant curves for the system parameters for which chaotic motions arise are presented.