Bifurcation Analysis of a Rigid Impact Oscillator with Bilinear Damping

Abstract

This paper studies a rigid impact oscillator with bilinear damping developed as the mechanical model of an impulsive switched system. The stability and the bifurcation of periodic orbits in the impact oscillator are determined by using the mapping methods. One-parameter bifurcation analyses under variation of forcing frequency and amplitude of external excitation are carried out. Coexisting attractors and various types of bifurcations, such as grazing, period-doubling, and saddle-node, are observed, which show the complex phenomena inhered in this impact oscillator.