Local and global stability of a piecewise linear oscillator

Abstract

Machines and mechanisms with moving parts, subjected to periodic excitation, often show unexpected dynamic behaviour, and impacts due to their connection clearances may occur. The most simple mathematical model is a one degree-of-freedom nonlinear oscillator governed by a piecewise linear symmetric function to describe the restoring force. The systems response, which can be quite rich and complicated, is described in detail. Modern methods for a combined analytical and numerical analysis are used to study local and global bifurcation conditions, coexisting solutions and their associated domains of attraction.