Numerical Bifurcation Analysis of Discontinuous 2-DOF Vibroimpact System. Part 2: Frequency-Amplitude Response

Abstract

This paper discusses bifurcations in nonlinear vibroimpact system. It is a discontinuous dynamical system. We were studying stability and bifurcations in specific two-body two-degree-of-freedom vibroimpact system by numerical parameter continuation method. We adapted parameter continuation technique for this system. Theoretical basis for dynamic characteristics composition was presented in [1]. The instability zones and bifurcation points for loading curves were determined in [1] under excitation amplitude variation. In this paper we investigate the instability zones and bifurcation points under variation of excitation frequency when we consider the frequency-amplitude response. We have observed phenomena unique for nonsmooth systems with discontinuous right-hand side: discontinuous bifurcation points where set-valued Floquet multipliers cross the unit circle by jump. At these points monodromy matrix is changed by jump too. We also have observed chattering regimes leading to chaos.