Bifurcations of Single-impact Periodic Motions of a Three-degree-of-freedom Vibratory System with a Gap

摘要

A Three-degree-of-freedom vibratory system with a gap is considered in this paper. The system is uncoupled by using modal matrix approach. Based on the impacting conditions and the matching conditions according to the impact law, the single-impact periodic motion and the Poincar(e) mapping of the system are derived analytically.Stability and local bifurcations of single-impact periodic motion are analyzed theoretically by using Jacobian matrix of the Poincar(e) mapping. It is certain that Neimark-Sacker bifurcation and period doubling bifurcation exist in this kind of vibratory system under the suitable system parameters. The Neimark-Sacker bifurcation and period doubling bifurcation are shown in the projected Poincar(e) sections by numerical simulations.Here two typical routes from Neimark-Sacker bifurcation of single-impact periodic motion via phase locking and torus doubling to chaos are discussed.