Hopf bifurcation of a two-degree-of-freedom vibro-impact system

The bifurcation problem of a two-degree-of-freedom system vibrating against a rigid surface is studied in this paper. It is shown that there exist Hopf bifurcations in the vibro-impact systems with two or more degrees of freedom under suitable system parameters. In the paper, a centre manifold theorem technique is applied to reduce the Poincare map of the vibro-impact system to a two-dimensional one, and then the theory of Hopf bifurcation of maps in R-2 is applied to conclude the existence of Hopf bifurcation of the vibro-impact system. The theoretical solutions are verified by numerical computations. The quasi-periodic response of the system, represented by invariant circles in the projected Poincare sections, is obtained by numerical simulations, and routes of quasi-periodic impacts to chaos are stated briefly. (C) 1998 Academic Press Limited.