STABILITY AND BIFURCATIONS OF PERIODIC MOTION IN A THREE-DEGREE-OF-FREEDOM VIBRO-IMPACT SYSTEM

A three-degree-of-freedom vibro-impact system is considered in this paper. Based on the solutions of differential equations between impacts, impact conditions and match conditions of periodic motion, the six- dimension Poincaré maps of n-1 periodic motion are established. The stability of the periodic motion is determined by computing eigenvalues of Jacobian matrix of the maps. If some eigenvalues are on the unit circle, bifurcation occurs as controlling parameter varies. By numerical simulation, Hopf bifurcation and period- doubling bifurcation of 1-1 periodic motion are analyzed. As controlling parameter varies further, the routes from periodic motion to chaos via quasi-periodic bifurcation and period-doubling bifurcation are investigated, respectively. One of the routes is found to be non-typical.