The dynamical model of a twodegreeoffreedom vibroimpact system with two motion limiting constraints was established, whose sticking conditions were given. The analysis shows that there exist sticking motions. According to the shooting method, the unstable periodic motion of vibroimpact, i.e. the fixed point of Poincaré section, was solved by the method of varied step and gradual iteration. Hopf bifurcation and perioddoubling bifurcation were analyzed under certain parameters by numerical simulation. At the same time the quasiperiodic responses of the system represented by invariant circles in the projected Poincaré section of twodegreeoffreedom system with two motion limiting constraints were obtained by numerical simulations. As the controlling parameter varied further, the routes of the twodegreeoffreedom system with two motion limiting constraints to chaos via quasiperiod bifurcation and perioddoubling bifurcation were investigated respectively.
林梅,丁旺才,武俊虎.两点碰撞振动系统的周期运动与分叉[J].动力学与控制学报,2006,4(1):16~21; Lin Mei, Ding Wangcai, Wu Junhu. Periodic motion and bifurcation of a vibroimpact system with two motion limiting constraints[J]. Journal of Dynamics and Control,2006,4(1):16-21.