一类两自由度碰撞振动系统的周期运动稳定性与分岔

本文建立了一类两自由度变碰撞面的碰撞振动系统动力学模型，获得了系统的周期响应，推导出系统n-1周期运动的四维Poincaré映射。利用Poincaré映射方法，对系统单碰撞周期运动的稳定性与分岔进行分析，分析了系统n-1周期运动的Hopf分岔、周期倍化分岔及强共振情况下的亚谐分岔，研究了当分岔参数变化时碰撞振动系统由概周期碰撞运动向混沌运动的演化过程，为冲击振动系统的优化设计提供了理论依据。

Stabilty and Bifurcatuons of Periodic Moton in a Two-degree-of-freedom Vibro-Impact System

A two-degree-of-freedom vibro-impact system is discussed in this paper. Based on the solutions of differential equations between impacts, impact conditions and match conditions of periodic motion, the four-dimension Poincaré maps of n-1 periodic motion are established. The stability of the periodic motions is investigated by the Poincaré map and numerical simulation. Hopf bifurcation, subharmonic in strong resonance case and multi-impact periodic motion are analyzed by local bifurcation criterion and numerical simulation. As controlling parameter varies further, the routes of quasi-periodic impact motions to chaos are studied. It is possible to optimize practical system parameters by investigation of bifurcation and chaos.