两自由度碰撞振动系统的动力学分析

基于Poincaré映射的方法，通过解析的方法导出了一类具有阻尼的两自由度碰撞振动系统的单碰周期n次谐运动存在性判据，经过数值模拟验证了理论分析的正确性，并给出了分析其稳定性的判别公式，通过数值模拟，讨论系统的局部分岔与全局分岔，同时比较了系统参数变化对其周期运动的影响，发现在强阻尼、弱激励、小质量比、较大恢复系数下系统将会出现较多的有规律的周期碰撞．

Dynamic Analysis of Two-Degree-of-Freedom Vibro-Impact Systems

The vibro-impaet systems are familiar with the non-smooth dynamic systems. The dynamics research of the vibro-impact systems not only is significant in theory but also has practical values in engineering. Firstly, using the Poinearé map method, we get an existent criterion of single impact period-n motion in a two-degree-of-freedom vibroimpact system with damper. It is shown that our conclusions are valid through the numerical simulations. Moreover, the satiability of periodic motions is studied and the corresponding Jaeobian matrix formula is derived. Finally we debate the effect of system parameters on periodic motions exploiting the numerical simulations method, the local bifurcation and global bifurcation, and the influence of the change of parameters in the system on its periodic motion, and find that the vibro-impaet systems appear more disciplinary periodic impact under strong damping, feeble harmonic excitation, small ratio of quality and quite big coefficient of restitution.