二自由度含间隙碰撞振动系统的分岔与混沌

针对二自由度含间隙碰撞振动系统，建立了正弦激励作用下的碰撞振动方程，推导了振动系统满足稳定碰撞的周期解参数和解存在的充要条件，给出了Poincare映射的数学关系.在此基础上，进行了周期运动的稳定性分析，研究了系统随参数改变出现分叉和通向混沌运动的途径.计算结果表明，该振动系统存在复杂丰富的动力学行为.在一定的参数条件下，系统除了存在稳定的周期运动形态之外，还存在着倍周期分叉、Hopf分叉以及其他分叉，系统会沿着倍周期分叉、Hopf分叉等多种途径进入混沌运动.

Bifurcation and chaos of impact vibration system with two degrees of freedom and clearance

Under a periodic excitation, the dynamic equation of the impact vibration system with two degrees of freedom and clearance was established. The condition of the periodic impact was deduced and the mathematical relation of the Poincare map was obtained. Based on this, the stability of periodic motion was discussed, and the bifurcation and chaotic motion of the system with clearance was researched by using Poincare map and numerical simulation. The computed results showed that the vibration system has complex and various dynamic behaviors. With changes of parameters, besides stable periodic motion the system will lead to chaotic motion by ways of period doubling bifurcation and Hopf bifurcation.