随机激励下二自由度碰撞振动系统的响应分析

研究了一类二自由度碰撞振动系统在随机噪声激励下的响应问题.展示了这种非光滑系统在倍周期分岔通向混沌的道路中存在的擦边分岔行为.通过定义一种随机响应的度量，讨论了随机噪声对于系统响应的影响，并发现在某些参数条件下，随机噪声对于系统响应的影响是明显的，甚至改变了运动的性质.数值模拟表明此法是研究噪声激励下非光滑系统响应的一种有效方法.关键词：非光滑系统二自由度碰撞振动系统擦边分岔倍周期分岔

Response analysis of two-degree-of-freedom impact oscillator to random excitation

The response of a two-degree-of-freedom impact oscillator to random excitation is investigated. The existence of grazing bifurcation involved in the period-doubling bifurcation is shown clearly. The effects of the random excitation are studied by defining a measure of the stochastic response. The idea that the random factor can change the property of the system in some conditions is proposed. Numerical simulations show that the method is effective.