随机干扰下碰撞振动系统的动力学分析

Dynamic analysis of a vibro-impact system with random disturbance

建立一类单自由度含间隙碰撞振动系统的动力学模型。推导了系统Poincar啨映射的解析表达式,用数值方法计算了系统的Lyapunov指数谱,讨论了随机干扰对碰撞振动系统的动力学影响。最后结合最大Lyapunov指数,讨论随机非光滑系统的随机分岔。数值研究表明随机非光滑系统同样存在着丰富的倍周期分岔现象,但和确定性系统的倍周期分岔现象存在本质的区别。

A one-degree-of-freedom vibro-impact system with clearance was established. The analytic expression of Poincar map of the system was derived,and the spectrum of Lyapunov exponents of the system was calculated numerically,the effects of the dynamic behavior of the vibro-impact system with random disturbance were analyzed. At last,with the largest Lyapunov exponent,the stochastic bifurcation of the random non-smooth system was studied. Numerical simulations showed that period-doubling bifurcation also exists in the random non-smooth system,but is different from that in the deterministic system.