随机干扰下碰撞振动系统的动力学分析

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振动与冲击 ›› 2009, Vol. 28 ›› Issue (9) : 163-167.

论文

随机干扰下碰撞振动系统的动力学分析

田海勇刘卫华赵日旭

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Analysis of the Dynamics of Vibro-impact Systemwith Random Disturbance

TIAN Haiyong LIU Weihua ZHAO Rixu

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摘要

建立了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Poincaré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，讨论了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。

Abstract

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

导出引用

田海勇刘卫华赵日旭. 随机干扰下碰撞振动系统的动力学分析[J]. 振动与冲击, 2009, 28(9): 163-167

TIAN Haiyong LIU Weihua ZHAO Rixu. Analysis of the Dynamics of Vibro-impact Systemwith Random Disturbance[J]. Journal of Vibration and Shock, 2009, 28(9): 163-167