高斯白噪声激励下粘弹性碰撞系统的稳定性

Stability of Viscoelastic System with Impacts Under the Excitation of Gaussian White Noise

采用Zhuravlev变换将粘弹性碰撞系统转化为连续的非碰撞系统,然后应用随机平均法得到了关于慢变量的随机微分方程,根据It?法则,建立了p阶平均It?微分方程,给出了系统的p阶矩Lyapunov指数表达式。最后通过理论结果和数值结果的分析,讨论了恢复因子、噪声强度和粘弹性参数对系统稳定性的影响。

The stabilities of viscoelastic system with impacts under the excitation of Gaussian white noise are investigated in this paper.First,the viscoelastic impact system is converted into a non-vibroimpact system with Zhuravlev transformation.Then,the slowly varing random process of ordinary differentiation equation is obtained by using the method of averaging.The averaged It？ differential equation governing the pth norm is established and the pth moment Lyapunov exponent is obtained.At last,the varations of the moment Lyapunov exponents with the restitution coeffient,the intensity of noise,and viscoelastic parameters are discussed.