有界噪声激励下粘弹性碰撞系统的稳定性

Stability of Viscoelastic System with Impacts Under Bound Noise Excitation

研究了粘弹性碰撞系统在有界噪声激励下的随机稳定性。采用Zhuravlev变换将粘弹性碰撞系统转化为非碰撞系统,用随机平均法得到了随机微分方程,根据Itǒ法则,建立了耦合的平均Itǒ微分方程。应用有界非正则变换,将耦合的Itǒ微分方程组的求解问题转化为特征值问题。通过求解特征值,得到了粘弹性系统的p阶矩Lyapunov指数的近似解析解。用Monte Carlo模拟数值结果验证了近似解析解的正确性。讨论了恢复因子、粘弹性参数和随机激励振幅对粘弹性碰撞系统稳定性的影响。

The stabilities of viscoelastic system with impacts under the excitation of bound noise are investigated.First,the viscoelastic impact system converts into a non-vibroimpact system with Zhuravlev transformation. Then,the random process of ordinary differentiation equation is obtained using the method of averaging. The averaged Itǒdifferential equation governing the pth norm is established and the eigenvalue problem governing the pth moment Lyapunov exponent is obtained. The moment Lyapunov exponents of the system can then be deter mined by solving the eigenvalue problem. At last, Monte Carlo simulation results are provided to investigate the validity of approximate analytical solution. The variations of the moment Lyapunov exponents with the restitution coefficient,viscoelastic parameters,the amplitude of the parametric excitation are discussed.