The response of stochastic vibro-impact system calculated by a new path integration algorithm

In this paper, a new path integration algorithm is proposed specifically for the stochastic vibro-impact system. By introducing the concept of absorption surface and the impact completion condition, this new path integration algorithm can be directly used to study the stochastic response of vibro-impact systems without any non-smooth approximation. The algorithm is suitable for arbitrary recovery coefficients and can retain the non-smooth characteristics of the vibro-impact system. Linear and nonlinear vibro-impact systems excited by the Gaussian white noise are used as examples to show the unique results obtained by our method. Finally, the Monte Carlo method is used to verify the efficiency and accuracy of this new algorithm.