Reliability analysis of nonlinear vibro-impact systems with both randomly fluctuating restoring and damping terms

In this paper, the reliability analysis of vibro-impact system with both randomly fluctuating restoring and damping terms is studied by a modified path integration (PI) method. Specifically, the Ivanov nonsmooth transformation technique is adopted to transform the vibro-impact system into the system without barrier, then the modified PI application on vibro-impact systems is applied, which is based on the Gaussian closure method and the localized approximation of moment function. According to the first passage theory, the reliability function, the first passage probability density function (PDF) and the mean first passage time are numerically calculated. In the framework of our numerical results, the influences of different random restoring terms, random damping terms and impact conditions on the system's reliability are discussed. The modified PI results are compared with the Monte Carlo Simulation (MCS) results, which shows that the proposed PI method can not only provide sufficiently accurate results to observe the weak influence of parameters, but also has obvious advantages in computational efficiency.