Numerical Solution of First Passage Problems in Random Vibrations Using Finite Difference Method

Abstract

The finite difference method is applied to estimate the reliability of the single degree of freedom system subjected to white noise excitation. In this paper, the probability that the system response stays within a safe region is used as the system reliability. It is difficult to obtain the accurate reliability from the probability density of the system response. Then the boundary condition of the finite difference scheme which we presented in the previous paper for the probability density of the system response is modified to obtain reliability directly from the Fokker-Planck equation, which governs the probability density. The reliability of the Duffing oscillator is calculated in the illustrated examples. The validity of the present method is demonstrated by comparison with the results of the Monte Carlo simulation.