First-passage failure of quasi-non-integrable-Hamiltonian systems

Abstract

The first-passage failure of multi-degree-of-freedom quasi-non-integrable-Hamiltonian systems with Gaussian white noise excitations is investigated. Based on the stochastic averaging method for quasi-non-integrable-Hamiltonian systems, the Hamiltonian can be approximated as a one-dimensional diffusion process, from which a backward Kolmogorov equation for conditional reliability function and generalized Pontryagin equations for the moments of first passage time can be established. The conditional reliability function, the conditional probability density of first-passage time and the moments of the first-passage time of any order can be obtained by solving these equations with suitable initial and boundary conditions. Two examples are studied in detail to illustrate the above procedure.