Stationary response and first passage failure of rayleigh oscillator under external white-noise excitation

The stationary response and first passage failure of Rayleigh oscillator under external Gauss white noise excitation are investigated. The motion equations is reduced to averaged stochastic differential equations, and a backward Kolmogorov equation governing the conditional reliability function and a generalized Pontrayagin equation governing the conditional monments of first-passage time are established. The statistical propertyies of the stationary response and first-passage failure are analyzed numerically with three groups of parameters.