First-passage time for randomly excited non-linear oscillators

An approximate method of computing first-passage probabilities for non-linear oscillators subjected to stationary wide-band random excitation is discussed. The method is based upon an approximation of the energy envelope of the oscillator response as a one-dimensional Markov process, governed by an appropriate diffusion equation. The adoption of suitable absorbing and reflecting boundary conditions enables the evolution of the first-passage probability to be computed. An efficient and simple algorithm for the numerical solution of the governing diffusion equation is outlined which is based upon an implicit, finite-difference approximation. Numerical results for the mean first-passage time are compared with the results of a finite element numerical solution of the exact two-dimensional Pontriagin-Vitt equation for this statistic.

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