Survival Probability Determination of Nonlinear Oscillators Subject to Evolutionary Stochastic Excitation

Abstract

A novel approximate analytical technique for determining the survival probability and firstpassage probability density function (PDF) of nonlinear/hysteretic oscillators subject to evolutionary stochastic excitation is developed. Specifically, relying on a stochastic averaging/linearization treatment of the problem, approximate closed form expressions are derived for the oscillator nonstationary marginal, transition, and jointresponse amplitude PDFs and, ultimately, for the timedependent oscillator survival probability. The developed technique exhibits considerable versatility, as it can handle readily cases of oscillators exhibiting complex hysteretic behaviors as well as cases of evolutionary stochastic excitations with timevarying frequency contents. Further, it exhibits notable simplicity since, in essence, it requires only the solution of a firstorder nonlinear ordinary differential equation (ODE) for the oscillator nonstationary response variance. Thus, the computational cost involved is kept at a minimum level. The classical hardening Duffing and the versatile Preisach (hysteretic) oscillators are considered in a numerical examples section, in which comparisons with pertinent Monte Carlo simulations data demonstrate the reliability of the proposed technique.