doi:10.3850/978-981-08-7619-7_P041

ABSTRACT

An approximate analytical method for the determination of the non-stationary response probability density function (PDF) of a broad class of randomly excited nonlinear oscillators is developed. Specifically, relying on the notion of the Wiener path integral and adopting a variational formulation the non-stationary PDF of processes with nonlinear drift and constant diffusion coefficients is expressed in terms of the most probable path. Further, resorting to the concepts of stochastic averaging and of statistical linearization it is shown that the response amplitude envelope of oscillators with nonlinear damping is governed by a first-order stochastic differential equation (SDE). The process possesses nonlinear drift and constant diffusion coefficients. Thus, the Wiener path integral solution method can be applied demonstrating its potential to address physically realistic problems. The significant advantage of the proposed method relates to the determination of the non-stationary response PDF without the need to advance the solution in short time steps as it is required for the existing alternative numerical path integral solution methods. The accuracy of the method is demonstrated by pertinent Monte Carlo simulations.

Keywords: Stochastic processes, Random vibration, Monte Carlo method, Nonlinear systems, Wiener path integral.

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