Stochastic response of nonlinear oscillators under non-homogeneous Poisson white noise excitations

Abstract

Poisson white noise is a typical non-Gaussian process. It is generally utilized to model stationary loadings by the assumed constant impulse arrival rate. Much research work has been done on that. However, the actual impulse arrival times of some discrete loadings are not uniform in the given time duration. The resulting arrival rate is a time-varying function instead of a constant one. Corresponding Poisson process is non-homogeneous. Less work in the literature has been found. In this paper, a Poisson white noise process with a time-varying impulse arrival rate is considered in the excitation model. Under such excitation the response of nonlinear system is a Markov process. The resulting generalized time-dependent Fokker–Planck equation becomes more complicated. The perturbation method, combined with the exponential-polynomial closure (EPC) method, is utilized to solve this equation. Examples of typical nonlinear systems under non-homogeneous Poisson white noise excitations are investigated. The effect of time-varying impulse arrival rate on the response is illustrated. Numerical results show that the response statistical characteristics depend strongly on the impulse arrival rate. Large errors would generate if the arrival rate varies fast over time and is still treated as an average constant.