Nonzero mean response of nonlinear oscillators excited by additive Poisson impulses

Abstract

This paper investigates the nonzero mean probability density function (PDF) of nonlinear oscillators under additive Poisson impulses. The PDF is governed by the generalized Fokker–Planck–Kolmogorov (FPK) equation which is also called the Kolmogorov–Feller (KF) equation. An exponential-polynomial closure (EPC) method is adopted to solve the equation. Five examples are considered in numerical analysis to show the effectiveness of the EPC method. The nonzero mean response of nonlinear oscillators is formulated due to either nonlinearity type or nonzero mean amplitude of Poisson impulses. The analysis shows that the PDFs obtained with the EPC method agree with the simulated results when the polynomial order is 4 or 6. This agreement is also observed in the tail regions of the obtained PDFs. The comparison further shows that the nonzero mean PDF of displacement is nonsymmetrically distributed. Comparatively, the PDF of velocity still has a symmetrical distribution pattern when the nonlinearity only exists in displacement.