Random Vibrations in Discrete Nonlinear Dynamic Systems

Abstract

A one-degree-of-freedom system and a two-degree-of-freedom system containing Dis-placement and velocity dependent nonlinearities subjected to stationary gaussian white noise excitation have been studied by the method of the Fokker-Planck equation. Non-linearities have been represented by suitable polynomials. The Fokker-Planck equations governing the stationary probability density function for these systems have been solved by representing the density function by a multiple series of Hermite polynomials. The constants in the series expansion were determined by Galerkin's method. Analysis is developed for the system containing nonlinearities described by suitable polynomials in velocity and displacement dependent forces. Comparisons were made between series and exact solutions for those special cases for which exact solutions are known.