A new approximate solution technique for randomly excited nonlinear oscillators (Q1117732)

A new technique is proposed to obtain an approximate probability density for the response of a non-linear oscillator under Gaussian white noise excitations. The random excitations may be either multiplicative (also known as parametric) or additve (also known as external), or both. In this new technique, the original non-linear oscillator is replaced by another oscillator belonging to the class of generalized stationary potential for which the exact solution is obtainable. The replacement oscillator is selected on the basis that the average energy dissipation remains unchanged. Examples are given to illustrate the application of the new procedure. In one of the examples, the new procedure leads to a better approximation than that obtained by stochastic averaging.