Response Analysis of a Nonlinear System Subjected to Combined Excitation of White Noise and Random Train of Impulses

Probability distribution of stationary responses of a nonlinear system subjected to a combined excitation of white noise and random train of impulses is analyzed. White noise and impulses are independent processes. The response distributions are obtained by employing moment equations approach and Gaussian sum approximation, which expresses the probability density function in terms of weighted sum of several Gaussian probability density functions. In the illustrative example, the response distributions of a Duffing oscillator are calculated and compared with simulation results. The effects of impulses upon a tail of these distributions are clarified.