DYNAMIC-RESPONSE OF NONLINEAR-SYSTEMS TO POISSON-DISTRIBUTED RANDOM IMPULSES

The dynamic response of non-linear systems to external excitations in form of a Poisson-distributed train of random impulses is considered. The state vector of the dynamical system under consideration is a Poisson-driven Markov vector process. The equations governing its joint statistical moments are obtained by making use of a generalized Itô's differential rule. The resulting infinite hierarchy of equations is truncated with the help of a cumulant-neglect closure of different orders. For a Duffing oscillator the time histories of the mean value, the variance and the skewness coefficient of the response are evaluated analytically and compared with those obtained from Monte Carlo simulations. It is found that if the departure of the Poisson-driven excitation process from Gaussianity ranges from small to moderately large, i.e., the expected arrival rate of impulses is not very low, the application of the fourth order cumulant-neglect closure technique, i.e., neglecting the cumulants above the fourth order, yields very good estimates of the response mean values and variances. © 1992.