Response distribution of non-linear systems excited by non-Gaussian impulsive noise

A perturbation scheme is devised to obtain an approximate stationary probability density for the response of a non-linear oscillator subjected to an impulsive-noise process which is statistically stationary but non-Gaussian. The excitation can be either additive or multiplicative. The effect of non-Gaussianity in the excitation process is found to be negligible if the product of the average arrival rate of the impulses and the relaxation time of the oscillator is of an order of 10 or greater. When this is not the case, the effect is not uniform; it may be more pronounced for one dynamic system than that of another. Numerical results are obtained for two examples, and they compare well with Monte Carlo simulations.