Stability of elastic and viscoelastic systems under stochastic non-Gaussian excitation

An effective numerical method to investigate the stability of elastic and viscoelastic systems under parametric excitation is suggested. Parametric forces are assumed in the form of stationary non-Gaussian processes. The proposed method is based on the simulation of random processes, the numerical solution of differential equations, describing the perturbed motion of the considered system, and the calculation of the top Lyapunov exponent. The considered method makes it possible to estimate the level of the almost sure stability and the stability with respect to statistical moments of the different order.