Transient Behaviors of Linear and Nonlinear Systems under Stationary Non-Gaussian Random Excitation

Time evolution of the probability density is investigated for initially quiescent dynamical systems exposed suddenly to random excitations. A variety of dynamical systems is considered, including the usual linear oscillator, and nonlinear oscillators of hardening spring, of softening spring, and of the van del Pol type. The random excitations are assumed to be stationary stochastic processes, sharing the same spectral density, but with different non-Gaussian probability distributions. Each excitation process is generated by passing a Brownian motion process through a nonlinear filter, which is governed by an Itô stochastic differential equation. Monte Carlo simulations are carried out to obtain the transient probability distribution of the system response in each case. It is shown that, under different non-Gaussian excitations, the transient probability distributions of the system response can be markedly different. The differences tend to diminish, however, as time of exposure to the excitations increases. Key-Words: Random vibration, Nonlinear system, Monte Carlo simulation