Response of MDOF Systems to Nonstationary Random Excitation

Responses of linear, dynamic systems to nonstationary random excitation are calculated using a state formulation. Analytical expressions for evolutionary covariance matrices are derived for the case of evolutionary white noise excitation. As an example, responses of a 4-DOF system to ground acceleration are calculated. Modal decomposition is utilized and the relative importance of the cross covariance among the modes is quantified. Approximate first passage probabilities for high thresholds are calculated by using the evolutionary variances of a response and its time derivative and by making the Poisson assumption. An augmented dynamic system is proposed for the case of nonwhite excitation. The transition matrix for the augmented system is given.