An explicit closed-form solution for linear systems subjected to nonstationary random excitation

Explicit, closed-form solutions are presented for the correlation matrix and evolutionary power spectral density matrix of the response of a linear, classically damped MDOF system subjected to a uniformly modulated random process with the gamma envelope function. The effects of the statistical cross-modal correlations on the evolutionary mean square responses are investigated. A simple MDOF system subjected to ground motion is used as an illustrative example. Through this study, additional insight is gained into the nonstationary behavior of linear dynamic systems.