Non-stationary mean square response due to uniformly amplitude modulated random excitations

Abstract

Abstract The non-stationary random response problem of a time-invariant linear system subjected to uniformly amplitude modulated random excitations is studied. Based on the time-domain modal analysis of random vibrations, the time-dependent correlation function matrix of the response is obtained in closed form, so that the time-dependent mean square random response is easily obtained without resort to cumbersome integration. The method is straightforward and efficient, since it reduces the complicated non-stationary random response problem to a solution with complex number algebraic operations only. The method is applicable to non-stationary response problems of linear systems, whether they are symmetrical ones with classical damping or non-symmetrical ones with non-classical damping. Numerical examples of a 3-DOF time-invariant, non-classically damped linear system under modulated white noise or modulated filtered white noise excitations are included. Some remarks on the structural properties of the time-dependent correlations functions of the non-stationary random response, that we consider useful, are put in the Appendix.