Perturbation Solutions for Random Linear Structural Systems subject to Random Excitation using Stochastic Differential Equations

The paper deals with the first and second order statistical moments of the response of linear systems with random parameters subject to random excitation modelled as white-noise multiplied by an envelope function with random parameters. The method of analysis is basically a second order perturbation method using stochastic differential equations. The joint statistical moments entering the perturbation solution are determined by considering an augmented dynamic system with state variables made up of the displacement and velocity vector and their first and second derivatives with respect to the random parameters of the problem. Equations for partial derivatives are obtained from the partial differentiation of the equations of motion. The zero time-lag joint statistical moment equations for the augmented state vector are derived from the Itô differential formula. General formulation is given for multi-degree-of-freedom (MDOF) systems and the method is illustrated for a single-degree-of-freedom (SDOF) oscillator. The results are compared to those of exact results for a random oscillator subject to white noise excitation with random intensity