A solution method for linear and geometrically nonlinear MDOF systems with random properties subject to random excitation

A method for computing the lower-order moments of response of randomly excited multi-degree-of-freedom (MDOF) systems with random structural properties is proposed. The method is grounded in the techniques of stochastic calculus, utilizing a Markov diffusion process to model the structural system with random structural properties. The resulting state-space formulation is a system of ordinary stochastic differential equations with random coefficients and deterministic initial conditions which are subsequently transformed into ordinary stochastic differential equations with deterministic coefficients and random initial conditions. This transformation facilitates the derivation of differential equations which govern the evolution of the unconditional statistical moments of response. Primary consideration is given to linear systems and systems with odd polynomial nonlinearities, for in these cases there is a significant reduction in the number of equations to be solved. The method is illustrated for a five-story shear-frame structure with nonlinear interstory restoring forces and random damping and stiffness properties. The results of the proposed method are compared to those estimated by extensive Monte-Carlo simulation.