Solution Methods for Structures with Random Properties Subject to Random Excitation

This paper deals with the lower order statistical moments of the response of structures with random stiffness and random damping properties subject to random excitation. The arising stochastic differential equations (SDE) with random coefficients are solved by two methods, a second order perturbation approach and a Markovian method. The second order perturbation approach is grounded on the total probability theorem and can be compactly written. Moreover, the problem to be solved is independent of the dimension of the random variables involved. The Markovian approach suggests transforming the SDE with random coefficients with deterministic initial conditions to an equivalent nonlinear SDE with deterministic coefficient and random initial conditions. In both methods, the statistical moment equations are used. Hierarchy of statistical moments in the markovian approach is closed by the cumulant neglect closure method applied at the fourth order level.