Stochastic Response Cumulants of MDOF Linear Systems

Abstract

This study addresses the complexities that arise in developing algorithms to formulate and subsequently solve the very large system of equations describing the stochastic response cumulants of multi-degree-of-freedom (MDOF) linear systems subjected to nonnormal filtered delta-correlated processes. A general method is presented that takes advantage of the symmetry of the cumulant tensors to simplify the analysis. New computationally efficient algorithms based on modal analysis of the large linear system of cumulants are proposed for calculating the nonstationary response cumulants. A modal truncation technique is subsequently used in which a selected number of modes for the system of cumulants is retained in the analysis. With the exception of a small number of modes corresponding to low eigenvalues, most of the higher contributing modes are treated statically in the modal expansion. The methodology provides insight into the conditions for neglecting a mode, as well as treating a contributing mode statically or dynamically. An example structure is used to illustrate various aspects concerning the computational efficiency of the methodology and the accuracy of the modal truncation technique.