Response Cumulant Equations for Dynamic Systems under Delta-Correlated Processes

Abstract

This paper develops response cumulant differential equations (CDEs) that can be used to calculate response cumulants for dynamic systems under non-Gaussian, delta-correlated excitations. The derived CDEs apply to both linear and nonlinear systems, an improvement over the previous CDEs that are only applicable to linear systems. The new CDEs also can be used much more efficiently than the previous version. The problem of a second-order, single-degree-of-freedom (SDOF) linear system subjected to non-Gaussian, delta-correlated excitations is given to illustrate how to use the new CDEs for calculating response cumulants. Closed-form solutions for the stationary response cumulants are presented.