A new methodology is presented for formulating the equations governing the evolution of the response cumulants of MDOF nonlinear systems subjected to delta-correlated processes. The system nonlineaxities are represented by polynomial terms involving the system variables, Appropriate recursive relationships are developed to relate the joint cumulants involving powers of the response variables with the joint cumulants involving the original response variables. Cumulant closure techniques, in which the joint cumulants of the response variables with order higher than a specified order are neglected, can be directly incorporated and efficiently used in the analysis to truncate the infinite hierarchy of the resulting system of cumulant equations. The effect of the order of the cumulant closure on the accuracy is demonstrated using a scalar first-order nonlinear differential equation. Important computational aspects are also addressed using a MDOF linear structural model.
展开▼
