Non-linear systems of multiple degrees of freedom under both additive and multiplicative random excitations

A quasi-linearization procedure is developed for non-linear systems under both additive and multiplicative white-noise excitations to obtain response statistical properties, including moments, correlation functions, and spectral densities. In the proposed procedure, only the system properties are linearized, while all excitations are kept unchanged. In particular, the basic characteristics associated with the multiplicative excitations are preserved, which is the key factor for the accuracy of the approach. Numerical examples are given, and the accuracy of the procedure is substantiated by comparing the analytical results with those obtained from Monte Carlo simulations.