Nonlinear MDOF system stochastic response determination via a dimension reduction approach

An approximate analytical dimension reduction approach is developed for determining the response of a multi-degree-of-freedom (MDOF) nonlinear/hysteretic system subject to a non-stationary stochastic excitation vector. The approach is based on the concepts of statistical linearization and of stochastic averaging. It is readily applicable even for excitations possessing evolutionary in time power spectra. Further, it can be potentially used in conjunction with design spectrum based analyses to obtain peak system response estimates. Numerical examples include MDOF systems comprising the versatile Bouc–Wen (hysteretic) model. The reliability of the approach is demonstrated by pertinent Monte Carlo simulations.