Response of MDOF Systems to Vector Random Excitation

A model time history random vibration analysis is presented. The random excitation is nonwhite, nonstationary, vector-valued and correlated. Excitation components may have different frequency contents and variations in intensity with time. The correlation between any two components can be a function of time. The formulation is appropriate for any linear MDOF system which has been decoupled into modes. Analytical expressions are derived for the evolutionary mean and covariance matrices of a modal system augmented by filters and subjected to vector-valued excitation having piece-wise linear strength functions. Then, using modal superposition, evolutionary mean and covariance matrices of any response vector are computed. A three degree-of-freedom system, subjected to vector-valued earthquake excitation, is analyzed. The formulation captures the effects of nonstationarity and correlation between earthquake components.