A method for the random analysis of linear systems subjected to non-stationary multi-correlated loads

The paper shows a procedure for evaluating the correlation matrix and the evolutionary power spectral density matrix of the response of linear structural systems subjected to random non-stationary multi-correlated vector processes. The approach reduces this problem to the solution of some corresponding stationary problems. It is shown that the assumption of a modulating matrix function, whose elements are the sum of exponential functions, allows to transform the initial non-stationary problem into a stationary one. This stationary problem can be solved by well-known unconditionally stable step-by-step numerical procedures in the time domain, and, in closed form, in the frequency domain. The comparison of the results obtained using the proposed approach with those obtained by Monte Carlo Simulations (MCS) has revealed a very good level of accuracy.