An approximate approach for nonlinear system response determination under evolutionary stochastic excitation

A method based on the concepts of stochastic averaging and equivalent linearization is presented for determining the response of a lightly damped nonlinear single-degree-of-freedom oscillator to a random excitation with an evolutionary broad-band power spectrum. The nonlinearities could be either of the hysteretic or the 'zero-memory' kind. Approximate analytical relationships for evaluating the response variance are derived for a number of oscillators. The efficiency and accuracy of the approach is demonstrated by pertinent digital Monte Carlo simulations. The significant advantage of the proposed approach relates to the fact that it is readily applicable for excitations possessing even non-separable evolutionary power spectra circumventing ad hoc pre-filtering and pre-processing excitation treatments associated with existing alternative schemes of linearization.