Abstract
The method of equivalent linearization is applied to the general problem of the response of non-linear discrete systems to non-stationary random excitation. Conditions for minimum equation difference are determined which do not depend explicitly on time but only on the instantaneous statistics of the response process. Using the equivalent linear parameters, a deterministic non-linear ordinary differential equation for the covariance function is derived. The theoretical analyses are verified by numerical results. An example is given of a damped Duffing oscillator subjected to modulated white noise.
Keywords: Random Vibration, Linearization, Spectral Density, Standard Deviation, Response