A method is developed that can be used to calculate the stationary response of randomly excited nonlinear systems. The method iterates to obtain the fast Fourier transform of the system response, returning to the time domain at each iteration to take advantage of the ease in evaluating nonlinearities there. The updated estimates of the nonlinear terms are transformed back into the frequency domain in order to continue iterating on the frequency spectrum of the staionary response.
This approach is used to calculate the response of a one degree of freedom system with friction damping that is subjected to random excitation. The one degree of freedom system provides a single mode approximation of systems (e.g. turbine blades) with friction damping. This study investigates various strategies that can be used to optimize the friction load so as to minimize the response of the system.