Response Spectral Density for Oscillators with Nonlinear Damping

Abstract

The concept of equivalent nonlinearization is used to obtain approximate solutions for the frequency response function and power spectral density (PSD) function of the response for oscillators with nonlinear damping. When harmonic excitation is considered the energy of the response is assumed to oscillate around a mean energy level. Assuming that the response is harmonic with energy-dependent amplitude an approximate frequency response function is obtained. The PSD function of the response to white noise excitation at a given energy level is obtained by an expression similar to the expression for a linear system, where the damping is replaced by an energy-dependent damping function. The total PSD function is obtained as a weighted average of the damping at all energy levels, and the method can be considered an extension of the method of equivalent nonlinearization to the frequency domain. The accuracy of the methods is verified by numerical examples.