Summary
The equivalent linearization method can yield an accurate and computationally efficient estimate of the variance of the response of a nonlinear system subject to random excitation, even in the presence of strong nonlinearity. However, spectra yielded by the method are usually inaccurate, and the method cannot predict any loss in coherence between the excitation and the response. An alternative approach is presented here which is equally efficient and which yields good approximations for response spectra and coherence levels. The method is based on finding the first Wiener kernel of the response and then using detailed balance considerations to express the total response spectrum in terms of this kernel. For simplicity the method is presented here for a single degree of freedom system, although it can also be applied to more complex systems.
