The response spectrum of an oscillator with bilinear stiffness excited by band-limited Gaussian white noise is considered. The response is obtained by integrating over all energy levels weighting each with the stationary probability density of the energy. The procedure presented leads to estimates of linear and nonlinear response spectra in frequency domain and agrees well with those obtained by direct numerical simulation. Development of stochastic-based response spectra based on the frequency information concerning ground motions is important in engineering. Approximation of non-stationary ground motions by band-limited white noise is shown to be adequate for systems at the structural periods of engineering interest. Formulating the nonlinear response based on the excitation frequency information opens a door for wider use of seismological theory for regions with scarcely available recorded ground motion data. Despite simplicity and computational efficiency of the method, it provides an accurate prediction of the observed nonlinear response spectra on average.
