Linear Response to Nonstationary Random Excitation

The class of inputs considered herein is that of a stationary process multiplied by a deterministic intensity function. Both the stationary process and the intensity function may be arbitrarily specified. The approximate solution is constructed from a fundamental partial solution which is independent of the intensity function. The intensity is approximated by a staircase function and the principle of superposition is applied to generate the total mean-square response. Closed form solutions are derived for a single-degree-of-freedom system excited by correlated noise having an intensity function of the general staircase type, and an exponentially decaying intensity function. Approximate solutions based on 2, 4 and 8 step staircase approximations of the latter, illustrate the convergence of the method. Response to narrow-band excitation shaped by a half-sine pulse is also presented and compared to some previously published results.