Transient Random Response of Bilinear Oscillators

Results of an empirical study of the transient mean-square response of bilinear hysteretic oscillators to random excitation are presented. The oscillators considered include a moderately nonlinear system, a nearly elasto-plastic system, and the truly elasto-plastic system. The random excitation considered is an approximate simulation of stationary, Gaussian white noise. Generation of the ensemble of time histories of excitation, and integration of the nonlinear equation of motion to obtain the ensemble of time histories of response were performed on a digital computer. It is found that a constant parameter linear system (such as the Krylov-Bogoliubov system) can give acceptable predictions of the transient mean square response of a moderately nonlinear system, but not of a nearly elasto plastic system. A variable coefficient linear system which does give acceptable response predictions for the nearly elastoplastic system is also presented.