Bilinear Oscillator Research Articles

The Response of an Oscillator With Bilinear Hysteresis to Stationary Random Excitation

By applying the technique of stochastic averaging, a simple analytical result is obtained for the joint distribution of the displacement and velocity of a bilinear oscillator excited by a stationary random process. A comparison of theoretical results deduced from this distribution with corresponding digital simulation results shows that the theory is accurate in circumstances where the response is narrow-band in nature.

Erratum for “Transient Random Response of Bilinear Oscillators”

Erratum for “Transient Random Response of Bilinear Oscillators”

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.