Stationary random response of bilinear hysteretic systems

Abstract

This study of the stationary random vibration of single degree of freedom bilinear hysteretic oscillators consists of both experimental investigations and approximate analytical investigations. The experimental results are obtained from a differential analyzer electrical analog computer excited by an approximately white, Gaussian source. Measurements of mean squared levels, power spectral density and probability distribution of oscillator response are reported. The applicability of certain approximate analytical techniques is investigated by comparing analytical predictions and experimental measurements of the statistics of the response. The analog computer results indicate that for a system containing viscous damping, yielding may sometimes act to increase the rms level of displacement response. In addition, the experimental results show that yielding has a marked effect on the response power spectral density, and in some instances this statistic has the general character of that for a two mode linear system. The response probability distribution is also affected by yielding and is generally not Gaussian. An extension of the Krylov-Bogoliubov method of equivalent linearization and a method based on defining an approximately equivalent nonlinear nonhysteretic system are considered. The KrylovBogoliubov method gives a reasonable estimate of the rms velocity response for all cases considered but gives meaningful information about the rms displacement response only for cases of moderate nonlinearity. The second approximate method is shown to be quite good for predicting rms levels of response for cases of high yield level where the Krylov-Bogoliubov method is less successful. The application of the second method to other cases and to the problem of predicting probability distributions is also discussed.