Random Vibration of Yielding Oscillator

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Abstract
An approximate analytical method is developed for predicting the stationary rms levels of response of a yielding oscillator subjected to white noise random excitation. The method is based on a power balance between the exciting force and the energy dissipating elements. Certain average period or frequency assumptions made in earlier power balance analyses have been modified to make the method significantly more accurate. The results of the analytical method have been compared with empirical data for moderately nonlinear and nearly elasto-plastic bilinear hysteretic systems (slope ratios of 1/2, 1/10, and 1/21). The empirical data include new results from a digital simulation as well as previously published analog computer results. The results of the modified power balance method are shown to agree quite well with the empirical data, particularly when the system contains little or no viscous damping. The new method is considerably more accurate than the Krylov-Bogoliubov method for nearly elasto-plastic systems.

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