Random Vibration of Degrading Systems with General Hysteretic Behavior

Three mathematical models which are capable of representing general degradation behavior of hysteretic structural elements, including hysteresis pinching, as a function of hysteretic energy dissipation are presented. Two of the models are series models consisting of Bouc-Baber-Wen smooth hysteresis with two "slip-lock" elements. One of these slip-lock elements is designated as the BN and the other one as NB model. The third model has a single form and is designated as Single Element Pinching (SEP) model.

Behavior of a SDOF system of each model under cyclic and general loading is studied and the obtained results illustrate the versatility of all three models in reproducing various types of general degradation including pinching hysteretic behavior.

With the assumption of gradual degradation equivalent linearization solutions are obtained for these models for zero mean excitation case. Linearization for BN and SEP models are obtained in closed form and for NB model linearization is derived numerically. Nonstationary RMS response statistics obtained for zero mean excitaion, compare well with response statistics computed using Monte Carlo simulation. Comparison for NB and SEP models are better than those for BN model.

Response an analysis of a SDOF system of BN and SEP model, subjected to nonzero mean input excitation is studied and approximate solutions are obtained by subtracting mean responses from the governing stochastic differential equations and then applying equivalent linearization. The response predictions of the linearized model compare well for the SEP model and reasonably well for BN model. At all levels of excitation, the linearized models predict qualitatively the response of the system.