Stochastic averaging of Preisach hysteretic systems

The sustained progress in the study of the hysteretic behavior of structural and mechanical systems has led to the adoption of increasingly sophisticated and reliable mathematical representations. Models based on the distributed elements (hysterons) appear to be quite versatile. Among these, the Preisach hysteretic model has received considerable attention in the field of engineering mechanics. In this paper, the stochastic response of a Preisach hysteretic system driven by a white noise process is investigated. In this regard, the method of stochastic averaging is modified to be applicable for the determination of the probability density of the stationary system response envelope. Remarkably, this probability density expression in conjunction with the response of an auxiliary linear system can also be used to determine the power spectrum of the system response. The approximate theoretical solutions are validated by data derived by a pertinent Monte Carlo study.