Random response analysis of Preisach hysteretic systems with symmetric weight distribution

The present study is intended to develop a new method for analyzing nonlinear stochastic dynamic response of the Preisach hysteretic systems based on covariance and switching probability analysis of a nonlocal memory hysteretic constitutive model. A nonlinear algebraic covariance equation is formulated for the single-degree-of-freedom Preisach hysteretic system subjected to stationary Gaussian white noise excitation, from which the stationary mean square response of the system is obtained. The correlation coefficients of hysteretic restoring force with response in the covariance equation are evaluated by using the second moments and switching probabilities that are derived from the disjoint event probability and the mathematical machinery of an exit problem. In recognizing the symmetry of the classical Preisach weighting function, an approximation of equal "up" and "down" switching probabilities is introduced, which greatly simplifies the evaluation of the correlation coefficients. An example of the Preisach hysteretic system with Gaussian distribution weighting function is presented and the analytical results are compared with the digital simulation findings to verify the accuracy of the derived formulas. Computation results show that there exists a sharp drop in the mean square responses with the increase of a hysteresis parameter, and the mean square responses are affected only in a certain range of the Preisach weighting function.