Bouc Hysteresis Under White Noise Excitation Using Nonlinear Mapping and the Beta Distribution

Abstract

The Bouc model describes the behavior of hysteretic materials using three-coupled differential equations. Under white noise excitation, the probability density of the state variables can be approximated using closure methods. Here, a new closure approach is presented that utilizes the beta distribution for hysteretic softening together with a nonlinear mapping using the inverse hyperbolic tangent. The beta distribution properly models the distribution of the force-proportional displacement, the required nonlinear relation between displacement, velocity, and force-proportional displacement is, however, not entirely captured for large excitation levels leading to deviations from the Monte-Carlo simulations.