Gaussian closure technique for Bouc's hysteretic model under white noise excitation

Bouc developed a hysteretic model for materials like rubber under dynamic excitation. The response of a hysteretic system under white noise excitation is normally estimated by means of the statistical linearization or a related method. Disadvantages of this method are the assumption of a Gaussian nature of the random distributions, the high computational efforts caused by the iterations needed and the instability of the iteration in certain parameter regions. Using the assumption of Gaussian random distributions, the Gaussian closure technique can be applied. Analytic solutions of the integrals occurring in this approximation were found and are presented. This solution allows for an explicit time step procedure for the random moments in the transient case. For the stationary case a fast and stable iteration about a set of non linear equations is needed. Both procedures allow to calculate the moments in a fast manner and allow to solve problems with more than one degree of freedom with limited computational efforts.