Time Varying Loads and White Noise on an SDOF System with Bouc Hysteresis Using Gaussian Closure

Abstract

In a recent publication [H. Waubke and C. Kasess, Gaussian closure technique applied to the hysteretic Bouc model with nonzero mean white noise excitation, J. Sound Vibr. 382 (2016) 258–273], the response of a single-degree-of-freedom (SDOF) system under Gaussian white noise and a constant dead load is presented. The system has a hysteresis described by Bouc [R. Bouc, Forced vibration of mechanical systems with hysteresis, in Proc. Fourth Conference on Nonlinear Oscillation (Prague, 1967), p. 315]. New is the usage of a slowly time-varying deterministic load added to the Gaussian white noise process. The transient solution is calculated using the Gaussian closure technique together with an explicit time step procedure. All moments in the Gaussian closure technique are evaluated analytically. The results of the Gaussian closure technique are in good agreement with the results from the Monte-Carlo method.