First-passage study and stationary response analysis of a BWB hysteresis model using quasi-conservative stochastic averaging method

The quasi-conservative stochastic averaging (QCSA) method is applied to a Bouc-Wen-Baber hysteretic system (BWB) under Gaussian white noise excitations. The stationary probability density of the systemʹs response amplitude and energy is obtained for different excitation levels and different damping ratios. These results are compared with the studies presented by Cai and Lin in A New Solution Technique for Randomly Excited Hysteretic Structures, Technical Report on Grant No. NCEER-88-0012, State University of New York, Buffalo, NY, 1988. The first-passage time problem for the hysteretic system is also studied using the method of QCSA. The results for the expected time to failure as a function of the initial total energy are shown, for different excitation levels and for different threshold values of energy. The relationship between the expected time to failure when initial total energy is zero and excitation level is shown for a wide range of hysteresis shape parameters.