Conclusions and Recommendations

The first passage problem for the single degree-of-freedom oscillator incorporating the modified Bouc hysteresis model has been solved by a Petrov-Galerkin finite element method. Solutions have been obtained for the first six ordinary moments of first passage time and for the cumulative distribution and probability density functions. Results have been presented for several hysteretic oscillators, and the accuracy of these results has been demonstrated by extensive Monte Carlo simulation. Finally, an effective method to estimate the reliability of a system having several prescribed moments has been examined. In the absence of an analytical solution, these results are the most accurate reported to date.