An approach to the first-passage problem in random vibration

Abstract A series solution to the first-passage problem in random vibration is derived which is valid for any type of response process and for both single and double-sided barriers. The partial sums of this series form successive upper and lower bounds to the first-passage density function. The special case of a normal response process is discussed in some detail and a procedure for evaluating the first three terms in the series is outlined. The theory is applied to the case of a lightly damped oscillator excited by white noise and some results are displayed for both types of barrier configuration. It is shown that when the probability of failure is small the convergence of the series is quite rapid and that close bounds to the first-passage density function may be obtained in these circumstances.