First-excursion failure of randomly excited structures

The probability for a randomly excited structure to survive a service time interval without suffering a first-excursion failure is determined analytically. The first-excursion failure occurs when, for the first time, the structural response passes out of a prescribed safety domain. The problem is formulated from the viewpoint of the Stratonovich-Kuznetsov theory of random points. The exact solution is expressed two equivalent series forms, one reducible to Rice's in and exclusion series. The first order truncation of the second series corresponds to Poisson random points and the second order truncation to random points with pseudo Gaussian arrival rate. Numerical results are presented for a single-degree-offreedom linear oscillator under Gaussian white noise excitation based on these truncations and the model of nonapproaching random points suggested by Stratonovich.