An Integral Equation Method for the First-Passage Problem in Random Vibration

[+] Author and Article Information
P. H. Madsen, S. Krenk

Riso̸ National Laboratory, Roskilde, Denmark

J. Appl. Mech 51(3), 674-679 (Sep 01, 1984) (6 pages) doi:10.1115/1.3167691 History: Received October 01, 1983; Revised January 01, 1984; Online July 21, 2009


The first-passage problem for a nonstationary stochastic process is formulated as an integral identity, which produces known bounds and series expansions as special cases, while approximation of the kernel leads to an integral equation for the first-passage probability density function. An accurate, explicit approximation formula for the kernel is derived, and the influence of uni or multi modal frequency content of the process is investigated. Numerical results provide comparisons with simulation results and alternative methods for narrow band processes, and also the case of a multimodal, nonstationary process is dealt with.

Copyright © 1984 by ASME
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