On Statistics of First-Passage Failure

[+] Author and Article Information
G. Q. Cai, Y. K. Lin

Center for Applied Stochastics Research, Florida Atlantic University, Boca Raton, FL 33431

J. Appl. Mech 61(1), 93-99 (Mar 01, 1994) (7 pages) doi:10.1115/1.2901427 History: Received May 01, 1992; Revised October 22, 1992; Online March 31, 2008


The event in which the response of a randomly excited dynamical system passes, for the first time, a critical magnitude z c is investigated. When the response variable in question can be modeled as a one-dimensional diffusion process, defined on [z l , z c ], the statistical moment of the first passage time of an arbitrary order is governed by the classical Pontryagin equation, subject to suitable boundary conditions. It is shown that, when a boundary is singular, it must be either an entrance, a regular boundary, or a repulsive natural boundary in order that a solution for the Pontryagin equation is physically meaningful. Boundary conditions are obtained for three types of singular boundaries and applied to the second-order oscillators in which the amplitude or energy process can be approximated as a Markov process. Illustrative examples are given of linear and nonlinear oscillators under additive and/or multiplicative random excitations.

Copyright © 1994 by The American Society of Mechanical Engineers
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