First-Passage Time for Oscillators With Nonlinear Damping

[+] Author and Article Information
J. B. Roberts

School of Engineering and Applied Sciences, University of Sussex, Falmer, Brighton, Sussex, England

J. Appl. Mech 45(1), 175-180 (Mar 01, 1978) (6 pages) doi:10.1115/1.3424223 History: Received January 01, 1977; Revised June 01, 1977; Online July 12, 2010


A simple numerical scheme is proposed for computing the probability of first passage failure, P(T), in an interval O-T, for oscillators with nonlinear damping. The method depends on the fact that, when the damping is light, the amplitude envelope, A(t), can be accurately approximated as a one-dimensional Markov process. Hence, estimates of P(T) are found, for both single and double-sided barriers, by solving the Fokker-Planck equation for A(t) with an appropriate absorbing barrier. The numerical solution of the Fokker-Planck equation is greatly simplified by using a discrete time random walk analog of A(t), with appropriate statistical properties. Results obtained by this method are compared with corresponding digital simulation estimates, in typical cases.

Copyright © 1978 by ASME
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