Some First-Passage Problems in Random Vibration

[+] Author and Article Information
S. H. Crandall, R. G. Cook

Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Mass.

K. L. Chandiramani

Bolt, Beranek, and Newman, Inc., Cambridge, Mass.

J. Appl. Mech 33(3), 532-538 (Sep 01, 1966) (7 pages) doi:10.1115/1.3625118 History: Received July 22, 1965; Revised January 27, 1966; Online September 15, 2011


First-passage problems for a lightly damped linear oscillator excited by white noise are described for two types of initial conditions and three different types of barrier configurations. The qualitative behavior of the probability distribution of the time to first passage is discussed. Two numerical procedures utilizing high-speed digital computers are outlined, and quantitative results for first-passage probability densities are displayed. The asymptotic behavior of this density for long mean times to failure is discussed, and a table of experimentally determined mean times to failure is included.

Copyright © 1966 by ASME
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