First-Passage Probability for Two-Mode Systems
Publication: Journal of Engineering Mechanics
Volume 109, Issue 6
Abstract
First-passage probabilities are investigated for the absolute value of the zero-start response of 2DF linear oscillators excited by stationary white noise having a normal probability distribution. Only the long-time portion of the response has been studied. Most attention is given to the exponential decay rate of the probability of survival, but some data is also given for the generally less important multiplier of the exponential term. A two-dimensional Markov amplitude model is shown to provide a relatively economical method to supplement and extend the results of a 2DF Monte Carlo simulation. Relatively simple empirical equations are given to approximate the values of the probability of survival for a fairly wide range of situations. These approximations appear to be acceptable when damping is between 1% and 10%, modal frequencies are separated by at least a factor of two, the low frequency mode contributes at least 50% of the response, and the barrier level is at least two times the rms value of the response.
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Information & Authors
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Published In
Journal of Engineering Mechanics
Volume 109 • Issue 6 • December 1983
Pages: 1358 - 1374
Copyright
Copyright © 1983 ASCE.
History
Published online: Dec 1, 1983
Published in print: Dec 1983
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