On the Probability Distribution of the Number of Crossings of a Certain Response Level in Random Vibration

Abstract

Presented are the results of analysis of a kind of threshold-value crossing problem in random vibration. Probability of crossings of a certain response level by a given number of times is formulated in terms of the “n-th passage time density”, from which approximate solutions are derived under the renewal process approximation. Discussions are made in comparison with the simple Poisson process approximation.