Nonstationary Maximum Response Statistics for Linear Structures

Abstract

The mean and the variance are investigated for the maximum absolute value of a nonstationary process that represents the response buildup of a linear oscillator. The mean and variance are computed both by simulation and approximate analytical techniques, with emphasis on a comparative evaluation of available techniques and proposed procedures. The cumulative distribution function of the maximum value is represented by a form that is a function of a conditional rate of barrier crossings. This rate is computed by using a nonstationary approximation of Poisson crossings, and also by using available empirical expressions. In addition, existing expressions are used to estimate the mean and the variance of the maximum value of a nonstationary process by defining a shortened duration for an “equivalent” stationary process. Finally, the first passage problem is also posed as one governed by classical state‐space moment equations, and a modified Gaussian closure technique is used to obtain an approximate solution.