First passage times of stationary non-Gaussian structural responses

Abstract

The main focus of this paper is the development of an analytical moment-based procedure for calculating first passage times of a stationary non-Gaussian structural response. In the procedure, Winterstein’s polynomials based on response moments (skewness, kurtosis, etc.) are used to map a non-Gaussian structural response into a standard Gaussian process, and then the mean up-crossing rate of the original response process is estimated from the mapped standard Gaussian process. Through introducing the mean clump size and the probability of instantaneous failure of the original response process, the procedure accounts for effects of clumping and initial conditions on the up-crossing rate, and finally, first passage time. An analysis of a linear single-degree-of-freedom system (SDOF) system excited by a quadratic forcing function demonstrates the usage of the procedure. Comparisons between the results from the procedure and those from the Monte Carlo simulation method are also performed in the example.