Time-Variant Reliability Analysis of Linear Elastic Systems Subjected to Fully Nonstationary Stochastic Excitations

Abstract

This paper presents closed-form solutions for the nongeometric spectral characteristics of nonstationary stochastic processes representing the response of linear elastic structural models subjected to fully nonstationary excitation processes. These spectral characteristics provide a complete description of the nonstationary stochastic processes representing the dynamic response of linear structural models when the input excitation is a Gaussian process. In particular, the nongeometric spectral characteristics can be used to evaluate the time-variant central frequency and bandwidth parameters of nonstationary stochastic processes. The closed-form solutions derived in this paper are used to evaluate the time-variant statistics and the first-passage probability of the response of single-degree-of-freedom and multidegree-of-freedom linear elastic structural models subjected to a well-known, fully nonstationary earthquake ground motion model. The new analytical results presented in this paper can be used in a number of structural dynamic applications.