Response and first passage probability of linear elastic SDOF systems subjected to nonstationary stochastic excitation modelled through S-transform

The S-transform is a special type of Fourier transform with the time localization and frequency dependent window. It is viewed as a hybrid of continuous wavelet transform and short-time Fourier transform. In the present study, we propose an S-transform-based random vibration theory to evaluate the response of the linear elastic single-degree-of-freedom (SDOF) system subjected to nonstationary stochastic excitation. We show that within the established framework, the time–frequency power spectral density (TFPSD) function of the structural response could be represented as the multiplication of the square of the mechanical admittance function and the TFPSD function of the nonstationary stochastic excitation. This simple relation facilitates the computation and statistical characterization of the structural responses subjected to nonstationary stochastic excitation that is modelled based on the S-transform, which implicitly includes the time-varying amplitude and frequency characteristics. We illustrate the use of the TFPSD function to estimate the statistics of the responses and first passage probability of SDOF systems subjected to stochastic earthquake or wind excitations, where the stochastic excitations are represented using the TFPSD functions obtained from the S-transform.