A harmonic input method for computing time-varying response PSD of linear time-invariant structures subjected to nonstationary stochastic excitations

•A harmonic input method is proposed for computing time-varying PSD.•It can consider the influence of the transient response on the PSD.•Its accuracy and efficiency have been verified against the Monte Carlo simulation. A number of stochastic response analysis methods have been successfully developed for computing the time-varying response power spectral density (PSD) of structures subjected to nonstationary stochastic excitations. However, how to compute the time-varying response PSD when transient response components have significant impacts on the stochastic responses remains largely unsolved. To this end, this paper proposes a harmonic input method (HIM) for accurately and efficiently computing time-varying response PSD of linear time-invariant structures subjected to nonstationary stochastic excitations, which can consider the transient response impact. The accuracy of the proposed HIM method is verified via comparison against the Monte Carlo simulations of an SDOF system and an MDOF system, which outperforms the classical methods if the transient response components are of significance. This study offers a high-efficient and high-accurate approach for response PSD estimation, particularly for a low-damping structural system subjected to short-duration nonstationary stochastic excitations.