Analytical Study on Response Power Spectral Density of Structures Subjected to Nonstationary Excitation Considering Transient Responses

Abstract

Computing the response power spectral densities (PSDs) of structures from the excitation PSDs has always been a classical problem in structural random vibration. Conventional analytical methods ignore the frequency characteristics of the transient response and therefore yield an incomplete solution. An analytical solution is needed for the structural response PSDs induced by nonstationary excitations with slow-varying time modulation functions considering the transient response. Decomposing nonstationary stochastic excitation as a series of single-frequency excitations, the analytical solutions of the transient and the steady-state responses are derived. The total analytical solutions of the response PSDs are therefore established for single-degree-of-freedom (SDOF) and multidegree-of-freedom (MDOF) systems. Numerical examples validate that the proposed method can yield response PSDs with both the transient-state and the steady-state components. The proposed method can accurately compute time-varying response PSDs of structures subjected to short-duration nonstationary excitations.