Time–frequency varying response functions of non-classically damped linear structures under fully non-stationary stochastic excitations

Abstract

In order to reproduce typical characteristics of real earthquake ground-motion time histories, the seismic excitation should be modelled as a fully non-stationary stochastic process. For non-stationary input the time–frequency varying response (TFR) function plays a central role in the evaluation of the spectral characteristics of non-stationary response processes. In fact, by means of this function, it is possible to evaluate in explicit form the evolutionary power spectral density (EPSD) matrix function of the response and consequently the non-geometric spectral moments (NGSM s), which are required in the prediction of the safety of structural systems subjected to non-stationary random excitations.It has been recently recognized that by using supplemental devices it is possible to enhance the performance of structural systems exposed to seismic hazard. However, the introduction of supplemental devices into structures modifies their physical characteristics so that the common assumption of classical or proportional damping is inadequate. It follows that these modified structures must be correctly analysed as non-classically damped ones. To do this the complex modal analysis, which performs the modal superposition in terms of complex eigenvalues and eigenvectors, must be adopted.In this paper a method to evaluate in explicit closed-form solution the TFR vector function as well as the EPSD matrix function of the response of linear non-classically damped structural systems under fully non-stationary excitations is proposed.