Stochastic modeling of the seismic excitation for structural dynamics purposes

Abstract In many structural applications, satisfactory results can be achieved by modeling the time-history of the ground acceleration by a segment of stationary stochastic process. This segment can be modulated by a suitable intensity function in order to make the process non-stationary in time. Attention is focused here on the analytical form of the power spectral density (PSD) function of the stationary process. The classical Kanai-Tajimi PSD characterized by three parameters is often inadequate: experimental data show in fact a multimodal behaviour of the frequency contents. A n -modal PSD function characterized by 3 n parameters is introduced in this paper. The evaluation of the model parameters is made possible by the knowledge of closed-form expressions for the spectral moments of any order of the PSD considered. For this purpose the spectral moments are defined over a finite range of the frequency axis (0, ω u ). The results are strongly influenced by the value given to this upper-limit but, in seismic engineering, ω u is actually defined by the way in which the ground motions are recorded and handled. Application of the closed-form expressions for the spectral moments to other fields where ω u is not a priori known requires an additional preliminary analysis of the frequency range to be considered.