A novel analytical model of power spectral density function coherent with earthquake response spectra

In the most advanced seismic codes earthquake loads are often defined by means of pseudo-acceleration Response Spectra (RS) and the use of modal superposition analysis method is strongly encouraged. The effectiveness of the design procedures is thus limited by the underlying hypotheses, such as the linearity of the system and the reliability of the modal correlation coefficients used to combine the modal responses for MDOF systems. On the other hand, linear systems response statistics could be easily computed by using stochastic analysis tools, once a stochastic characterization of the seismic action is provided. In this paper a few-parameters analytical model for the definition of Power Spectral Density functions (PSD) coherent with Response Spectra is proposed. Closed-form relationships between the parameters involved in the definition of the PSD and the RS defined by several international seismic codes are provided. The reliability of this tool is assessed by means of a numerical campaign by comparing stochastic analysis and Monte-Carlo simulations. By using the proposed approach, the seismic action can be defined both in terms of RS and in terms of PSD, and, therefore, the engineer can choose the most appropriate analysis tool for his purpose