Explicit closed-form solution for the evolutionary power spectral density function of the stochastic response of structures subjected to artificial accelerograms consistent with pulse-like ground motions

The near-fault pulse-like ground motions are of great practical interest in seismic engineering. In fact, they tend to cause more serious damage to some types of structures than ordinary ground motions. However, the limited availability of pulse-like records significantly constrains studies involving the randomness of ground motion, such as reliability analysis. To address the scarcity of records, ground motion simulation methods should be used. In the literature, the most efficient one, according to the theory of random processes, is based on the generation of artificial accelerograms as samples of fully non-stationary Gaussian processes. By operating in this way, it is possible to reproduce the typical characteristics of recorded time histories, with both temporal and spectral nonstationarities, which fill the absence of available actual data. In this framework, the authors recently proposed a new model of the evolutionary power spectral density (EPSD) function to generate artificial accelerograms in such a way that a given target accelerogram can be considered as one of its own samples. The EPSD function can be simply evaluated once the frequency of peaks, the zero-level up-crossings, and the total energy of the target accelerogram are determined. This approach, previously applied to the case of ordinary accelerograms, is here extended to pulse-like ones. To effectively achieve this extension, some measures must be taken in the definition of the modulating function and the sub-processes that characterize the EPSD function. In this study, once the way to define the EPSD function of the input process is described, a procedure to evaluate in explicit closed form the EPSD function of the output process, in terms of displacements and velocities of the structural response, is proposed. Finally, the statistics of the structural response are evaluated, and a reliability analysis is performed in order to demonstrate the accuracy and efficiency of the proposed formulation.