A semi‐empirical method for the evaluation of the statistical characteristics of the mean, variance and the maximum response peak of a single degree of freedom linear system under seismic action is presented. The nonstationary ground motion is modeled filtering a white Gaussian random noise and enveloping the filtered noise by a deterministic shaping function. The linear differential equations for the determination of the spectral moments are examined and a closed‐form solution given. Extensive studies by means of digital simulation are made and the proposed semi‐empirical formulation is compared with other approximate methods available in the literature within the framework of the first passage problem.
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Paola et al. (1985) studied this question.
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