Characterization of response spectra through the statistics of oscillator response

Abstract

This paper presents the physical relationships that exist between the response spectra and the Fourier Transform of strong-motion accelerograms through the extreme value statistics of oscillator response. Under the assumption of a stationary response, it has been shown that the spectrum value depends only on two parameters: arms, the root-mean-square-value of the response, and, ɛ, a parameter which measures the distribution of the energy among the various frequencies. The influence of these parameters on the response statistics together with their physical meaning in terms of the oscillator's characteristics have been studied. Comparisons with the Damped Fourier Transform (Udwadia and Trifunac, 1973) computed velocity spectra and the statistically calculated maximum response are presented for three typical accelerograms. The results indicate that response spectra based on statistical computations lead to good first approximations of the actual response to strong ground motion. In addition to characterizing the response spectrum with statistical curves expressing the expected value and the most probable value of the peak response, the 5 and 95 per cent confidence levels are also indicated, thus giving the lower and upper bounds for these statistical spectral estimates. These confidence levels delineate the 90 per cent confidence interval.