Calculation of Power Spectra from Response Spectra

Abstract

A method is presented to determine the power spectral density functions from given smooth response spectra. It is assumed that the underlying excitations constitute a stationary Gaussian random process. The relationship between the response spectrum and the power spectral density function is established by the probability distribution of the extreme values. The power spectral density function is discretized by parameters and piecewise polynomials and the free parameters are determined iteratively by a least square fit. Due to this discretization all required integrations can be carried out analytically. It is also possible to obtain a least square fit value of the duration of the stationary output process. The numerical examples include the calculation of the power spectral density functions for selected response spectra.