Generation of artificial time-histories, rich in all frequencies, from given response spectra

Abstract

In the design of nuclear power plants, it has been found desirable in certain instances to use the time-history method of dynamic analysis to determine the plant response to seismic input. In the implementation of this method, it is necessary to determine an adequate representation of the excitation as a function of time. Because many design criteria are specified in terms of design response spectra, one is faced with the problem of generating a time-history spectra, one is faced with the problem of generating a time-history whose own response spectrum approximates as possible the originally specified design response spectrum. One objective of this paper is to present a method of synthesizing such time-histories from a given design response spectrum. The design response spectra may be descriptive of floor responses at a particular location in a plant, or they may be descriptive of seismic ground motions at a plant site. The method to be described in this paper allows the generation of time-histories that are rich in all frequencies in the spectrum. This richness is achieved by choosing a large number of closely-spaced frequency points such that the half-power points of adjacent frequencies overlap. Examples are given concerning seismic design response spectra, and a number of points are discussed concerning the effect of frequency spacing on convergence. In generating time-history representations of seismic ground motions, two points demand particular attention. First, the time-history should be recognizable as a realistic earthquake motion which is achieved in the present approach by the introduction of a modulating envelope. The second point arises when it is desired to excite the plant structural model with simultaneous seismic excitation components in two perpendicular horizontal directions and in the vertical direction. Usually the specified vertical spectrum differs from the horizontal spectrum, so that the corresponding time-histories differ as well. However, it is desirable in any event to generate two horizontal time-histories, which should be as unrelated as are earthquake records themselves. Statistically, one desires that their correlation coefficients should be low. In the second section of this paper, a method is suggested for generating a second time-history from the first time-history such that they have low correlation, while at the same time they have response spectra that approximate to a satisfactory degree the original design response spectrum. Finally, a number of alternative schemes of dual time-history generation are inspected, and the resulting correlation functions and spectra are discussed.