Keywords: compatible accelerogram, response spectra, frequency content.

A number of methods have been devised for generating the time-history of an artificial earthquake whose spectra are replicas of given design response spectra. The methods of Tsai [1] and of Rizzo et al. [2] essentially depend on the manipulation of the amplitude and phase of a Fourier representation of an existing accelerogram trace, for example of the 1940 El Centro N-S record. Using this record as an input, they obtained a trial response spectrum. For frequencies where the trial response spectrum was higher than desired, a filtering action is applied to the initial time history. For frequencies where the trial response was lower than desired, a damped sinusoid of that frequency was added to the initial time-history. The modified time-history was then used to compute a second response spectrum. The process of modifying the time-history and the computation of new response spectra was repeated until a satisfactory agreement between computed and desired response spectra was achieved. The last time-history used was taken as the desired time- history.

In the design of important structures like nuclear power plants, it is desirable in certain instances to use the time-history method of dynamic analysis to determine the plant response to seismic input. In 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, facing with the problem of generating a time-history spectra leads to the problem of generating a time-history whose own response spectrum approximates as possible the originally specified design response spectrum.

The objective of this paper is to propose a method for generating compatible accelerograms that match the design response spectrum through an analytical approach. In the current method, a function for frequency content containing a polynomial with unknown coefficients multiplied by an exponential as a function of loading frequency is considered. The corresponding coefficients are determined by matching the response obtained from the pre-calculated frequency content and the design response spectrum. In addition, the time-history accelerograms are generated, using the inverse Fourier transform applied on the function of frequency content.

If a single degree of freedom system is exerted by an excitation with frequency content , its corresponding point in the response spectrum is determined, multiplying that term by the amplification factor , where is the frequency of the structure. Likewise, for another loading with frequency content , another point in the response spectrum diagram is achieved. Therefore, for a motion containing several frequencies, the resulting response spectrum can be stated, using the superposition law, as the summation of these pre-calculated points or an integral over the range of loading frequencies.

Now, assume that the design response spectrum is considered such as the one in the Iranian Earthquake Code. The design response spectrum contains two discrete functions for two ranges of period of structure, and , in which the associated response spectrum for the first range of period is a constant and for the second range, the response spectrum equals . The problem is now to find functions of frequency content that match the given response spectrum. These functions can be mathematically obtained. Assume that the frequency content function is a product of a polynomial which is considered up to second order terms, and an exponential. Integrating by the product of the obtained frequency content and the amplification factor, and its comparison with the given design response spectrum, features a good fitness.

In addition, using the inverse Fourier transform, the accelerograms can be easily obtained from the frequency contents. Note that to obtain different artificial accelerograms with the same frequency content, it is sufficient to add a phase angle to each frequency in the inverse Fourier integral. There appears, however, to be a good latent possibility of time saving in earthquake response analysis by the method proposed herein.

1

Tsai, N.-C. (1972), "Spectrum-compatible motions for design purposes", J. Eng. Mech. Div., Proc. ASCE 98 (EM2) 345-356

2

Rizzo, P.C., Shaw, D.E., Jarecki, S.J. (1973), "Development of real/synthetic time-histories to match smooth design spectra", Paper K 1/5, Proc. Second International Conference on Structural Mechanics in Reactor Technology, Berlin, Germany.

3

Estekanchi, H.E., Soltani, A., Vafai, A. (2004), "Seismic behavior of steel frames with off-center bracing system", to be presented, 13th World Conference on Earthquake Engineering, August 1-6, 2004, vancouver, B.C., Canada, paper No. 1787.

4

Housner, G.W., Jennings, P.C. (1964.),"Generation of Artificial Earthquakes", Journal of the Engineering Mechanics Division, ASCE, Vol. 90,113-150.

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