| Popis: |
For the seismic design of some important structures, such as reactors in Nuclear Power Plants, it is often required by the regulatory bodies the generation of artificial time-histories compatible with a given design response spectrum. These artificial time histories shall retain the characteristics of actual seismic records. The purpose of this paper is to present a methodology for the generation of such time histories, circumventing some problems that frequently occur using more usual methodologies. The basis of this methodology is the traditional procedure due to Levy and Wilkinson. In this methodology, the time-histories are defined as a superposition of harmonic components distributed in a typical range of frequencies. The aleatory character of the process is assured through randomically generated phase angles; amplitudes of the harmonic components are iteratively adjusted until a good agreement with the design spectrum is achieved. An envelope curve in time is applied in order to simulate the typical periods of increase and decay of the accelerograms. Some details in this traditional methodology are herein improved in order to circumvent some frequent numerical problems. The following steps are followed: a) generation of the time-history following Levy-Wilkinson procedure, adjusting frequency amplitudes recursively up to a good adjustment to the given response spectrum. The initial values of the frequency components are taken as a function of a power spectrum density function compatible with the given response spectrum. It is found that a linear distance between the considered frequencies produces better results that the non-uniform distribution proposed by USNRC; b) adjust of velocity and displacement values to zero in the beginning and end of the time-history, using a forth degree polynomial function for the displacements with coefficients adjusted by a minimum square numerical process; c) since after this process, accelerations values are not equal to zero in the beginning and end of the time-history, they are manually adjusted in the vicinity of these points; d) after this, a conventional base-line correction is applied, using a fifth degree polynomial function for the displacements. With this, it is drastically reduced the necessary adjustment of step d) and the distortion caused by the high frequency components is practically annulated. The proposed methodology is automatizated in ARTQUAKE, a Mathcad spreadsheet. Examples of generated time-histories are presented, for illustrating the application of the considered procedures. |
