基于抛物线内插的反应谱计算公式及其精度分析
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摘要
基于反应谱的基本概念,对基于抛物线内插法的反应谱计算公式进行了严格的推导,并给出了详细的显式表达式,建立了当计算时间等步长离散时的基于抛物线内插法的反应谱计算连锁公式。通过对比简谐波输入时的反应谱计算结果,证明基于抛物线内插法的连锁公式的计算结果比广泛应用的反应谱计算方法"精确法"计算的结果更接近于解析解,有更高的计算精度。同时对多条实际记录的地震加速度时程进行了反应谱对比计算,结果表明该公式在计算反应谱时也是稳定的。作者同时发现,"精确法"计算的反应谱值与实际值相比一般是偏小的。
In this paper, the computation formulas of the earthquake response spectra based on parabolic interpolation method are derived, and the visual expressions of the formulas are presented in detail. With equal step length of time to discrete the earthquake records, the successive computation formulas of earthquake response spectra are presented according to the idea founded by prof.Wang Qianxin in 1962 based on the parabolic interpolation method. By analysing the results calculated by these different methods, it is proved that the values of earthquake response spectra obtained by the method presented in this paper are more close to the analytic values than that of the exact computation method presented by Nigan and Jennings(1969). At the same time, it is found that the values of the exact computation method are smaller than the actual values.
In this paper, the computation formulas of the earthquake response spectra based on parabolic interpolation method are derived, and the visual expressions of the formulas are presented in detail. With equal step length of time to discrete the earthquake records, the successive computation formulas of earthquake response spectra are presented according to the idea founded by prof.Wang Qianxin in 1962 based on the parabolic interpolation method. By analysing the results calculated by these different methods, it is proved that the values of earthquake response spectra obtained by the method presented in this paper are more close to the analytic values than that of the exact computation method presented by Nigan and Jennings(1969). At the same time, it is found that the values of the exact computation method are smaller than the actual values.
引文
[1] 朱 敏,朱镜清.反应谱计算的三角插值解析公式法[J].世界地震工程,2001(3):62-64.
[2] 李大华.计算地震反应谱的连锁公式[J].地震工程与工程振动,1999(2):47-52.
[3] 王前信.计算反应谱的一种简便方法[A].中国科学院土木建筑研究所地震工程研究报告集(第一集)[C].北京:地震出版社,1962.
[4] 谢礼立,于双久编著.强震观测与分析原理[M].北京:地震出版社,1983.
[5] N.C.NigamandP.C.Jennings.Calculationofre-sponsefromstrong-motionearthquakerecords[J].BSSA,1969,59(2):909-922.~~
[2] 李大华.计算地震反应谱的连锁公式[J].地震工程与工程振动,1999(2):47-52.
[3] 王前信.计算反应谱的一种简便方法[A].中国科学院土木建筑研究所地震工程研究报告集(第一集)[C].北京:地震出版社,1962.
[4] 谢礼立,于双久编著.强震观测与分析原理[M].北京:地震出版社,1983.
[5] N.C.NigamandP.C.Jennings.Calculationofre-sponsefromstrong-motionearthquakerecords[J].BSSA,1969,59(2):909-922.~~
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