Matlab程序计算反应谱的误差分析
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摘要
基于反应谱计算的基本原理,对于单自由度弹性体系在水平地震运动g(t)作用下的动力平衡微分方程,分别使用gradient和diff进行计算,并与使用cumtrapz命令积分计算的精确计算反应谱积分公式和简化的反应谱计算积分公式值进行了比较,g(t)分别选取了实测的爆炸震动数据和天然地震数据,经过计算发现,对于高频比较显著的爆炸震动波,用上述方法计算出的反应谱在低频部分有小的差别,对反应谱的整体特征影响不大。但对于低频比较显著的天然地震波,用cumtrapz积分计算的积分公式与用diff命令计算的微分方程结果接近,用gradient命令计算的结果误差较大,因此在计算富于低频的震动波的反应谱时,用gradient命令求微分方程是不合适的。
Based on the basic theory of response spectrum calculation, the response of a single-degree-of-freedom elastic system under the excitation of horizontal ground motion is calculated using the programs of 'gradient' and 'diff' in Matlab. And the results are compared with that from exact integral formula and predigest integral formula using the 'cumtrapz' program. Both real blast earthquakes and natural earthquakes are used as . The results show that for blast earthquake, which is rich of high-frequency contents, the response spectra calculated from the four methods have small differences at low frequencies, and it is considered the four methods has little influence on the overall response spectra; for natural earthquake, which is rich of low-frequency contents, the results calculated from 'cumtrapz' and 'diff'are similar, whereas large differences are found for the results from 'gradient'. It suggests that the 'gradient' program in Matlab may be unsuitable for the calculation of response spectrum.
Based on the basic theory of response spectrum calculation, the response of a single-degree-of-freedom elastic system under the excitation of horizontal ground motion is calculated using the programs of 'gradient' and 'diff' in Matlab. And the results are compared with that from exact integral formula and predigest integral formula using the 'cumtrapz' program. Both real blast earthquakes and natural earthquakes are used as . The results show that for blast earthquake, which is rich of high-frequency contents, the response spectra calculated from the four methods have small differences at low frequencies, and it is considered the four methods has little influence on the overall response spectra; for natural earthquake, which is rich of low-frequency contents, the results calculated from 'cumtrapz' and 'diff'are similar, whereas large differences are found for the results from 'gradient'. It suggests that the 'gradient' program in Matlab may be unsuitable for the calculation of response spectrum.
引文
[1]R.W.Clough,J.Penzien.DYNAMICS OF STRUCTURES[M].McGraw-Hill Inc.,1975.
[2]高振世,朱澄清,唐九如,等.建筑结构抗震设计[M].中国建筑工业出版社,1995.
[3]严东晋.后勤科研项目立项论证报告[R].总后勤部基建营房部,2007.
[4]Duane Hanselman,Bruce Littlefield.Mastering Matlab7[M].Pearson Education,Inc.,2005.
[2]高振世,朱澄清,唐九如,等.建筑结构抗震设计[M].中国建筑工业出版社,1995.
[3]严东晋.后勤科研项目立项论证报告[R].总后勤部基建营房部,2007.
[4]Duane Hanselman,Bruce Littlefield.Mastering Matlab7[M].Pearson Education,Inc.,2005.
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