基于三角函数内插法的波动反应谱计算精度分析
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摘要
以反应谱基本概念和线性插值法为理论基础提出了求解波动反应谱的三角函数内插法。推导了反应谱计算公式,建立了时间间隔相等的三角函数内插法的连锁递推反应谱计算公式。对简谐波动荷载进行三角函数内插法、解析法和"精确法"的反应谱计算,结果表明:采用三角函数内插法的反应谱计算值比反应谱计算方法(精确法)计算值更接近解析解,且计算精度更高。利用三角函数内插法对两条实际记录的波动加速度时程曲线进行反应谱的数值计算。分析表明:基于三角函数内插法得到的各反应谱值是稳定的,其反应谱值一般稍大于线性内插法所得结果,精度满足要求,能在一定程度上简化计算。
On the basis of the basic concept of response spectrum and linear interpolation method,the trigonometric interpolation method is proposed to solve the fluctuation response spectrum.Firstly,the calculation formula of response spectrum is deduced,and chain recursive formula of the response spectrum calculation in equal time interval is established.The response spectrum of the simple harmonic dynamic load is calculated by trigonometric interpolation method,the analytical method and "precision method".The comparative analysis results show that the spectrum response value got by trigonometric interpolation is closer than that got by "precision method" to the analytical solve,which is of higher precision.The numerical calculation is carried out on the spectrum response of the fluctuation acceleration curve of two actual records by trigonometric interpolation.The results showed that,the response spectrum values got by trigonometric interpolation method are stable,and the response spectrum values are generally slightly larger than the results obtained by the linear interpolation method.The response spectrum values got by trigonometric interpolation method meet the requirements of accuracy,which simplifies calculation to a certain extent.
On the basis of the basic concept of response spectrum and linear interpolation method,the trigonometric interpolation method is proposed to solve the fluctuation response spectrum.Firstly,the calculation formula of response spectrum is deduced,and chain recursive formula of the response spectrum calculation in equal time interval is established.The response spectrum of the simple harmonic dynamic load is calculated by trigonometric interpolation method,the analytical method and "precision method".The comparative analysis results show that the spectrum response value got by trigonometric interpolation is closer than that got by "precision method" to the analytical solve,which is of higher precision.The numerical calculation is carried out on the spectrum response of the fluctuation acceleration curve of two actual records by trigonometric interpolation.The results showed that,the response spectrum values got by trigonometric interpolation method are stable,and the response spectrum values are generally slightly larger than the results obtained by the linear interpolation method.The response spectrum values got by trigonometric interpolation method meet the requirements of accuracy,which simplifies calculation to a certain extent.
引文
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[2]Nigam N C,Jennings P C.Calculation of response spectra fromstrong-motion earthquake records[J].Bulletin of the SeismologicalSociety of America,1969,59(2):909-922.
[3]谢旭.桥梁结构地震响应分析与抗震设计[M].北京:人民交通出版社,2006.Xie Xu.Seismic Response and Earthquake Resistant Design ofBridges[M].Beijing:China Communications Press,2006.
[4]庄表中,梁以德,张佑启.结构随机振动[M].北京:国防工业出版社,1993.Zhuang Biaozhong,Liang Yide,Zhang Youqi.Random Vibration ofStructures[M].Beijing:National Defense Industry Press,1993.
[5]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,1990,10(2):47-50.Li Dahua.Successive computation formulation of earthquake responsespectrum[J].Earthquake Engineering and Engineering Vibration,1990,10(2):47-50.
[6]李大华,底青云.地震反应谱数值计算方法的研究[J].中国地震,1992,8(1):1-8.Li Dahua,Di Qingyun.On numerical algorithm of earthquake responsespectra[J].Earthquake Research in China,1992,8(1):1-8.
[7]张德丰.MATLAB数值计算方法[M].北京:机械工业出版社,2010.Zhang Defeng.MATLAB Numerical Method[M].Beijing:China Ma-chine Press,2010.
[8]陈国兴,庄海洋.基于抛物线内插的反应谱计算公式及其精度分析[J].防灾减灾工程学报,2003,23(3):56-61.Chen Guoxing,Zhuang Haiyang.Computation formulas of the earth-quake response spectra based on parabolic interpolation method andthe analysis of its precision[J].Journal of Disaster Prevention andMitigation Engineering,2003,23(3):56-61.
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