对应地震反应谱的当量功率谱密度函数的数值算法
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摘要
提出根据地震反应谱曲线求解当量功率谱密度函数曲线的一种数值算法,为结构随机地震反应分析中确定和计算地面运动功率谱密度提供依据。在相对位移谱与结构相对位移响应峰值的均值之间建立联系;在现有迭代方法的基础上,对算法公式作进一步的推导和整理,将迭代计算转变为线性方程组的求解计算,进而避免迭代方法的不收敛。通过对数值计算结果的分析发现,由于规范反应谱曲线存在斜率突变,采用本文算法计算出的功率谱密度曲线在规范反应谱曲线的两端和分段转折点处会出现倍周期分岔甚至混沌现象。为此建议适当增加低频范围内离散频率点的数目,且采取整体光滑的反应谱曲线,从而提高计算结果的稳定性。
A numerical algorithm,by which the seismic power spectral density can be determined according to the response spectrum,is proposed in this paper.It is used to calculate the power spectral density of ground motions in structural random seismic response analysis.A connection is established between the relative displacement spectrum and the mean value of the peak relative displacement responses.Based on the existing iterative method,the formulas are further developed,and the traditional iterative calculation procedure is replaced by solving a linear system of equations to avoid non-convergence problem.It is found from the numerical results that because of the slope saltation of the response spectrum,period doubling bifurcation,and even chaos occur at piecewise points and endpoints of the seismic power spectral density curves obtained from the proposed algorithm.Therefore,suggestions are made that appropriately increasing the number of discrete frequency points in low frequency range and adopting global smooth response spectrum curves during calculation can improve the stability of the results.
A numerical algorithm,by which the seismic power spectral density can be determined according to the response spectrum,is proposed in this paper.It is used to calculate the power spectral density of ground motions in structural random seismic response analysis.A connection is established between the relative displacement spectrum and the mean value of the peak relative displacement responses.Based on the existing iterative method,the formulas are further developed,and the traditional iterative calculation procedure is replaced by solving a linear system of equations to avoid non-convergence problem.It is found from the numerical results that because of the slope saltation of the response spectrum,period doubling bifurcation,and even chaos occur at piecewise points and endpoints of the seismic power spectral density curves obtained from the proposed algorithm.Therefore,suggestions are made that appropriately increasing the number of discrete frequency points in low frequency range and adopting global smooth response spectrum curves during calculation can improve the stability of the results.
引文
[1]GB 50011-2001建筑抗震设计规范[S].北京:中国建筑工业出版社,2001.
[2]Kaul MK.Stochastic characterization of earthquakes through their response spectrum[J].Earthquake Engineering&Structural Dynamics,1978,6(5):497-509.
[3]Sundararajan C.An iterative method for the generation of seismic power spectral density functions[J].Nuclear Engineering and Design,1980,61(1):13-23.
[4]孙景江,江近仁.与规范反应谱相对应的金井清谱的谱参数[J].世界地震工程,1990,6(1):42-48.
[5]汪梦甫,尹华伟,周锡元.从反应谱求功率谱的精确方法及其应用[J].地震工程与工程振动,2004,24(2):53-58.
[6]曹资,薛素铎.空间结构抗震理论与设计[M].北京:科学出版社,2005.
[7]张猛,张哲,李天.与规范反应谱相对应的Clough-Penzien模型参数研究[J].世界地震工程,2007,23(1):56-60.
[8]江近仁,洪峰.功率谱与反应谱的转换和人造地震波[J].地震工程与工程振动,1984,4(3):1-10.
[9]Davernport AG.Note on the distribution of the largest value of a random function with application to gust loading[C]//Pro Inst Civil Eng,1961,28:187-196.
[10]Clough R W,Penzien J.Dynamics of Structures.3rd Edition[M].Berkeley,CA:Computers&Structures,2004.
[11]Edward L Wilson.Three-Dimensional static and dynamic analysis of structures.[M].3rd ed.Berkeley,CA:Computers&Structures,2002.
[12]刘庆林,傅学怡.反应谱CQC法合理振型数确定的研究[J].建筑结构学报,2006,27(6):87-93.
[13]DGJ08-9-92建筑抗震设计规程[S].上海:上海工程标准定额管理站,1992.
[2]Kaul MK.Stochastic characterization of earthquakes through their response spectrum[J].Earthquake Engineering&Structural Dynamics,1978,6(5):497-509.
[3]Sundararajan C.An iterative method for the generation of seismic power spectral density functions[J].Nuclear Engineering and Design,1980,61(1):13-23.
[4]孙景江,江近仁.与规范反应谱相对应的金井清谱的谱参数[J].世界地震工程,1990,6(1):42-48.
[5]汪梦甫,尹华伟,周锡元.从反应谱求功率谱的精确方法及其应用[J].地震工程与工程振动,2004,24(2):53-58.
[6]曹资,薛素铎.空间结构抗震理论与设计[M].北京:科学出版社,2005.
[7]张猛,张哲,李天.与规范反应谱相对应的Clough-Penzien模型参数研究[J].世界地震工程,2007,23(1):56-60.
[8]江近仁,洪峰.功率谱与反应谱的转换和人造地震波[J].地震工程与工程振动,1984,4(3):1-10.
[9]Davernport AG.Note on the distribution of the largest value of a random function with application to gust loading[C]//Pro Inst Civil Eng,1961,28:187-196.
[10]Clough R W,Penzien J.Dynamics of Structures.3rd Edition[M].Berkeley,CA:Computers&Structures,2004.
[11]Edward L Wilson.Three-Dimensional static and dynamic analysis of structures.[M].3rd ed.Berkeley,CA:Computers&Structures,2002.
[12]刘庆林,傅学怡.反应谱CQC法合理振型数确定的研究[J].建筑结构学报,2006,27(6):87-93.
[13]DGJ08-9-92建筑抗震设计规程[S].上海:上海工程标准定额管理站,1992.
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