考虑一阶系统参与组合的复模态分解反应谱法
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摘要
对地震作用下结构反应的复模态分解反应谱法进行了研究,指出在复模态分解反应谱法中,具有实特征值的模态不必组成二阶振动系统,可按一阶线性系统参与模态组合,且一阶线性系统只需要一条反应谱。给出了相应的复模态完全平方组合(CCQC)系数计算公式,该公式包括了一阶系统响应的相关函数和一阶系统响应与二阶系统响应之间的相关函数。通过算例验证了方法的可行性。
This paper studies the complex modal superposition response spectrum method for analysis of structures under seismic loading.It states that when using complex modal superposition response spectrum method,one mode with real eigenvalue is not necessary to be combined with another real eigenvalue into 2nd order system and can be treated as 1st order system.The peak response solutions of both 2nd order system and 1st order system can be combined together using the complex complete quadratic combination(CCQC) method,and for 1st order system only one response spectrum is needed.Theory of random processes is used to developing the CCQC cross-correlation coefficient formula between 2nd order system and 1st order system.An example structure is used to check the feasibility of the proposed method.
This paper studies the complex modal superposition response spectrum method for analysis of structures under seismic loading.It states that when using complex modal superposition response spectrum method,one mode with real eigenvalue is not necessary to be combined with another real eigenvalue into 2nd order system and can be treated as 1st order system.The peak response solutions of both 2nd order system and 1st order system can be combined together using the complex complete quadratic combination(CCQC) method,and for 1st order system only one response spectrum is needed.Theory of random processes is used to developing the CCQC cross-correlation coefficient formula between 2nd order system and 1st order system.An example structure is used to check the feasibility of the proposed method.
引文
[1]欧进萍,吴斌,龙旭.耗能减振结构的抗震设计方法[J].地震工程与工程振动,1998,18(2):98-107.OU Jinping,WU Bin,LONG Xu.A seismic design methods of passive energy dissipation systems[J].Journal of Earthquake Engineering and Engi-neering Vibration,1998,18(2):98-107.(in Chinese).
[2]黄东梅,李创第.带TMD结构的大阻尼比复振型叠加反应谱法[J].哈尔滨工业大学学报,2009,41(12):181-185.HUANG Dongmei,LI Chuangdi.Complex mode superpositionresponse spectrum method with large damping ratio for structures with TMD[J].Jour-nal of Harbin Institute of Technology,2009,41(12):181-185.(in Chinese)
[3]周锡元,阎维明,杨润林.建筑结构的隔震、减振和振动控制[J].建筑结构学报,2002,(0):2-12.ZHOU Xiyuan,YAN Weiming,YANG Runlin.Seismic base isolation,energy dissipation and vibration control of building structures[J].Journal ofBuilding Structures,2002(2):2-12.(in Chinese)
[4]刘季,阎维明.土-结构相互作用地震反应的非经典振型分解反应谱方法[J].地震工程与工程振动,1987,7(2):25-42.LIU Ji,YAN Weiming.Nonclassical modal analysis response spectrum method for seismic response of soil-structure Interaction[J].Journal ofEarthquake Engineering and Engineering Vibration,1987,7(2):25-42.(in Chinese)
[5]GB50011-2010建筑抗震设计规范[S].北京:中国建筑工业出版社,2010.GB 50011-2010 Code for Seismic Design of Buildings[S].Beijing:China Architecture&Building Press,2010.(in Chinese)
[6]张树传,何玉敖,王亚勇.非比例阻尼线性体系振型组合法适用范围探讨[J].建筑结构,2011,41(5):63-67.ZHANG Shuchuan,HE Yuao,WANG Yayong.Discussion on application scope of mode combination method for non-classically damped linear sys-tem[J].Building Structure,2011,41(5):63-67.(in Chinese)
[7]邹经湘.结构动力学[M].哈尔滨:哈尔滨工业大学出版社,1996.ZOU Jingxiang.Structural dynamics[M].Harbin:Harbin Institute of Technology Press,1996.(in Chinese)
[8]克拉夫,彭津.结构动力学[M].2版.纽约:迈克劳-希尔出版社,1994.Ray Clough,Joseph Penzien.Dynamics of structures[M].2nd ed.New York:McGraw-Hill,1994.
[9]肖帕.结构动力学——理论及其在地震工程中的应用[M].2版.北京:清华大学出版社,2007.Chopra A K,Dynamics of structures,theory and applications to earthquake engineering[M].2nd ed.Beijing:Tsinghua University Press,2007.
[10]闫维明.非正交阻尼体系地震反应的非经典振型分解反应谱方法[J].华南建设学院西院学报,1997(2):9-14.YAN Weiming.Nonclassical modal analysis response spectral method on seismic response of a non-classically damped system[J].Journal ofSouth China Construction University,1997(2):9-14.(in Chinese)
[11]周锡元,马东辉,俞瑞芳.工程结构中的阻尼与复振型地震响应的完全平方组合[J].土木工程学报,2005,38(1):31-39.ZHOU Xiyuan,MA Donghui,YU Ruifang.Damping in structures and complete quadratic combination(CCQC)of complex mode seismic responses[J].China Civil Engineering Journal,2005,38(1):31-39.(in Chinese)
[12]周锡元,俞瑞芳.非比例阻尼线性体系基于规范反应谱的CCQC法[J].工程力学,2006,23(2):10-17.ZHOU Xiyuan,YU Ruifang.CCQC method for seismic response of non-classically damped linear system based on code response spectra[J].Engi-neering Mechanics,2006,23(2):10-17.(in Chinese)
[13]俞瑞芳,周锡元.具有过阻尼特性的非比例阻尼线性系统的复振型分解法[J].建筑结构学报,2006,27(1):50-58.YU Ruifang,ZHOU Xiyuan.Complex mode superposition method for non-classically damped linear system with over-critical damping peculiarity[J].Journal of Building Structures,2006,27(1):50-58.(in Chinese)
[2]黄东梅,李创第.带TMD结构的大阻尼比复振型叠加反应谱法[J].哈尔滨工业大学学报,2009,41(12):181-185.HUANG Dongmei,LI Chuangdi.Complex mode superpositionresponse spectrum method with large damping ratio for structures with TMD[J].Jour-nal of Harbin Institute of Technology,2009,41(12):181-185.(in Chinese)
[3]周锡元,阎维明,杨润林.建筑结构的隔震、减振和振动控制[J].建筑结构学报,2002,(0):2-12.ZHOU Xiyuan,YAN Weiming,YANG Runlin.Seismic base isolation,energy dissipation and vibration control of building structures[J].Journal ofBuilding Structures,2002(2):2-12.(in Chinese)
[4]刘季,阎维明.土-结构相互作用地震反应的非经典振型分解反应谱方法[J].地震工程与工程振动,1987,7(2):25-42.LIU Ji,YAN Weiming.Nonclassical modal analysis response spectrum method for seismic response of soil-structure Interaction[J].Journal ofEarthquake Engineering and Engineering Vibration,1987,7(2):25-42.(in Chinese)
[5]GB50011-2010建筑抗震设计规范[S].北京:中国建筑工业出版社,2010.GB 50011-2010 Code for Seismic Design of Buildings[S].Beijing:China Architecture&Building Press,2010.(in Chinese)
[6]张树传,何玉敖,王亚勇.非比例阻尼线性体系振型组合法适用范围探讨[J].建筑结构,2011,41(5):63-67.ZHANG Shuchuan,HE Yuao,WANG Yayong.Discussion on application scope of mode combination method for non-classically damped linear sys-tem[J].Building Structure,2011,41(5):63-67.(in Chinese)
[7]邹经湘.结构动力学[M].哈尔滨:哈尔滨工业大学出版社,1996.ZOU Jingxiang.Structural dynamics[M].Harbin:Harbin Institute of Technology Press,1996.(in Chinese)
[8]克拉夫,彭津.结构动力学[M].2版.纽约:迈克劳-希尔出版社,1994.Ray Clough,Joseph Penzien.Dynamics of structures[M].2nd ed.New York:McGraw-Hill,1994.
[9]肖帕.结构动力学——理论及其在地震工程中的应用[M].2版.北京:清华大学出版社,2007.Chopra A K,Dynamics of structures,theory and applications to earthquake engineering[M].2nd ed.Beijing:Tsinghua University Press,2007.
[10]闫维明.非正交阻尼体系地震反应的非经典振型分解反应谱方法[J].华南建设学院西院学报,1997(2):9-14.YAN Weiming.Nonclassical modal analysis response spectral method on seismic response of a non-classically damped system[J].Journal ofSouth China Construction University,1997(2):9-14.(in Chinese)
[11]周锡元,马东辉,俞瑞芳.工程结构中的阻尼与复振型地震响应的完全平方组合[J].土木工程学报,2005,38(1):31-39.ZHOU Xiyuan,MA Donghui,YU Ruifang.Damping in structures and complete quadratic combination(CCQC)of complex mode seismic responses[J].China Civil Engineering Journal,2005,38(1):31-39.(in Chinese)
[12]周锡元,俞瑞芳.非比例阻尼线性体系基于规范反应谱的CCQC法[J].工程力学,2006,23(2):10-17.ZHOU Xiyuan,YU Ruifang.CCQC method for seismic response of non-classically damped linear system based on code response spectra[J].Engi-neering Mechanics,2006,23(2):10-17.(in Chinese)
[13]俞瑞芳,周锡元.具有过阻尼特性的非比例阻尼线性系统的复振型分解法[J].建筑结构学报,2006,27(1):50-58.YU Ruifang,ZHOU Xiyuan.Complex mode superposition method for non-classically damped linear system with over-critical damping peculiarity[J].Journal of Building Structures,2006,27(1):50-58.(in Chinese)
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