工程结构中的阻尼与复振型地震响应的完全平方组合
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摘要
对工程结构中阻尼矩阵的简化处理途径做了简要评述 ,指出目前常用的比例阻尼理论对于小阻尼结构是适用的。但是随着机械阻尼器在结构工程中的广泛应用 ,结构的阻尼矩阵不再满足可以按照相应无阻尼结构振型解耦的条件 ,此时的振型是由实部和虚部组成的复数形式。由于缺乏基于反应谱的复振型地震反应叠加分析方法 ,也是为了简单起见 ,在抗震设计规范中建议采用强迫解耦的近似分析方法。文中对强迫解耦方法的基本概念和适用性进行了探讨 ,指出在一般情况下这一方法是可以接受的 ,但是对于过阻尼和其它特殊情况 ,误差也是比较大的。为了避免这样的误差 ,可以采用文中推荐的基于复振型的完全平方组合 (CCQC)方法。与目前常用的CQC法相比 ,文中建议的CCQC法是按照同样的假定在复振型条件下推导出来的近似分析方法 ,完全避免了复数运算 ,表达方式也一样简单实用 ,因此很适合在实际工程和抗震设计规范中应用。此外文中还讨论和介绍了在比例阻尼和非比例阻尼条件下如何将CQC和CCQC方法加以推广应用于多维地震输入的情况
A simplified approach in dealing with damping in structures is reviewed in this paper.It is pointed out that the proportional damping theory is adaptable for small damping structures.However as the mechanical damper is widely employed in structure engineering,the structural damping no longer satisfies the decoupling condition corresponding to the structural modes without damping,and the modes usually are in terms of complex variables.Due to the lack of complex mode response spectral superposition methodology for non-proportional damping systems and the purpose of simplification as well,the forced decoupling approach is proposed in seismic design code.The discussion in this paper is pointing out the basic concept and availability of the forced decoupling approach.It is pointed out that this approach is adoptable in general but considerable errors would be involved in case of very large damping.In order to avoid such errors,adopting complex complete quadratic combination (CCQC) method based on complex modes is a good solution.Comparing with normal complete quadratic combination (CQC) method,the proposed CCQC method is an approximate method based on the same assumptions as normal CQC method.It is also as concise as normal CQC and completely free of complex value calculation,and thus is adaptive in seismic design code.In addition,how to popularize these methods including CQC and CCQC methods into multi-component earthquake input is discussed and reviewed in this paper.
A simplified approach in dealing with damping in structures is reviewed in this paper.It is pointed out that the proportional damping theory is adaptable for small damping structures.However as the mechanical damper is widely employed in structure engineering,the structural damping no longer satisfies the decoupling condition corresponding to the structural modes without damping,and the modes usually are in terms of complex variables.Due to the lack of complex mode response spectral superposition methodology for non-proportional damping systems and the purpose of simplification as well,the forced decoupling approach is proposed in seismic design code.The discussion in this paper is pointing out the basic concept and availability of the forced decoupling approach.It is pointed out that this approach is adoptable in general but considerable errors would be involved in case of very large damping.In order to avoid such errors,adopting complex complete quadratic combination (CCQC) method based on complex modes is a good solution.Comparing with normal complete quadratic combination (CQC) method,the proposed CCQC method is an approximate method based on the same assumptions as normal CQC method.It is also as concise as normal CQC and completely free of complex value calculation,and thus is adaptive in seismic design code.In addition,how to popularize these methods including CQC and CCQC methods into multi-component earthquake input is discussed and reviewed in this paper.
引文
[1] 胡聿贤,周锡元.弹性体系地震反应的振型遇合问题[J],土木工程学报,1964,10(1)
[2] 周锡元,董娣,苏幼坡.非正交阻尼线性振动系统的复振型地震响应叠加分析方法[J],土木工程学报,2003,36(5):30～36
[3] ZhouXY ,YuRFandDongL .TheComplexCompleteQua draticCombination(CCQC)MethodforSeismicResponsesofNonClassicallyDampedLinearMDOFSystem[A].13WCEE[C].No.848,Vancouver,Canada,Aug.16,2004
[4] ZhouXY ,YuRFandDongD .Complexmodesuperpositionalgorithmforseismicresponsesofnon classicallydampedlinearsystem[J].JournalofEarthquakeEngineering,2004,8(4):597～641
[5] 大崎顺彦著,谢礼立等译.振动理论[M].地震出版社,北京,1990
[6] 朱镜清.结构抗震分析原理[M ].北京:地震出版社,2002
[7] FossFK .Co ordinateswhichuncouplethelineardynamicsys tems[J].J.App.Mech.,ASME ,1958,24,361～364
[8] CaugheyAK .Classicalnormalmodesindampedlineardy namicsystems[J].J .App.Mech.,ASME ,1960,27:269～271
[9] CaugheyAKandO’KellyMEJ .Classicalnormalmodesindampedlineardynamicsystems[J].J .App.Mech.,ASME ,1965,32:583～588
[10] HansonRDandSoongTT .Seismicdesignwithsupplementalenergydissipationdevices[M].EERI ,MNO 8,2001
[11] 胡聿贤.地震工程学[M].地震出版社,1988,北京
[12] WilsonEL ,DerKiureghianS ,andBayoEP .Areplace mentfortheSRSSmethodinseismicanalysis[J].Earth quakeEngineeringandStructuralDynamics,1981,9:187～194
[13] CloughRW ,PenzienJ .DynamicsofStructures(Secondedition)[M].McGrawHill,Inc,1993
[14] JamesHM ,NicholsNBAndPhilipsRS ,eds.,TheoryofServomechanics[M],Dover,1965
[15] GB 50011—2001,建筑抗震设计规范[S],2001
[16] 周锡元,高晓安,马东辉.在结构地震反应完全平方组合公式中振型相关系数的简化[J].北京工业大学学报,(待刊)
[17] 沈聚敏,周锡元,高小旺,刘晶波.抗震工程学[M],北京:中国建筑工程出版社,北京,2000
[18] 桂国庆.非比例阻尼结构体系近似解耦分析中的误差研究[J],工程力学,1994,11(4):40～47
[19] 俞瑞芳,周锡元.非比例阻尼弹性结构地震反应强迫解耦方法的理论背景和数值检验[J],工业建筑,2005年,(待刊)
[20] GaoXA ,ZhouXYandWangL .Multi componentseismicanalysisforirregularstructures[A].13WCEE [C].PaperNo.1516,Vancouver,B .C .,Canada,August16,2004
[21] GrecoAandSantiniA .Comparativestudyondynamicanaly sesofnon classicallydampedlinearsystem[J].StructuralEngineeringandMechanics,2002,14(6):679～698
[22] 周锡元.一般有阻尼线性体系地震反应的振型分解方法[A],见中国地震工程研究进展[M],北京:地震出版社,1992
[23] 俞瑞芳,周锡元.非比例阻尼线性系统考虑过阻尼影响的复振型分解法[J],(已投建筑结构学报)
[24] 周锡元,俞瑞芳.非比例阻尼线性系统基于规范反应谱的CCQC法[J],工程力学,2005(待刊)
[25] YUR .F .,WANGL ,LIUHandZHOUXY .TheCCQC3methodformulti componentseismicresponsesofnon classical lydampedirregularstructures[A].2005AmericaStructuresCongress[C],ASCE .No.6064,NewYork,2005
[2] 周锡元,董娣,苏幼坡.非正交阻尼线性振动系统的复振型地震响应叠加分析方法[J],土木工程学报,2003,36(5):30～36
[3] ZhouXY ,YuRFandDongL .TheComplexCompleteQua draticCombination(CCQC)MethodforSeismicResponsesofNonClassicallyDampedLinearMDOFSystem[A].13WCEE[C].No.848,Vancouver,Canada,Aug.16,2004
[4] ZhouXY ,YuRFandDongD .Complexmodesuperpositionalgorithmforseismicresponsesofnon classicallydampedlinearsystem[J].JournalofEarthquakeEngineering,2004,8(4):597～641
[5] 大崎顺彦著,谢礼立等译.振动理论[M].地震出版社,北京,1990
[6] 朱镜清.结构抗震分析原理[M ].北京:地震出版社,2002
[7] FossFK .Co ordinateswhichuncouplethelineardynamicsys tems[J].J.App.Mech.,ASME ,1958,24,361～364
[8] CaugheyAK .Classicalnormalmodesindampedlineardy namicsystems[J].J .App.Mech.,ASME ,1960,27:269～271
[9] CaugheyAKandO’KellyMEJ .Classicalnormalmodesindampedlineardynamicsystems[J].J .App.Mech.,ASME ,1965,32:583～588
[10] HansonRDandSoongTT .Seismicdesignwithsupplementalenergydissipationdevices[M].EERI ,MNO 8,2001
[11] 胡聿贤.地震工程学[M].地震出版社,1988,北京
[12] WilsonEL ,DerKiureghianS ,andBayoEP .Areplace mentfortheSRSSmethodinseismicanalysis[J].Earth quakeEngineeringandStructuralDynamics,1981,9:187～194
[13] CloughRW ,PenzienJ .DynamicsofStructures(Secondedition)[M].McGrawHill,Inc,1993
[14] JamesHM ,NicholsNBAndPhilipsRS ,eds.,TheoryofServomechanics[M],Dover,1965
[15] GB 50011—2001,建筑抗震设计规范[S],2001
[16] 周锡元,高晓安,马东辉.在结构地震反应完全平方组合公式中振型相关系数的简化[J].北京工业大学学报,(待刊)
[17] 沈聚敏,周锡元,高小旺,刘晶波.抗震工程学[M],北京:中国建筑工程出版社,北京,2000
[18] 桂国庆.非比例阻尼结构体系近似解耦分析中的误差研究[J],工程力学,1994,11(4):40～47
[19] 俞瑞芳,周锡元.非比例阻尼弹性结构地震反应强迫解耦方法的理论背景和数值检验[J],工业建筑,2005年,(待刊)
[20] GaoXA ,ZhouXYandWangL .Multi componentseismicanalysisforirregularstructures[A].13WCEE [C].PaperNo.1516,Vancouver,B .C .,Canada,August16,2004
[21] GrecoAandSantiniA .Comparativestudyondynamicanaly sesofnon classicallydampedlinearsystem[J].StructuralEngineeringandMechanics,2002,14(6):679～698
[22] 周锡元.一般有阻尼线性体系地震反应的振型分解方法[A],见中国地震工程研究进展[M],北京:地震出版社,1992
[23] 俞瑞芳,周锡元.非比例阻尼线性系统考虑过阻尼影响的复振型分解法[J],(已投建筑结构学报)
[24] 周锡元,俞瑞芳.非比例阻尼线性系统基于规范反应谱的CCQC法[J],工程力学,2005(待刊)
[25] YUR .F .,WANGL ,LIUHandZHOUXY .TheCCQC3methodformulti componentseismicresponsesofnon classical lydampedirregularstructures[A].2005AmericaStructuresCongress[C],ASCE .No.6064,NewYork,2005
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