基于复阻尼假定的不同材料阻尼特性混合结构抗震分析反应谱CCQC法
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摘要
寻求合理高效的方法求得构件材料阻尼特性不同结构的地震作用及其效应是工程抗震界最为关注的问题之一。近年来提出的反应谱CCQC法(Complex Complete Quadratic Combination)使问题得到了基本令人满意的解决,该法是基于黏性阻尼假定得到的,但黏性阻尼假定存在能量耗散与激振频率有关的缺陷,导致结构高频模态地震作用效应偏小。复阻尼假定避免了黏性阻尼假定的不足,但通常求得的地震作用效应为复数,不便于工程上应用。采用虚拟激励法推导出新的适合复阻尼假定和平稳随机地震动反应谱CCQC法原始表达式(Original Complex Complete Quadratic Combination,OCCQC)和传统简化表达式(Traditional Complex Complete Quadratic Combination,TCCQC),两个表达式计算结果均为实数,易于工程上应用。与平稳随机振动分析结果相比,OCCQC计算结果较接近,TCCQC计算结果偏小,说明OCCQC比TCCQC更为合理。此外,还借助模态有效质量系数提出模态截断控制方法。
One of the most concerned problems in seismic engineering is to seek reasonable and efficient method to obtain earthquake action and its effects on structures of different material damping characteristics in components.In recent years,a method called response spectrum CCQC(Complex Complete Quadratic Combination) based on viscous damping assumption has been put forward and proved to be in general a satisfactory method to solve the above problem.But viscous damping assumption has disadvantages,e.g.,the energy dissipation is related to excitation frequencies,so that earthquake effects of high frequencies may be less than reality.Complex damping assumption can avoid the disadvantages of the viscous damping assumption,but usually it brings out complex form results which may be inconvenient to use.Based on assumptions of complex damping and stationary random excitation process,a pseudo-excitation method was used to acquire a new expression of complex complete quadratic combination method(OCCQC) and its simplified form according to the traditional approach(TCCQC).Results of both expressions are in real format,and can be easily used in engineering.Comparing with the results of stationary random vibration analysis,the results of OCCQC were in good agreement,while the results of TCCQC are much less,which shows that OCCQC is more rational than TCCQC.Futhermore,practical method for truncation of modes was also put forth by way of modal effective mass factor.
One of the most concerned problems in seismic engineering is to seek reasonable and efficient method to obtain earthquake action and its effects on structures of different material damping characteristics in components.In recent years,a method called response spectrum CCQC(Complex Complete Quadratic Combination) based on viscous damping assumption has been put forward and proved to be in general a satisfactory method to solve the above problem.But viscous damping assumption has disadvantages,e.g.,the energy dissipation is related to excitation frequencies,so that earthquake effects of high frequencies may be less than reality.Complex damping assumption can avoid the disadvantages of the viscous damping assumption,but usually it brings out complex form results which may be inconvenient to use.Based on assumptions of complex damping and stationary random excitation process,a pseudo-excitation method was used to acquire a new expression of complex complete quadratic combination method(OCCQC) and its simplified form according to the traditional approach(TCCQC).Results of both expressions are in real format,and can be easily used in engineering.Comparing with the results of stationary random vibration analysis,the results of OCCQC were in good agreement,while the results of TCCQC are much less,which shows that OCCQC is more rational than TCCQC.Futhermore,practical method for truncation of modes was also put forth by way of modal effective mass factor.
引文
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[3]Xu J.A synthesis formulation of explicit damping matrix fornon-classically damped systems[J].Nuclear Engineeringand Design,2004,227(2):125-132
[4]Bilbao A,Aviles R,Agirrebeitia J,et al.Proportionaldamping approximation for structures with addedviscoelastic dampers[J].Finite Elements in Analysis andDesign,2006,42(6):492-502
[5]Zhou Xiyuan,Yu Ruifang,DongDi.Complexmodesuperpositionalgorithm for seismic response of non-classically damped linearMDOF system[J].Journal of Earthquake Engineering,2004,8(4):597-641
[6]周锡元,董娣,苏幼波.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(Zhou Xiyuan,Dong Di,Su Youbo.Newmethod for linear systems with non-classical damping underground motion[J].China Civil Engineering Journal,2003,36(5):30-36(in Chinese))
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[10]俞瑞芳,周锡元.非比例阻尼线性体系地震响应的部分平方组合(CPQC)法[J].土木工程学报,2006,39(11):43-49(Yu Ruifang,Zhou Xiyuan.A complex partialquadratic combination(CPQC)method for seismicresponses of non-classically damped linear system[J].China Civil Engineering Journal,2006,39(11):43-49(inChinese))
[11]朱镜清.关于复阻尼理论的两个基本问题[J].固体力学学报,1992,13(2):113-118(Zhu Jingqing.On the twobasic problems of complex damping theory[J].ChineseJournal of Solid Mechanics,1992,13(2):113-118(inChinese))
[12]丁海平,刘长和.复阻尼理论的一点注记[J].地震工程与工程振动,2001,21(1):61-63(Ding Haiping,LiuChanghe.A note on complex damping theory[J].Earthquake Engineering and Engineering Vibration,2001,21(1):61-63(in Chinese))
[13]何钟怡,廖振鹏,王小华.关于复阻尼理论的几点注记[J].地震工程与工程振动,2002,22(1):1-6(HeZhongyi,Liao Zhenpeng,Wang Xiaohua.Some notes ontheory of complex damping[J].Earthquake Engineeringand Engineering Vibration,2002,22(1):1-6(inChinese))
[14]Clough R W,Penzien J.Dynamics of structures[M].3rdEdition.Berkeley,California,USA:Computers andStructures,Inc.,2003
[15]曹树谦,张文德,萧龙翔.振动结构模态分析[M].天津:天津大学出版社,2001
[16]林家浩,张亚辉.随机振动的虚拟激励法[M].北京:科学出版社,2004
[17]朱镜清,朱敏.复阻尼地震反应谱的计算方法及其它[J].地震工程与工程振动,2000,20(2):19-23(ZhuJingqing,Zhu Min.Calculation of complex dampingresponse spectra from earthquake records[J].EarthquakeEngineering and Engineering Vibration,2000,20(2):19-23(in Chinese))
[18]朱敏,朱镜清.复阻尼地震反应谱计算的再研究[J].地震工程与工程振动,2001,21(2):36-40(Zhu Min,ZhuJingqing.Further studies on calculation of complexdamping response spectra[J].Earthquake Engineering andEngineering Vibration,2001,21(2):36-40(inChinese))
[19]朱敏,朱镜清.复阻尼振动方程频域解法中有关问题的研究[J].世界地震工程,2004,20(2):23-28(Zhu Min,Zhu Jingqing.Some problems in frequency domain solutionof complex damping system[J].World EarthquakeEngineering,2004,20(2):23-28(in Chinese))
[20]朱镜清,朱敏.复阻尼多自由度系统动力分析的模态叠加法[J].地震工程与工程振动,2004,24(2):55-58(ZhuJingqing,Zhu Min.Two mode-superposition methods fordynamic analysis of MDOF systems with complex dampingcharacteristics[J].Earthquake Engineering andEngineering Vibration,2004,24(2):55-58(inChinese))
[21]Kiureghian A D.A response spectrum method for randomvibration analysis of MDF systems[J].EarthquakeEngineering and Structural Dynamics,1981,9(5):419-435
[22]Kiureghian A D.Structural response to stationary excitation[J].Journal of the Engineering Mechanics Division,1980,106(6):1195-1213
[23]Davenport A G.Note on the distribution of the largest valueof a random function with application to gust loading[J].Proceedings of Institution of Civil Engineers,1964,28:187-196
[24]GB 50011—2001建筑抗震设计规范[S].北京:中国建筑工业出版社,2001(GB 50011—2001 Code for seismicdesign of buildings[S].Beijing:China Architecture&Building Press,2001(in Chinese))
[25]Song J W,Chu Y L,Liang Z,et al.Modal analysis ofgenerally damped linear structure subjected to seismicexcitation[R].New York:University at Buffalo,StateUniversity of New York,2008
[26]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(Liu Qinglin,FuXueyi.Study on determination of reasonable mode numbersfor response spectrum CQC method[J].Journal of BuildingStructures,2006,27(6):87-93(in Chinese))
[27]MSC.Nastran version 68:basic dynamic analysis user’sguide[M].Santa Ana,USA:MSC SoftwareCorporation,2005
[28]MSC.Nastran version70:advanced dynamic analysis user’sguide[M].Santa Ana,USA:MSC Software Corporation,2005
[29]MSC.Random user’s guide[M].Santa Ana,USA:MSCSoftware Corporation,2004
[30]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,1990,8(1):42-48(SunJingjiang,Jiang Jinren.Parameters of Kanai-Tajimispectrum consistent with state code[J].World EarthquakeEngineering,1990,8(1):42-48(in Chinese))
[31]傅学怡.整浇钢筋混凝土建筑结构抗震设计理念探究[J].建筑结构,2005,35(5):9-12(Fu Xueyi.Updatephilosophy of cast-in-situ RC building structure aseismicdesign[J].Building Structure,2005,35(5):9-12(inChinese))
[2]Lee D G,Hong S,Kim J.Efficient seismic analysis ofbuilding structures with added viscoelastic dampers[J].Engineering Structures,2002,24(9):1217-1227
[3]Xu J.A synthesis formulation of explicit damping matrix fornon-classically damped systems[J].Nuclear Engineeringand Design,2004,227(2):125-132
[4]Bilbao A,Aviles R,Agirrebeitia J,et al.Proportionaldamping approximation for structures with addedviscoelastic dampers[J].Finite Elements in Analysis andDesign,2006,42(6):492-502
[5]Zhou Xiyuan,Yu Ruifang,DongDi.Complexmodesuperpositionalgorithm for seismic response of non-classically damped linearMDOF system[J].Journal of Earthquake Engineering,2004,8(4):597-641
[6]周锡元,董娣,苏幼波.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(Zhou Xiyuan,Dong Di,Su Youbo.Newmethod for linear systems with non-classical damping underground motion[J].China Civil Engineering Journal,2003,36(5):30-36(in Chinese))
[7]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 response[J].ChinaCivil Engineering Journal,2005,38(1):31-39(inChinese))
[8]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):9-17(ZhouXiyuan,Yu Ruifang.CCQC method for seismic response ofnon-classically damped linear system based on coderesponse spectra[J].Engineering Mechanics,2006,23(2):9-17(in Chinese))
[9]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):50-59(Yu Ruifang,Zhou Xiyuan.Complex modesuperposition method for non-classically damped linearsystem with over-critical damping peculiarity[J].Journalof Building Structures,2006,27(1):50-59(inChinese))
[10]俞瑞芳,周锡元.非比例阻尼线性体系地震响应的部分平方组合(CPQC)法[J].土木工程学报,2006,39(11):43-49(Yu Ruifang,Zhou Xiyuan.A complex partialquadratic combination(CPQC)method for seismicresponses of non-classically damped linear system[J].China Civil Engineering Journal,2006,39(11):43-49(inChinese))
[11]朱镜清.关于复阻尼理论的两个基本问题[J].固体力学学报,1992,13(2):113-118(Zhu Jingqing.On the twobasic problems of complex damping theory[J].ChineseJournal of Solid Mechanics,1992,13(2):113-118(inChinese))
[12]丁海平,刘长和.复阻尼理论的一点注记[J].地震工程与工程振动,2001,21(1):61-63(Ding Haiping,LiuChanghe.A note on complex damping theory[J].Earthquake Engineering and Engineering Vibration,2001,21(1):61-63(in Chinese))
[13]何钟怡,廖振鹏,王小华.关于复阻尼理论的几点注记[J].地震工程与工程振动,2002,22(1):1-6(HeZhongyi,Liao Zhenpeng,Wang Xiaohua.Some notes ontheory of complex damping[J].Earthquake Engineeringand Engineering Vibration,2002,22(1):1-6(inChinese))
[14]Clough R W,Penzien J.Dynamics of structures[M].3rdEdition.Berkeley,California,USA:Computers andStructures,Inc.,2003
[15]曹树谦,张文德,萧龙翔.振动结构模态分析[M].天津:天津大学出版社,2001
[16]林家浩,张亚辉.随机振动的虚拟激励法[M].北京:科学出版社,2004
[17]朱镜清,朱敏.复阻尼地震反应谱的计算方法及其它[J].地震工程与工程振动,2000,20(2):19-23(ZhuJingqing,Zhu Min.Calculation of complex dampingresponse spectra from earthquake records[J].EarthquakeEngineering and Engineering Vibration,2000,20(2):19-23(in Chinese))
[18]朱敏,朱镜清.复阻尼地震反应谱计算的再研究[J].地震工程与工程振动,2001,21(2):36-40(Zhu Min,ZhuJingqing.Further studies on calculation of complexdamping response spectra[J].Earthquake Engineering andEngineering Vibration,2001,21(2):36-40(inChinese))
[19]朱敏,朱镜清.复阻尼振动方程频域解法中有关问题的研究[J].世界地震工程,2004,20(2):23-28(Zhu Min,Zhu Jingqing.Some problems in frequency domain solutionof complex damping system[J].World EarthquakeEngineering,2004,20(2):23-28(in Chinese))
[20]朱镜清,朱敏.复阻尼多自由度系统动力分析的模态叠加法[J].地震工程与工程振动,2004,24(2):55-58(ZhuJingqing,Zhu Min.Two mode-superposition methods fordynamic analysis of MDOF systems with complex dampingcharacteristics[J].Earthquake Engineering andEngineering Vibration,2004,24(2):55-58(inChinese))
[21]Kiureghian A D.A response spectrum method for randomvibration analysis of MDF systems[J].EarthquakeEngineering and Structural Dynamics,1981,9(5):419-435
[22]Kiureghian A D.Structural response to stationary excitation[J].Journal of the Engineering Mechanics Division,1980,106(6):1195-1213
[23]Davenport A G.Note on the distribution of the largest valueof a random function with application to gust loading[J].Proceedings of Institution of Civil Engineers,1964,28:187-196
[24]GB 50011—2001建筑抗震设计规范[S].北京:中国建筑工业出版社,2001(GB 50011—2001 Code for seismicdesign of buildings[S].Beijing:China Architecture&Building Press,2001(in Chinese))
[25]Song J W,Chu Y L,Liang Z,et al.Modal analysis ofgenerally damped linear structure subjected to seismicexcitation[R].New York:University at Buffalo,StateUniversity of New York,2008
[26]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(Liu Qinglin,FuXueyi.Study on determination of reasonable mode numbersfor response spectrum CQC method[J].Journal of BuildingStructures,2006,27(6):87-93(in Chinese))
[27]MSC.Nastran version 68:basic dynamic analysis user’sguide[M].Santa Ana,USA:MSC SoftwareCorporation,2005
[28]MSC.Nastran version70:advanced dynamic analysis user’sguide[M].Santa Ana,USA:MSC Software Corporation,2005
[29]MSC.Random user’s guide[M].Santa Ana,USA:MSCSoftware Corporation,2004
[30]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,1990,8(1):42-48(SunJingjiang,Jiang Jinren.Parameters of Kanai-Tajimispectrum consistent with state code[J].World EarthquakeEngineering,1990,8(1):42-48(in Chinese))
[31]傅学怡.整浇钢筋混凝土建筑结构抗震设计理念探究[J].建筑结构,2005,35(5):9-12(Fu Xueyi.Updatephilosophy of cast-in-situ RC building structure aseismicdesign[J].Building Structure,2005,35(5):9-12(inChinese))
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