基于复阻尼假定的不同材料阻尼特性混合结构抗震分析复模态叠加法
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摘要
寻求合理高效的方法求得不同材料阻尼特性混合结构的地震作用及其效应是工程抗震界较为关注的问题之一。目前,用于计算不同材料阻尼特性混合结构地震作用效应的复模态叠加法和直接积分法都是基于黏性阻尼假定推导而来。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,且阻尼矩阵与复模态分析结果相互影响,计算结果不唯一,合理性不易被判定。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,不便于工程应用。为此提出一种基于复阻尼假定的复模态叠加法,直接在物理空间中求解,计算结果唯一,比基于黏性阻尼假定的复模态叠加法计算效率更高。与运用本文方法计算的地震作用效应结果相比,广为采用的折算阻尼比方法计算结果是不合理的。此外,给出了基于复阻尼假定的计算模态有效质量系数的方法,可用于确定合理的叠加模态个数。
One of the much concerned problems in seismic engineering is to seek reasonable and efficient method to obtain earthquake action and its effects on structures of various material damping characteristics in components.Currently,the most often used complex mode superposition method and direct integration method to calculate transient earthquake responses are developed based on viscous damping assumption.Viscous damping assumption has disadvantages.For example,the earthquake effects of high frequencies may be underestimated since the energy dissipation is related to excitation frequencies according to the viscous damping assumption.Furthermore,since the damping matrix interacts with results of complex mode analysis,results of above mentioned methods are not unique and the rationality of the results is difficult to be determined.Complex damping assumption can avoid disadvantages of viscous damping assumption,though usually it brings out complex form results which may be inconvenient to use.A complex mode superposition method based on the complex damping assumption which resolves directly in physics space and obtains unique results was put forward.It is proved that the new method is more efficient than that based on the viscous damping assumption.Compared with results of the new method,results of widely used equivalent damping ratio method are unreasonable.In addition,method for calculating modal effective mass factor which can be used to determine reasonable number of superimposed modes based on the complex damping assumption was also put forward.
One of the much concerned problems in seismic engineering is to seek reasonable and efficient method to obtain earthquake action and its effects on structures of various material damping characteristics in components.Currently,the most often used complex mode superposition method and direct integration method to calculate transient earthquake responses are developed based on viscous damping assumption.Viscous damping assumption has disadvantages.For example,the earthquake effects of high frequencies may be underestimated since the energy dissipation is related to excitation frequencies according to the viscous damping assumption.Furthermore,since the damping matrix interacts with results of complex mode analysis,results of above mentioned methods are not unique and the rationality of the results is difficult to be determined.Complex damping assumption can avoid disadvantages of viscous damping assumption,though usually it brings out complex form results which may be inconvenient to use.A complex mode superposition method based on the complex damping assumption which resolves directly in physics space and obtains unique results was put forward.It is proved that the new method is more efficient than that based on the viscous damping assumption.Compared with results of the new method,results of widely used equivalent damping ratio method are unreasonable.In addition,method for calculating modal effective mass factor which can be used to determine reasonable number of superimposed modes based on the complex damping assumption was also put forward.
引文
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[17]刘庆林,傅学怡.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[J].土木工程学报,2011,44(3):61-71.(Liu Qinglin,Fu Xueyi.Aresponse spectrum CCQC method for aseismic analysisof structures of multiple material damping characteristicsbased on complex damping assumption[J].China CivilEngineering Journal,2011,44(3):61-71.(inChinese))
[18]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.(Zhu Jingqing,Zhu Ming.Calculation of complexdamping response spectra from earthquake records[J].Earthquake Engineering and Engineering Vibration,2000,20(2):19-23.(in Chinese))
[19]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.(ZhuMing,Zhu Jingqing.Further studies on calculation ofcomplex damping response spectra[J].EarthquakeEngineering and Engineering Vibration,2001,21(2):36-40.(in Chinese))
[20]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 Ming,Zhu Jingqing.Some problems in frequencydomain solution of complex damping system[J].WorldEarthquake Engineering,2004,20(2):23-28.(inChinese))
[21]MSC Software Corporation.MSC/Nastran basic dynamicanalysis user’s guide:version 68[M].CA,USA:MSC Software Corporation,2005.
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[23]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.Update philosophy of cast-in-situ RC building structureaseismic design[J].Building Structure,2005,35(5):9-12.(in Chinese))
[2]傅学怡.国家游泳中心水立方结构设计[M].北京:中国建筑工业出版社,2009:178-186.(Fu Xueyi.Structural design of National Swimming Centre WaterCube[M].Beijing:China Architecture&BuildingPress,2009:178-186.(in Chinese))
[3]Ray Clough,Joseph Penzien.Dynamics of structures[M].2nd ed.Berkeley,California,USA:Computersand Structures,Inc.,2003:219-256.
[4]Zhou Xiyuan,Yu Ruifang,Dong di.Complex modesuperposition algorithm for seismic response of non-classically damped linear MDOF system[J].Journal ofEarthquake Engineering,2004,8(4):597-641.
[5]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):30-45.(Zhou Xiyuan,Dong Di,SuYoubo.New method for linear systems with non-classical damping under ground motion[J].China CivilEngineering Journal,2003,36(5):30-36.(inChinese))
[6]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.(Zhou Xiyuan,Yu Ruifang.CCQC method for seismicresponse of non-classically damped linear system basedon code response spectra[J].Engineering Mechanics,2006,23(2):9-17.(in Chinese))
[7]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.Complexmode superposition method for non-classically dampedlinear system with over-critical damping peculiarity[J].Journal of Building Structures,2006,27(1):50-59.(in Chinese))
[8]邱吉宝,向树红,张正平.计算结构动力学[M].合肥:中国科学技术大学出版社,2009:196-221.(QiuJibao,Xiang Shuhong,Zhang Zhengping.Computational structural dynamics[M].Hefei:University of Science and Technology of China Press,2009:196-221.(in Chinese))
[9]刘晶波,杜修力.结构动力学[M].北京:机械工业出版社,2005:64-69.(Liu Jingbo,Du Xiuli.Dynamicsof structures[M].Beijing:China Machine Press,2005:64-69.(in Chinese))
[10]刘庆林,傅学怡.基于黏性阻尼假定反应谱CCQC法的改进及与基于复阻尼假定反应谱CCQC法的比较[R].深圳:深圳大学,2011.(Liu Qinglin,Fu Xueyi.An improved response spectrum CCQC method based onviscous damping assumption and comparison with theresponse spectrum CCQC method based on complexdamping assumption[R].Shenzhen:ShenzhenUniversity,2011.(in Chinese))
[11]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,2001:5-40.(Cao Shuqian,Zhang Wende,Xiao Longxiang.Modal analysis ofvibrating structures[M].Tianjin:Tianjin UniversityPress,2001:5-40.(in Chinese))
[12]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.(Zhu Jingqing,Zhu Ming.Two mode-superpositionmethods for dynamic analysis of MDOF systems withcomplex damping characteristics[J].EarthquakeEngineering and Engineering Vibration,2004,24(2):55-58.(in Chinese))
[13]Song Jianwei,Chu Yilun,Liang Zach,et al.Modalanalysis of generally damped linear structure subjectedto seismic excitation[R].Technical Report MCEER-08-0005.Buffalo:University at Baffalo,The State ofUniversity of New York,2008.
[14]朱镜清.关于复阻尼理论的两个基本问题[J].固体力学学报1,992,13(2):113-118.(Zhu Jingqing.Onthe two sasic problems of complex damping theory[J].Chinese Journal of Solid Mechanics,1992,13(2):113-118.(in Chinese))
[15]何钟怡.复本构理论中的对偶原则[J].固体力学学报,1994,15(2):177-180.(He Zhongyi.The dualprinciple in theory of complex constitutive equations[J].Chinese Journal of Solid Mechanics,1994,15(2):177-180.(in Chinese))
[16]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 noteson theory of complex damping[J].EarthquakeEngineering and Engineering Vibration,2002,22(1):1-6.(in Chinese))
[17]刘庆林,傅学怡.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[J].土木工程学报,2011,44(3):61-71.(Liu Qinglin,Fu Xueyi.Aresponse spectrum CCQC method for aseismic analysisof structures of multiple material damping characteristicsbased on complex damping assumption[J].China CivilEngineering Journal,2011,44(3):61-71.(inChinese))
[18]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.(Zhu Jingqing,Zhu Ming.Calculation of complexdamping response spectra from earthquake records[J].Earthquake Engineering and Engineering Vibration,2000,20(2):19-23.(in Chinese))
[19]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.(ZhuMing,Zhu Jingqing.Further studies on calculation ofcomplex damping response spectra[J].EarthquakeEngineering and Engineering Vibration,2001,21(2):36-40.(in Chinese))
[20]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 Ming,Zhu Jingqing.Some problems in frequencydomain solution of complex damping system[J].WorldEarthquake Engineering,2004,20(2):23-28.(inChinese))
[21]MSC Software Corporation.MSC/Nastran basic dynamicanalysis user’s guide:version 68[M].CA,USA:MSC Software Corporation,2005.
[22]MSC Software Corporation.MSC/Nastran advanceddynamic analysis user’s guide:version 70[M].CA,USA:MSC Software Corporation,2005.
[23]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.Update philosophy of cast-in-situ RC building structureaseismic design[J].Building Structure,2005,35(5):9-12.(in Chinese))
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