钢和混凝土竖向混合结构阻尼特性研究
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摘要
下部混凝土结构与上部钢结构串联形成竖向混合结构(以下简称S/RC结构),由于建筑和结构上优势,该结构体系已在国内重大工程中得以应用。S/RC体系上、下部分材料不同,整体结构的阻尼参数难以确定,工程设计被迫采用钢材和混凝土两种不同阻尼参数进行计算。从阻尼矩阵和模态阻尼比两个方面研究分块Rayleigh模型和模态应变能模型这两个阻尼模型,并从理论上对模型的物理意义和应用基础进行分析。之后,以12层RC框架和12层S/RC框架的振动台试验为基础,从频域和时域两个层面对两个阻尼模型的有效性进行检验。结果表明,分块Rayleigh模型的阻尼矩阵为非比例阻尼,其难以用于常规的模态分析。模态应变能阻尼模型具有耗能等效的物理概念,且该模型在时域和频域内均具有更高的预测精度,建议在S/RC结构抗震分析中采用。
This paper presents an appropriate representation of the damping behavior of vertical structures with upper steel and lower concrete components(S/RC structure).Two types of models are selected theoretically for the damping behavior of S/RC frames,which include an equivalent damping ratio model based on the dissipated energy of Modal Strain Energy(MSE) and a damping matrix model directly assembled by Rayleigh damping matrices for steel and concrete components.A 12-story S/RC frame and a 12-story RC frame are then designed and tested on the shaking table.Based on these tests,two expressions for measuring the damping behavior for the steel and the concrete component within the S/RC frame are derived,and the expressions are employed to form the damping expression for the S/RC frame in accordance with both of the damping models,respectively.Comparing the damping behavior represented by the two models with that identified in the shaking table tests for the S/RC frame,the damping models are assessed both in frequency domain and in time domain.The conclusions are therefore obtained based on theoretical analyses and experimental evaluation.The first model on assembled Rayleigh damping is not applicable to conventional modal analyses due to its non-proportional characteristics.The second damping model is formed on equivalence of the dissipated MSE of structure which embodies the essence of damping.In comparison with the test results,the second model gives better predictions on the damping behavior of the S/RC frame in both domains than the first damping model.In addition,complex modal analyses are used to predict seismic responses of the S/RC frame to exclude the errors due to non-proportional damping in conventional modal analyses.
This paper presents an appropriate representation of the damping behavior of vertical structures with upper steel and lower concrete components(S/RC structure).Two types of models are selected theoretically for the damping behavior of S/RC frames,which include an equivalent damping ratio model based on the dissipated energy of Modal Strain Energy(MSE) and a damping matrix model directly assembled by Rayleigh damping matrices for steel and concrete components.A 12-story S/RC frame and a 12-story RC frame are then designed and tested on the shaking table.Based on these tests,two expressions for measuring the damping behavior for the steel and the concrete component within the S/RC frame are derived,and the expressions are employed to form the damping expression for the S/RC frame in accordance with both of the damping models,respectively.Comparing the damping behavior represented by the two models with that identified in the shaking table tests for the S/RC frame,the damping models are assessed both in frequency domain and in time domain.The conclusions are therefore obtained based on theoretical analyses and experimental evaluation.The first model on assembled Rayleigh damping is not applicable to conventional modal analyses due to its non-proportional characteristics.The second damping model is formed on equivalence of the dissipated MSE of structure which embodies the essence of damping.In comparison with the test results,the second model gives better predictions on the damping behavior of the S/RC frame in both domains than the first damping model.In addition,complex modal analyses are used to predict seismic responses of the S/RC frame to exclude the errors due to non-proportional damping in conventional modal analyses.
引文
[1]吕西林.复杂高层建筑结构抗震理论与应用[M].北京:科学出版社,2007
[2]Adhikari S.Damping modelling using generalized proportionaldamping[J].Journal of Sound and Vibration,2006,293(1/2):156-170
[3]包世华.结构动力学[M].武汉:武汉理工大学出版社,2005
[4]Clough R W,Penzien J.Dynamics of structures[M].2ndEdition.Berkeley,California:Computers&Structures,Inc.,2003
[5]汤燕波.带不同材料塔楼多高层建筑的抗震设计方法研究[D].上海:同济大学,2005
[6]Charney F A.Unintended consequences of modeling dampingin structures[J].Journal of Structural Engineering,2008,134(4):581-592
[7]Chopra A K.Dynamics of structures:theory and applicationsto earthquake engineering[M].New Jersey:PearsonEducation,Inc.,2001
[8]尚世英.考虑土壤影响时高层建筑等效模态阻尼比的计算方法[J].地震工程与工程振动,1994,14(1):83-88(Shang Shiying.Estimation methods of equivalent modaldamping ratio of tall buildings with soil-structure interaction[J].Earthquake Engineering and Engineering Vibration,1994,14(1):83-88(Chinese))
[9]Wang Y K.Seismic analysis of coupled structural systemswith non-proportional damping[D].New York:Polytechnic University,1999
[10]Hwang J S,Chang K C,Tsai M H.Composite dampingratio of seismically isolated regular bridges[J].Engineering Structures,1997,19(1):55-62
[11]Wang J.Intrinsic damping:modeling techniques for engineeringsystems[J].Journal of Structural Engineering,2009,135(3):282-291
[12]Feriani A,Perotti F.The formation of viscous dampingmatrices for the dynamic analysis of MDOF systems[J].Earthquake Engineering&Structural Dynamics,1996,25(7):689-709
[13]Guide specifications for seismic isolation design[S].3rdEdition.Washington,DC:American Association of StateHighway and Transportation Officials,2010
[14]Manual for menshin design of highway bridges[S].Japan:Public Work Research Institute,1992
[15]Kawashima K,Nagashima H,Iwasaki H.Evaluation ofmodal damping ratio based on strain energy proportionaldamping method[J].Journal of Structural Engineering,1994,40:953-965
[16]薛彦涛,韦承基,孙仁范,等.采用不同材料加层时结构阻尼比计算方法(应变能法)[J].工程抗震与加固改造,2008,30(2):91-95(Xue Yantao,Wei Chengji,SunRenfan,et al.Calculation method for damping ration ofdifferent story added structures(strain energy method)[J].Earthquake Resistant Engineering and Retrofitting,2008,30(2):91-95(in Chinese))
[17]吕西林,李培振,陈跃庆.12层钢筋混凝土标准框架振动台模型试验的完整数据[R].上海:同济大学,2004(Lu Xilin,Li Peizhen,Chen Yueqing.Benchmark test ofa 12-story reinforced concrete frame model on shaking table[R].Shanghai:Tongji University,2004(in Chinese))
[18]李国强,李杰.工程结构动力检测理论与应用[M].北京:科学出版社,2002
[19]Jeary A P.The description and measurement of nonlineardamping in structures[J].Journal of Wind Engineeringand Industrial Aerodynamics,1996,59(2/3):103-114
[20]樊海涛,何益斌,肖宏彬.钢筋混凝土建筑非线性阻尼性能及阻尼比表达式研究[J].地震工程与工程振动,2005,25(5):85-90(Fan Haitao,He Yibin,XiaoHongbin.Study on non-linear damping performance anddamping ratio formula of reinforced concrete buildings[J].Earthquake Engineering and Engineering Vibration,2005,25(5):85-90(in Chinese))
[21]Li Q S,Yang K,Wong C K,et al.The effect ofamplitude-dependent damping on wind-induced vibrationsof a super tall building[J].Journal of Wind Engineeringand Industrial Aerodynamics,2003,91(9):1175-1198
[22]Newmark N M,Hall W J.Earthquake spectra and design[M].Berkeley:Earthquake Engineering ResearchInstitute,1982
[23]楼梦麟,范幺清.求解非比例阻尼体系复模态的实模态摄动法[J].力学学报,2007,39(1):112-118(LouMenglin,Fan Yaoqing.Modal perturbation method forobtaining complex modal characteristics of non-proportionaldamping systems[J].Chinese Journal of Theoretical andApplied Mechanics,2007,39(1):112-118(in Chinese))
[24]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 qudratic combination(CCQC)of complex mode seismic responses[J].ChinaCivil Engineering Journal,2005,38(1):31-39(inChinese))
[25]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):30-36,45(Zhou Xiyuan,Dong Di,SuYoupo.New method for linear systems with non-classicaldamping under ground motion[J].China Civil EngineeringJournal,2003,36(5):30-36,45(in Chinese))
[26]王树青,李华军.利用消去刚度法进行剪切型系统物理参数识别[J].中国海洋大学学报:自然科学版,2004,34(6):1085-1089(Wang Shuqing,Li Huajun.Stiffnesselimination algorithm for physical parameters identificationof shearing structures[J].Periodical of Ocean University ofChina,2004,34(6):1085-1089(in Chinese))
[2]Adhikari S.Damping modelling using generalized proportionaldamping[J].Journal of Sound and Vibration,2006,293(1/2):156-170
[3]包世华.结构动力学[M].武汉:武汉理工大学出版社,2005
[4]Clough R W,Penzien J.Dynamics of structures[M].2ndEdition.Berkeley,California:Computers&Structures,Inc.,2003
[5]汤燕波.带不同材料塔楼多高层建筑的抗震设计方法研究[D].上海:同济大学,2005
[6]Charney F A.Unintended consequences of modeling dampingin structures[J].Journal of Structural Engineering,2008,134(4):581-592
[7]Chopra A K.Dynamics of structures:theory and applicationsto earthquake engineering[M].New Jersey:PearsonEducation,Inc.,2001
[8]尚世英.考虑土壤影响时高层建筑等效模态阻尼比的计算方法[J].地震工程与工程振动,1994,14(1):83-88(Shang Shiying.Estimation methods of equivalent modaldamping ratio of tall buildings with soil-structure interaction[J].Earthquake Engineering and Engineering Vibration,1994,14(1):83-88(Chinese))
[9]Wang Y K.Seismic analysis of coupled structural systemswith non-proportional damping[D].New York:Polytechnic University,1999
[10]Hwang J S,Chang K C,Tsai M H.Composite dampingratio of seismically isolated regular bridges[J].Engineering Structures,1997,19(1):55-62
[11]Wang J.Intrinsic damping:modeling techniques for engineeringsystems[J].Journal of Structural Engineering,2009,135(3):282-291
[12]Feriani A,Perotti F.The formation of viscous dampingmatrices for the dynamic analysis of MDOF systems[J].Earthquake Engineering&Structural Dynamics,1996,25(7):689-709
[13]Guide specifications for seismic isolation design[S].3rdEdition.Washington,DC:American Association of StateHighway and Transportation Officials,2010
[14]Manual for menshin design of highway bridges[S].Japan:Public Work Research Institute,1992
[15]Kawashima K,Nagashima H,Iwasaki H.Evaluation ofmodal damping ratio based on strain energy proportionaldamping method[J].Journal of Structural Engineering,1994,40:953-965
[16]薛彦涛,韦承基,孙仁范,等.采用不同材料加层时结构阻尼比计算方法(应变能法)[J].工程抗震与加固改造,2008,30(2):91-95(Xue Yantao,Wei Chengji,SunRenfan,et al.Calculation method for damping ration ofdifferent story added structures(strain energy method)[J].Earthquake Resistant Engineering and Retrofitting,2008,30(2):91-95(in Chinese))
[17]吕西林,李培振,陈跃庆.12层钢筋混凝土标准框架振动台模型试验的完整数据[R].上海:同济大学,2004(Lu Xilin,Li Peizhen,Chen Yueqing.Benchmark test ofa 12-story reinforced concrete frame model on shaking table[R].Shanghai:Tongji University,2004(in Chinese))
[18]李国强,李杰.工程结构动力检测理论与应用[M].北京:科学出版社,2002
[19]Jeary A P.The description and measurement of nonlineardamping in structures[J].Journal of Wind Engineeringand Industrial Aerodynamics,1996,59(2/3):103-114
[20]樊海涛,何益斌,肖宏彬.钢筋混凝土建筑非线性阻尼性能及阻尼比表达式研究[J].地震工程与工程振动,2005,25(5):85-90(Fan Haitao,He Yibin,XiaoHongbin.Study on non-linear damping performance anddamping ratio formula of reinforced concrete buildings[J].Earthquake Engineering and Engineering Vibration,2005,25(5):85-90(in Chinese))
[21]Li Q S,Yang K,Wong C K,et al.The effect ofamplitude-dependent damping on wind-induced vibrationsof a super tall building[J].Journal of Wind Engineeringand Industrial Aerodynamics,2003,91(9):1175-1198
[22]Newmark N M,Hall W J.Earthquake spectra and design[M].Berkeley:Earthquake Engineering ResearchInstitute,1982
[23]楼梦麟,范幺清.求解非比例阻尼体系复模态的实模态摄动法[J].力学学报,2007,39(1):112-118(LouMenglin,Fan Yaoqing.Modal perturbation method forobtaining complex modal characteristics of non-proportionaldamping systems[J].Chinese Journal of Theoretical andApplied Mechanics,2007,39(1):112-118(in Chinese))
[24]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 qudratic combination(CCQC)of complex mode seismic responses[J].ChinaCivil Engineering Journal,2005,38(1):31-39(inChinese))
[25]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):30-36,45(Zhou Xiyuan,Dong Di,SuYoupo.New method for linear systems with non-classicaldamping under ground motion[J].China Civil EngineeringJournal,2003,36(5):30-36,45(in Chinese))
[26]王树青,李华军.利用消去刚度法进行剪切型系统物理参数识别[J].中国海洋大学学报:自然科学版,2004,34(6):1085-1089(Wang Shuqing,Li Huajun.Stiffnesselimination algorithm for physical parameters identificationof shearing structures[J].Periodical of Ocean University ofChina,2004,34(6):1085-1089(in Chinese))
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