高层剪力墙结构动力模型建立及地震响应
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摘要
用连续—离散化方法建立地震作用下高层剪力墙结构动力模型,通过分布参数建立剪力墙运动方程,楼层集中质量的影响通过边界条件引入,从而推导出高层剪力墙结构频率方程,然后通过数值方法求得频率及振型。通过应用Betti定律,推导出具有集中分布参数高层剪力墙结构的振型正交条件。建立每层剪力墙与楼层集中质量地震作用下的运动方程,通过引入推导的振型正交条件,进行运动方程的解耦,从而得到广义质量及广义荷载,然后通过振型叠加的方法求得结构的地震响应。通过Simulink对一幢16层剪力墙结构进行动力特性及地震作用下的仿真分析。结果表明:应用本文建立的动力模型及动力响应求解方法进行高层剪力墙结构动力特性与动力响应分析的结果与有限元分析结果基本一致,在不同连梁刚度、不同剪力墙高宽比情况下,本文动力模型及动力响应求解方法计算结构动力特性及地震响应的误差较小,满足应用的要求。
The dynamic model for tall shear-wall building was presented by continuous-discrete method and the frequency equation of tall shear-wall building was obtained by the vibration theory of system with distributed parameters and introducing the boundary conditions of concentrated parameters,then frequency and mode shape were obtained by the numerical method.On the basis of the Betti law,the orthogonal conditions of modes of tall shear-wall building with concentrated and distributed parameters were deduced.Founding the motion equations of shear wall in each story and concentrated mass of each story under earthquake,the motion equations of tall shear-wall building were decoupled by orthogonal conditions and generalized mass and stiffness were obtained,then the responses of structure under earthquake excitation were solved by the mode superposition method.In order to validate the correctness of constructed dynamic model and the method of solving seismic response for tall shear-wall building,a sixteen-story shear wall building was chosen to analyze dynamic character and seismic response by Simulink simulation.Simulation results show that dynamic characteristic and seismic response obtained by constructed dynamic model and the method of solving seismic response are basically consistent with finite element,and the errors of dynamic character and seismic response obtained by constructed dynamic model and the method of solving seismic response are analyzed in the case of different stiffness of linking beam and different depth-width ratio of shear wall,which can meet the demand of application.
The dynamic model for tall shear-wall building was presented by continuous-discrete method and the frequency equation of tall shear-wall building was obtained by the vibration theory of system with distributed parameters and introducing the boundary conditions of concentrated parameters,then frequency and mode shape were obtained by the numerical method.On the basis of the Betti law,the orthogonal conditions of modes of tall shear-wall building with concentrated and distributed parameters were deduced.Founding the motion equations of shear wall in each story and concentrated mass of each story under earthquake,the motion equations of tall shear-wall building were decoupled by orthogonal conditions and generalized mass and stiffness were obtained,then the responses of structure under earthquake excitation were solved by the mode superposition method.In order to validate the correctness of constructed dynamic model and the method of solving seismic response for tall shear-wall building,a sixteen-story shear wall building was chosen to analyze dynamic character and seismic response by Simulink simulation.Simulation results show that dynamic characteristic and seismic response obtained by constructed dynamic model and the method of solving seismic response are basically consistent with finite element,and the errors of dynamic character and seismic response obtained by constructed dynamic model and the method of solving seismic response are analyzed in the case of different stiffness of linking beam and different depth-width ratio of shear wall,which can meet the demand of application.
引文
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[10]唐意,顾明.某超高层建筑TMD风振控制分析[J].振动与冲击,2006,25(2):16-19.TANG Yi,GU Ming.Analysis on control of wind induced vibration of a super-tall building with TMD[J].Journal of Vibration and Shock,2006,25(2):16-19.
[11]黄斌,刘晖.智能TMD对高层建筑风振响应的抑制[J].振动与冲击,2003,22(4):58-61.HUANG Bin,LIU Hui.Semi-active control of wind vibration for high-rise building with smart TMD[J].Journal of Vibration and Shock,2003,22(4):58-61.
[12]李国强,李杰,苏小卒.建筑抗震设计[M].北京:中国建筑工业出版社,2005:146-149.LI Guo-qiang,LI Jie,SU Xiao-zu.Seismic design for building[M].Beijing:China Building Industry Press,2005:146-149.
[13]克拉夫R W,彭津J.结构动力学[M].王光远,译.北京:科学出版社,1981:204-205.Clough R W,Penzien J.Dynamics of structure[M].WANG Guang-yuan,Transl.Beijing:Science Press,1981:204-205.
[14]杜永峰,刘彦辉,李慧.串联电气设备支架隔震体系地震响应半解析法[J].力学学报,2009,41(3):440-448.DU Yong-feng,LIU Yan-hui,LI Hui.Semi-analytical solution of seismic response of serially isolated equipment and supporter[J].Chinese Journal of Theoretical and Applied Mechanics,2009,41(3):440-448.
[15]杜永峰,刘彦辉,李慧.高压电气设备支架串联体系地震响应半解析法[J].计算力学学报,2010,24:225-231.DU Yong-feng,LIU Yan-hui,LI Hui.Response of serial system of equipment and supporter under earthquake based on semi-analytical method[J].Chinese Journal of Computational Mechanics,2010,24:225-231.
[16]GB50011-2001.建筑抗震设计规范[S].GB50011-2001.Seismic design code for building[S].
[2]Bikce A M,Emsen E,Arslan H M.A simplified dynamic analysis of multi-bay stiffened coupled shear walls[J].Engineering Software,2007,38:552-560.
[3]沈蒲生,刘杨,孟焕陵.框架-剪力墙结构扭转计算方法[J].重庆建筑大学学报,2007,29(1):61-64.SHEN Pu-sheng,LIU Yang,MENG Huan-ling.Calculation method of torsion effect in frame-shear wall structures[J].Journal of Chongqing Jianzhu University,2007,29(1):61-64.
[4]Kuang J S,Ng S C.Coupled lateral-torsion vibration of asymmetric shear-wall structures[J].Thin-walled Structures,2000,38(2):93-104.
[5]程选生,何晴光,刘彦辉.高层建筑结构设计理论[M].北京:机械工业出版社,2010:123-128.CHENG Xuan-sheng,HE Qing-guang,LIU Yan-hui.Design theory for high-rise building[M].Beijing:China Machine Press,2010:123-128.
[6]程志辉,张俊胜.带地下室高层结构的动力计算模型[J].华南理工大学学报:自然科学版,2005,33(6):89-93.CHENG Zhi-hui,ZHANG Jun-sheng.Dynamic calculating models of high-rise building structures with basements[J].Journal of South China University of Technology:Natural Science,2005,33(6):89-93.
[7]Li Q S,Fang J Q,Jeary A P.Calculation of vertical dynamic characteristics of tall buildings withviscous damping[J].J SolidStructures,1998,35(24):316-317.
[8]李桂清,徐家云.结构控制与控制结构计算理论和方法[M].北京:地震出版社,1996:46-58.LI Gui-qing,XU Jia-yun.Computational theory and method of structure control and controlled structure[M].Beijing:Earthquake Press,1996:46-58.
[9]刘文锋,高丽燕,何玉敖.消能减震剪力墙结构体系的最优设计[J].工程力学,2005,22(3):97-101.LIU Wen-feng,GAO Li-yan,HE Yu-ao.Optimization of shear wall structure with energy dissipation devices[J].Engineering Mechanics,2005,22(3):97-101.
[10]唐意,顾明.某超高层建筑TMD风振控制分析[J].振动与冲击,2006,25(2):16-19.TANG Yi,GU Ming.Analysis on control of wind induced vibration of a super-tall building with TMD[J].Journal of Vibration and Shock,2006,25(2):16-19.
[11]黄斌,刘晖.智能TMD对高层建筑风振响应的抑制[J].振动与冲击,2003,22(4):58-61.HUANG Bin,LIU Hui.Semi-active control of wind vibration for high-rise building with smart TMD[J].Journal of Vibration and Shock,2003,22(4):58-61.
[12]李国强,李杰,苏小卒.建筑抗震设计[M].北京:中国建筑工业出版社,2005:146-149.LI Guo-qiang,LI Jie,SU Xiao-zu.Seismic design for building[M].Beijing:China Building Industry Press,2005:146-149.
[13]克拉夫R W,彭津J.结构动力学[M].王光远,译.北京:科学出版社,1981:204-205.Clough R W,Penzien J.Dynamics of structure[M].WANG Guang-yuan,Transl.Beijing:Science Press,1981:204-205.
[14]杜永峰,刘彦辉,李慧.串联电气设备支架隔震体系地震响应半解析法[J].力学学报,2009,41(3):440-448.DU Yong-feng,LIU Yan-hui,LI Hui.Semi-analytical solution of seismic response of serially isolated equipment and supporter[J].Chinese Journal of Theoretical and Applied Mechanics,2009,41(3):440-448.
[15]杜永峰,刘彦辉,李慧.高压电气设备支架串联体系地震响应半解析法[J].计算力学学报,2010,24:225-231.DU Yong-feng,LIU Yan-hui,LI Hui.Response of serial system of equipment and supporter under earthquake based on semi-analytical method[J].Chinese Journal of Computational Mechanics,2010,24:225-231.
[16]GB50011-2001.建筑抗震设计规范[S].GB50011-2001.Seismic design code for building[S].
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