框架结构水平向动力频散特性研究
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摘要
框架结构可看作其标准层结构沿竖向堆积而成的一种周期结构,这种几何周期性赋予了框架结构一些独特的动力特性。首先,基于结构设计理论提出框架结构频散特性简化计算模型,结合Bloch-Floquet定理和波动控制方程推导框架结构频散方程,将有限单元法拓展应用于频散关系计算并给出了一钢筋混凝土框架结构的频散曲线;其次,模态分析讨论了框架结构的频散特性,并给出了两种衰减域边界频率简化计算方法(简化模型法和等效单自由度体系法);最后,通过有限周期框架结构谐响应分析验证了周期结构理论分析框架结构的合理性。
Frame structures can be viewed as a periodic system with its standard floor arranged one-by-one in vertical direction.Because of the geometrical periodicity,frame structures have some novel dynamic properties.Using the Bloch-Floquet theory and the finite element method,this paper conducts a theoretical study on the dynamic dispersion properties of frame structures in horizontal direction.First,based on the structure design theory,a simplified model is proposed to analyzed the dipersion property of the frame structures.Combing the Bloch-Floquet theory and the wave equations,the dispersion equations are derived.And then the finite element method is developed to calculate the dispersion relationship.With the help of the propose method,the dispersion curves of a planar RC frame structure are calculated.Second,the dispersion properties of the considered frame structure are discussed based on the wave modal analysis,from which two simplified methods(simplified model method and the equivalent SDOF method)are proposed to calculate the bound frequencies of the first attenuation zone.Third,the rationality of the present method is verified through the harmonic analysis of a finite frame structure.
Frame structures can be viewed as a periodic system with its standard floor arranged one-by-one in vertical direction.Because of the geometrical periodicity,frame structures have some novel dynamic properties.Using the Bloch-Floquet theory and the finite element method,this paper conducts a theoretical study on the dynamic dispersion properties of frame structures in horizontal direction.First,based on the structure design theory,a simplified model is proposed to analyzed the dipersion property of the frame structures.Combing the Bloch-Floquet theory and the wave equations,the dispersion equations are derived.And then the finite element method is developed to calculate the dispersion relationship.With the help of the propose method,the dispersion curves of a planar RC frame structure are calculated.Second,the dispersion properties of the considered frame structure are discussed based on the wave modal analysis,from which two simplified methods(simplified model method and the equivalent SDOF method)are proposed to calculate the bound frequencies of the first attenuation zone.Third,the rationality of the present method is verified through the harmonic analysis of a finite frame structure.
引文
[1]施卫星,王进.钢筋混凝土框架结构动力特性研究[J].地震工程与工程振动,2010,30(06):87-91.SHI Wei-xin,WANG Jin.Research on dynamic characteristics of reinforced concrete frame structures[J].Journal of Earthquake Engineering and Engineering Vibration,2010,30(06):87-91.
[2]谢献忠,易伟建,陈文新.钢筋混凝土框架结构模型动力识别试验研究[J].工程力学,2009,26(07):170-175.XIE Xian-zhong,YI Wei-jian,CHEN Wen-xin.Experimental study on dynamic identification of reinforced concrete frame structure[J].Engineering Mechanics,2009,26(07):170-175.
[3]余江滔,张远淼,陆洲导,等.混凝土框架震损与修复过程动力特性的试验研究[J].工程力学,2013,30(06):154-161.YU Jiang-tao,ZHANG Yuan-miao,LU Zhou-dao,et al.Study on dynamic characteristics of RC frame during damage and rehabilitation process[J].Engineering Mechanics,2013,30(06):154-161.
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[7]石志飞,程志宝,向宏军.周期结构理论及其在隔震减振中的应用[M].北京:科学出版社,2017.SHI Zhi-fei,CHENG Zhi-bao,XIANG Hong-jun.Peirodic Structures Theory and Applications to Seismic Isolation and Vibration Reduction[M].Beijing:China Science Publishing&Media Let.,2017.
[8]LU Jian-fei,SHA Xuan,WU Jia-bin.Resonance and cancellation phenomena caused by equidistant moving loadings in a periodic structure-A pile-supported periodic viaduct[J].European Journal of Mechanics A/Solids,2016,59(0):114-123.
[9]罗福金,陆建飞.含缺陷周期性高架铁路的地震响应分析[J].世界地震工程,2016,32(01):195-202.LUO Fu-jin,LU Jian-fei,Seismic response analysis of defective periodic viaduct[J].World Earthquake Engineering,2016,32(01):195-202.
[10]吕西林.建筑结构抗震设计理论与实例[M].上海:同济大学出版社,2015.LV Xi-lin.Seismic Design of Building Structures:Theory and Examples[M].Shanghai:Tongji University Press,2015.
[11]姜迎春,刘铁林,于忠诚.高层结构动力响应的波动分析方法[J].沈阳建筑大学学报(自然科学版),2008,24(05):778-782.JIANG Ying-chun,Liu Tie-lin,Yu Zhong-cheng.Dynamic response analysis of high-rise structure by wave approach[J].Journal of Shenyang Jianzhu University(Natural Science),2008,24(05):778-782.
[12]Chopra A K.Dynamics of Structures:Theory and Applications to Earthquake Engineering[M].2nd ed.New Jersey:Prentice Hall,2000.
[13]夏桂云,李传习.考虑剪切变形影响的杆系结构理论与应用[M].北京:人民交通出版社,2008.XIA Gui-yun,Li Chuan-xi.Theory and Applications of Beam Structure Considering the Effect of Shear Deformation[M].Beijing:China Communications Press,2008.
[14]周世军.一组新的Timoshenko梁单元一致矩阵公式[J].兰州铁道学院学报,1994,13(2):1-7.ZHOU Shi-jun.A set of new consistent matrix for formulations of Timoshenko beam element[J].Journal of Lanzhou Railway Institute,1994,13(2):1-7.
[15]Cheng Zhi-bao,Shi Zhi-fei,Yi-Lung Mo.Complex dispersion relations and evanescent waves in periodic beams via the extended differential quadrature method[J].Composite Structures,2018,187:122-136.
[16]Xiang Hong-jun,Shi Zhi-fei.Analysis of flexural vibration band gaps in periodic beams using differential quadrature method[J].Computers&Structures,2009,87(23-24):1559-1566.
[17]Cheng Zhi-bao,Lin Wen-kai,Shi Zhi-fei.Wave dispersion analysis of multi-story frame building structures using the periodic structure theory[J].Soil Dynamics and Earthquake Engineering,2018,106:215-230.
[2]谢献忠,易伟建,陈文新.钢筋混凝土框架结构模型动力识别试验研究[J].工程力学,2009,26(07):170-175.XIE Xian-zhong,YI Wei-jian,CHEN Wen-xin.Experimental study on dynamic identification of reinforced concrete frame structure[J].Engineering Mechanics,2009,26(07):170-175.
[3]余江滔,张远淼,陆洲导,等.混凝土框架震损与修复过程动力特性的试验研究[J].工程力学,2013,30(06):154-161.YU Jiang-tao,ZHANG Yuan-miao,LU Zhou-dao,et al.Study on dynamic characteristics of RC frame during damage and rehabilitation process[J].Engineering Mechanics,2013,30(06):154-161.
[4]温熙森,温激鸿,郁殿龙,等.声子晶体[M].北京:国防科技出版社,2009.WEN Xi-sen,Wen Ji-hong,Yu Dian-long,et al.Phononic Crystal[M].Beijing:National Defense Industry Press,2009.
[5]Yuan Bo,Humphrey Victor F,Wen Ji-hong,et al.On the coupling of resonance and Bragg scattering effects in three-dimensional locally resonant sonic materials[J].Ultrasonics,2013,53(07):1332-1343.
[6]程志宝.周期性结构及周期性隔震基础[D].北京:北京交通大学,2014.CHENG Zhi-bao.Peirodic structure and periodic foundation[D].Beijing:Beijing Jiaotong University,2014.
[7]石志飞,程志宝,向宏军.周期结构理论及其在隔震减振中的应用[M].北京:科学出版社,2017.SHI Zhi-fei,CHENG Zhi-bao,XIANG Hong-jun.Peirodic Structures Theory and Applications to Seismic Isolation and Vibration Reduction[M].Beijing:China Science Publishing&Media Let.,2017.
[8]LU Jian-fei,SHA Xuan,WU Jia-bin.Resonance and cancellation phenomena caused by equidistant moving loadings in a periodic structure-A pile-supported periodic viaduct[J].European Journal of Mechanics A/Solids,2016,59(0):114-123.
[9]罗福金,陆建飞.含缺陷周期性高架铁路的地震响应分析[J].世界地震工程,2016,32(01):195-202.LUO Fu-jin,LU Jian-fei,Seismic response analysis of defective periodic viaduct[J].World Earthquake Engineering,2016,32(01):195-202.
[10]吕西林.建筑结构抗震设计理论与实例[M].上海:同济大学出版社,2015.LV Xi-lin.Seismic Design of Building Structures:Theory and Examples[M].Shanghai:Tongji University Press,2015.
[11]姜迎春,刘铁林,于忠诚.高层结构动力响应的波动分析方法[J].沈阳建筑大学学报(自然科学版),2008,24(05):778-782.JIANG Ying-chun,Liu Tie-lin,Yu Zhong-cheng.Dynamic response analysis of high-rise structure by wave approach[J].Journal of Shenyang Jianzhu University(Natural Science),2008,24(05):778-782.
[12]Chopra A K.Dynamics of Structures:Theory and Applications to Earthquake Engineering[M].2nd ed.New Jersey:Prentice Hall,2000.
[13]夏桂云,李传习.考虑剪切变形影响的杆系结构理论与应用[M].北京:人民交通出版社,2008.XIA Gui-yun,Li Chuan-xi.Theory and Applications of Beam Structure Considering the Effect of Shear Deformation[M].Beijing:China Communications Press,2008.
[14]周世军.一组新的Timoshenko梁单元一致矩阵公式[J].兰州铁道学院学报,1994,13(2):1-7.ZHOU Shi-jun.A set of new consistent matrix for formulations of Timoshenko beam element[J].Journal of Lanzhou Railway Institute,1994,13(2):1-7.
[15]Cheng Zhi-bao,Shi Zhi-fei,Yi-Lung Mo.Complex dispersion relations and evanescent waves in periodic beams via the extended differential quadrature method[J].Composite Structures,2018,187:122-136.
[16]Xiang Hong-jun,Shi Zhi-fei.Analysis of flexural vibration band gaps in periodic beams using differential quadrature method[J].Computers&Structures,2009,87(23-24):1559-1566.
[17]Cheng Zhi-bao,Lin Wen-kai,Shi Zhi-fei.Wave dispersion analysis of multi-story frame building structures using the periodic structure theory[J].Soil Dynamics and Earthquake Engineering,2018,106:215-230.
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