曲线梁桥振型主方向判定方法研究
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摘要
由于曲线梁桥独特的构造特点,其振型存在"弯扭耦合"现象。为了判定曲线梁桥各阶"弯扭耦合"振型的主方向是弯曲或纯扭转,把曲线梁桥的每阶振型分解为竖向弯曲、纯扭转、横向弯曲和纵向移动4个子方向,把每阶振型的能量亦分成竖向弯曲能量、扭转能量、横向弯曲能量和沿纵向平移能量4个方向上的能量,引入4个方向参数来分别表示各子方向能量所占各阶振型能量的比值。然后从结构动力学理论知识出发,根据无阻尼系统每阶振型动能和变形能之和为常数的基本原理,推导了4个方向参数的计算公式,推导结果显示,方向系数仅为结构质量、截面几何特性和振型向量的表达式。最后提出了一种根据方向参数值的大小判定曲线梁桥各阶振型以哪个子方向为主的方法,并通过实例介绍了该方法的应用。
Due to the special construction feature,the mode shape of a curved bridge has "flexure-torsion coupling" situation.In order to determine whether the main direction of the mode shape is flexure or torsion,each mode shape was divided into four sub directions which are vertical bending,pure torsion,transverse bending and longitudinal shift respectively.Accordingly,the energy of each mode was also subdivided into four directions.The ratios between the energy of sub direction and the total energy of a mode were denoted by four direction parameters.Theoretical derivation for the direction parameters was given based on the energy conservation principle of each mode of undamped system.The derivation result reveals that four formulas of the direction parameters are only related to structural mass,sectional geometric characteristics and mode vectors.Finally,the method of determining the main sub direction of mode shapes of a curved bridge was given according to the values of the four parameters,and how to use the method was presented too by a instance.
Due to the special construction feature,the mode shape of a curved bridge has "flexure-torsion coupling" situation.In order to determine whether the main direction of the mode shape is flexure or torsion,each mode shape was divided into four sub directions which are vertical bending,pure torsion,transverse bending and longitudinal shift respectively.Accordingly,the energy of each mode was also subdivided into four directions.The ratios between the energy of sub direction and the total energy of a mode were denoted by four direction parameters.Theoretical derivation for the direction parameters was given based on the energy conservation principle of each mode of undamped system.The derivation result reveals that four formulas of the direction parameters are only related to structural mass,sectional geometric characteristics and mode vectors.Finally,the method of determining the main sub direction of mode shapes of a curved bridge was given according to the values of the four parameters,and how to use the method was presented too by a instance.
引文
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[2]单德山,李乔.曲线弯梁桥振动分析方法[J].土木工程学报,2005,38(10):61-65.SHAN Deshan,LI Qiao.Analytical Method of Vibration Anal-ysis for Curved-girder Bridges[J].China Civil EngineeringJournal,2005,38(10):61-65.
[3]MAGDY S,JOHN B K,KHALED S.Dynamic Analysis ofCurved Continuous Multiple-Box Girder Bridges[J].Journalof Bridge Engineering,2007,12(2):184-193.
[4]MAGDY S,JOHN B K,KHALED S.Impact Factor forCurved Continuous Composite Multiple-Box Girder Bridges[J].Journal of Bridge Engineering,2007,12(1):80-88.
[5]HUANG Dongzhou.Full-scale Test and Analysis of a CurvedSteel-box Girder Bridge[J].Journal of Bridge Engineering,2008,13(5):492-500.
[6]焦驰宇,李青宁.城市曲线高架桥的计算模型与动反应分析[D].西安:西安建筑科技大学,2005.JIAO Chiyu,LI Qingning.Research on Computation ModuleDynamic Response of Urban Curved Viaduct[D].Xi’an:Xi’an University of Arch and Technology,2005.
[7]魏双科,李鸿晶,罗寒松,等.立交桥曲线箱梁动力分析模型[J].地震工程与工程振动,2006,26(4):168-174.WEI Shuangke,LI Hongjing,LUO Hansong,et al.A Dy-namic Model of Curved Box Girder Beam in Highway Inter-changes[J].Earthquake Engineering and Engineering Vibra-tion,2006,26(4):168-174.
[8]谢志英,濮中标.混凝土曲线梁桥的自振频率分析[J].西部探矿工程,2005,116(12):208-209.XIE Zhiying,PU Zhongbiao.Analysis on Natural Vibration Fre-quency of Concrete Curved Beam Bridges[J].West-China Explo-ration Engineering,2005,116(12):208-209.
[9]王元丰,WILSON J F.近于优化跨度连续曲梁桥的自由振动[J].北方交通大学学报,1999,23(1):94-98.WANG Yuanfeng,WILSON J F.Free Vibration of Near-opti-mal Span Continuous Curved Beams[J].Journal of NorthernJiaotong University,1999,23(1):94-98.
[10]牛帅,李青宁.考虑桩-土-结构共同作用的曲线高架桥地震反应分析[D].西安:西安建筑科技大学,2008.NIU Shuai,LI Qingning.Analysis of Earthquake Response ofCurved Viaduct with Pile-soil-structure Coaction[D].Xi’An:Xi’an university of Arch and technology,2008.
[11]刘华,叶见曙.公路混凝土弯箱梁桥的动反应[J].东南大学学报:自然科学版,2006,36(2):278-282.LIU Hua,YE Jianshu.Dynamical Response of Highway Con-crete Curved Box Girder Bridges[J].Journal of Southeast U-niversity:Natural Science Edition,2006,36(2):278-282.
[12]夏淦,邵容光.弯梁桥[M].北京:人民交通出版社,1994.XIA Gan,SHAO Rongguang.Curved Bridge[M].Beijing:China Communications Press,1994.
[13]谢官模.振动力学[M].北京:国防工业出版社,2007.XIE Guanmo.Vibration Mechanics[M].Beijing:NationalDefense Industry Press,2007.
[14]克拉夫R,彭津J.结构动力学[M].2版.北京:高等教育出版社,2007.CLOUGH R,PENZIEN J.Structural Dynamics[M].2nd ed.Beijing:Higher Education Press,2007.
[15]杜嘉斌,罗旗帜,张学文.计算连续梁桥的有限段法[J].佛山科学技术学院学报:自然科学版,2004,22(4):51-54.DU Jiabin,LUO Qizhi,ZHANG Xuewen.Finite Segment Methodfor Calculating Continuous Curved Girder Bridges[J].Journal ofFoshan University:Natural Science Edition,2004,22(4):51-54.
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