预应力简支梁的车桥耦合分析
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摘要
车桥耦合理论主要研究的是非预应力简支梁在车辆荷载作用下梁的振动响应，而对于生活中常见的预应力梁车桥耦合振动研究的却很少，因此本文在前人所做工作的基础上推导了预应力梁的车桥耦合振动微分方程并对其进行求解。全文结构和主要内容大致如下：
第一章介绍了预应力简支梁车桥耦合分析的选题背景和国内外研究现状。
第二章分两节分别介绍了常见的桥梁和车辆计算模型，然后通过位移协调条件和作用力平衡关系将两个模型组合起来建立匀速滚动质量车桥耦合模型及其振动微分方程。
第三章介绍RKF法和Newmark法求解二阶振动微分方程的基本原理和计算步骤，然后以MATLAB为计算平台比较了这两种方法对同一非预应力T形梁耦合振动微分方程进行数值迭代的计算误差；
第四章是本文的主要内容。本章以预应力梁和非预应力梁在理论计算方面的相似为前提条件，在前面介绍的非预应力T形梁耦合振动微分方程的基础上推导了预应力T形梁的耦合振动微分方程，并通过RKF法分析比较了不同速度和预应力条件下梁跨中挠度、速度的变化规律同时还对加速度的频谱进行了分析。
第五章是本文的结尾，主要是全文主要结论的总结和对后期工作展望。
Vehicle-bridge coupling theory is mainly concerning the vibration response ofnon-prestressed simply supported beam but rarely on prestressed simply supported beam sovibration differential equation of it will be checked and solved in the previous work done byothers. The full text structure and main content are as follows:
Chapter I introduces the research background and research status of axle coupling ofprestressed simply supported beam.
Chapter II introduces several common bridge and vehicle computing model in two sectionindividually and then to establish the quality of the uniform rolling axle coupled model and itsvibration differential equation through displacement compatibility conditions and force balancebetween the two models combined.
Chapter III is devoted to basic principles and calculation steps of RKF method andNewmark method for solving second-order vibration differential equation of, also comparingthese two iteration methods on the same vibration coupled differential equations of the samemodel of T-shaped, non-prestressed beam on the computing platform of MATLAB and thencompares the calculation error of each;
Chapter IV is the main content of this article. We get the coupling vibration differentialequation of prestressed T-beam from non-prestressed T-beam mentioned above on theprecondition of the similar of the theoretical calculations of them. At the end of this chapteranalysis and comparison of variations of the deflection and speed and spectrum analysis ofacceleration at the middle span of the beam in different speeds and prestressed conditions willbe made by RKF method.
Chapter V is the final chapter of this article. It is the summary of this paper and outlookfollowing up.
第一章介绍了预应力简支梁车桥耦合分析的选题背景和国内外研究现状。
第二章分两节分别介绍了常见的桥梁和车辆计算模型，然后通过位移协调条件和作用力平衡关系将两个模型组合起来建立匀速滚动质量车桥耦合模型及其振动微分方程。
第三章介绍RKF法和Newmark法求解二阶振动微分方程的基本原理和计算步骤，然后以MATLAB为计算平台比较了这两种方法对同一非预应力T形梁耦合振动微分方程进行数值迭代的计算误差；
第四章是本文的主要内容。本章以预应力梁和非预应力梁在理论计算方面的相似为前提条件，在前面介绍的非预应力T形梁耦合振动微分方程的基础上推导了预应力T形梁的耦合振动微分方程，并通过RKF法分析比较了不同速度和预应力条件下梁跨中挠度、速度的变化规律同时还对加速度的频谱进行了分析。
第五章是本文的结尾，主要是全文主要结论的总结和对后期工作展望。
Vehicle-bridge coupling theory is mainly concerning the vibration response ofnon-prestressed simply supported beam but rarely on prestressed simply supported beam sovibration differential equation of it will be checked and solved in the previous work done byothers. The full text structure and main content are as follows:
Chapter I introduces the research background and research status of axle coupling ofprestressed simply supported beam.
Chapter II introduces several common bridge and vehicle computing model in two sectionindividually and then to establish the quality of the uniform rolling axle coupled model and itsvibration differential equation through displacement compatibility conditions and force balancebetween the two models combined.
Chapter III is devoted to basic principles and calculation steps of RKF method andNewmark method for solving second-order vibration differential equation of, also comparingthese two iteration methods on the same vibration coupled differential equations of the samemodel of T-shaped, non-prestressed beam on the computing platform of MATLAB and thencompares the calculation error of each;
Chapter IV is the main content of this article. We get the coupling vibration differentialequation of prestressed T-beam from non-prestressed T-beam mentioned above on theprecondition of the similar of the theoretical calculations of them. At the end of this chapteranalysis and comparison of variations of the deflection and speed and spectrum analysis ofacceleration at the middle span of the beam in different speeds and prestressed conditions willbe made by RKF method.
Chapter V is the final chapter of this article. It is the summary of this paper and outlookfollowing up.
引文
[1]Willis. R.:“The Effect Produced by Causing Weights to Travel Over Elastic Bars, Appendixto the Report of the Commissioners Appointed to Inquire into the Application of Iron to RailwayStructures”. H. M. Stationery Office. London,1949.
[2]Krylov. A. N,(Крылов. A. H.):“Uber die Erzwungen Schwingungen Von Gleich ElastischenStaben”.Math.Ann.V.61.(1905)
[3]Timoshenko.S.:“Erzwungene Schwingungen Prismatische Stabe”. Z. Math.u.Phys.V.59.(1911)
[4]Timoshenko. S.:“On the Transverse Vibrations of Bars of Uniform Cross Section” Phil. Mag.V.43.(1922)
[5]章长玖.公路桥梁车桥藕合振动分析[D]:[硕士学位论文].郑州:郑州大学,2011:10-12.
[6]Kolousek Vetal. Civil Engineering Struetures Subjeetedti Dynamie Loads [M]. SVTL,Bratislava,1967
[7]Chatter P K, Datta T K. Vibration of continues bridges under moving vehicles[J]. Journal ofSound and Vibration,1994,169(5):619-632
[8]Wang Ton-Lo, Huang Dong-zhou, Mohsen Shahawy. Dynamic behavior of slant-leggedrigid-frame highway bridge[J].Journal of structural engineering,1994,120(3):885-902
[9]Kawatani M, Komatsu S. Nonstationary random response of highway bridges under a seriesof moving vehicles[J].Structural Engineering/Earthquake Engineering,JSCE,1988,5(2):285-292.
[10]Kawatani M, Shimada T. Nonstationary random response and impact of girder bridges undermoving vehicles[J]. Proceeding of JSCE,1988,398(10):303-309.
[11]Bhatti, M.H. Vertical and Lateral Dynamic Response of Railway Bridges Due to NonlinearVehicles and Track Irregularities, Thesis Presented to the Illinois Institute of Technology, atChicago, Illinois, in Partial Fulfillment of the Requirements for the Degree of Doctor ofPhilosophy.1982:92-97.
[12]Chu K. H, Grag V. K. Wiriyachai A. Dynamic Interaction of Railway Trains and Bridge.Vehicles System Dynamics,1980,(4):207-236
[14]Clough. Ray Wand Joseph Penaien. Dynamics of Structural Dynamics[M], New York,1975.
[15]Graig. Roy R Jr. Str Uetural Dynamics[M], New York; Wiley,1981.
[16]Giorgio Monti, Camillo Nuti, Paolo E. Pinio. Nonlinear Response of Bridges underMultisupport Exertion[J], Journal of structural Engineering, Vol.122, No.10, October,1996.
[17]Da Silva J. G. S. Dynamical performance of highway bridge decks with irregular pavementsurface[J]. Computers and Structures,2004,82(11-12):871-881.
[18]Green M. F., Cebon D. Dynamic response of highway bridges to heavy vehicle loads:Theory and experimental validation[J].Journal of Sound and Vibration,1994,170(1):51-78.
[19]田仲初,杜嘉骅.车辆变速行驶状态下的车-桥耦合振动研究[J].公路与汽车,2011(6):1-4.
[20]汪家正.钢-混组合箱梁的车桥耦合振动影响分析[J].桥隧工程,2011:1-6.
[21]裴强.高墩大跨桥梁车桥祸合振动行车安全性与舒适性评价方法[D].[硕士学位论文].西安:长安大学,2011:9-11.
[22]柴小鹏.公路斜拉桥车桥耦合振动分析[D].[硕士学位论文].哈尔滨:哈尔滨工业大学,2011:1-12.
[23]肖艳平,沈火明.连续梁车桥耦合振动方法比较及特征分析[M].中国交通土建工程学术论文集,2006:1-5.
[24]韩万水,王涛.基于模型修正梁格法的车桥耦合振动分析系统[J].中国公路学报,2011,24(5):1-4.
[25]李永乐,向活跃.双车交会过程的风-车-桥耦合振动研究[J].土木工程学报,2011,44(12):1-6.
[26]杜宪亭,夏禾,余竹.车桥耦合动力分析中地震动输入模式的研究[J].中国铁道学报,2011,32(6):1-3.
[27]孔树清.公路钢箱梁车桥耦合振动的精细化有限元分析[D].[硕士学位论文].宁波:宁波大学,2011:4-11.
[28]薛军平.车桥耦合振动模型方程的建立及动力响应分析[D].[硕士学位论文].天津:天津大学,2011:6-10.
[29]姚玲森,项海帆.桥梁工程[M].北京:人民交通出版社,2008,75-84.
[30]刘福寿.基于车桥耦合振动的混凝土简支梁桥动力特性研究[D].[硕士学位论文].长春:吉林大学,2011:4-11.
[31]宋一帆.公路桥梁动力学[M].北京:人民交通出版社,1999,74-94.
[32]李鸿晶,王通,廖旭.关于Newmark-β法机理的一种解释[J].地震工程与工程振动,2011,2(31):1-2.
[33]龚纯,王正林.MATLAB语言常用算法程序集[M].北京:电子工业出版社,2008:167-187.
[34]宋叶志,贾东永. MATLAB数值分析与应用[M].北京:机械工业出版社,2009:387-392.
[35]徐涛.数值计算方法[M].长春:吉林科学技术出版社,1996:337-347.
[36]徐士良.数值分析与算法[M].北京:机械工业出版社,2009
[37]王国荣,俞耀明,徐兆亮.数值分析[M].北京:机械工业出版社,2010,430-548.
[38]吴兆金,王国英,范红军.数值分析[M].北京:人民邮电出版社,2010:305-312.
[39]马明书.龙哥-库塔法的级数与阶数[J].河南机专学报(自然科学版),1994:2(2):1-3.
[40]叶见曙,李国平.结构设计原理[M].北京:人民交通出版社,1996:222-338.
[41]熊学玉,预应力结构原理与设计[M].北京:中国建筑工业出版社,2004:120-128.
[42] M. Saiidi, B. Douglas, S. Feng. Prestress ForceEffect on Vibration Frequency of ConcreteBridges[J]. Journal of Structure Engineering,1994,120(7):2233-2241.
[43]张魁元,赵建华.大学数学——微积分（下册）[M].北京:高等教育出版社,2004:312-344.
[44]陈亚勇. MATLAB信号处理详解[M].北京:人民邮电出版社,2001:36-43.
[2]Krylov. A. N,(Крылов. A. H.):“Uber die Erzwungen Schwingungen Von Gleich ElastischenStaben”.Math.Ann.V.61.(1905)
[3]Timoshenko.S.:“Erzwungene Schwingungen Prismatische Stabe”. Z. Math.u.Phys.V.59.(1911)
[4]Timoshenko. S.:“On the Transverse Vibrations of Bars of Uniform Cross Section” Phil. Mag.V.43.(1922)
[5]章长玖.公路桥梁车桥藕合振动分析[D]:[硕士学位论文].郑州:郑州大学,2011:10-12.
[6]Kolousek Vetal. Civil Engineering Struetures Subjeetedti Dynamie Loads [M]. SVTL,Bratislava,1967
[7]Chatter P K, Datta T K. Vibration of continues bridges under moving vehicles[J]. Journal ofSound and Vibration,1994,169(5):619-632
[8]Wang Ton-Lo, Huang Dong-zhou, Mohsen Shahawy. Dynamic behavior of slant-leggedrigid-frame highway bridge[J].Journal of structural engineering,1994,120(3):885-902
[9]Kawatani M, Komatsu S. Nonstationary random response of highway bridges under a seriesof moving vehicles[J].Structural Engineering/Earthquake Engineering,JSCE,1988,5(2):285-292.
[10]Kawatani M, Shimada T. Nonstationary random response and impact of girder bridges undermoving vehicles[J]. Proceeding of JSCE,1988,398(10):303-309.
[11]Bhatti, M.H. Vertical and Lateral Dynamic Response of Railway Bridges Due to NonlinearVehicles and Track Irregularities, Thesis Presented to the Illinois Institute of Technology, atChicago, Illinois, in Partial Fulfillment of the Requirements for the Degree of Doctor ofPhilosophy.1982:92-97.
[12]Chu K. H, Grag V. K. Wiriyachai A. Dynamic Interaction of Railway Trains and Bridge.Vehicles System Dynamics,1980,(4):207-236
[14]Clough. Ray Wand Joseph Penaien. Dynamics of Structural Dynamics[M], New York,1975.
[15]Graig. Roy R Jr. Str Uetural Dynamics[M], New York; Wiley,1981.
[16]Giorgio Monti, Camillo Nuti, Paolo E. Pinio. Nonlinear Response of Bridges underMultisupport Exertion[J], Journal of structural Engineering, Vol.122, No.10, October,1996.
[17]Da Silva J. G. S. Dynamical performance of highway bridge decks with irregular pavementsurface[J]. Computers and Structures,2004,82(11-12):871-881.
[18]Green M. F., Cebon D. Dynamic response of highway bridges to heavy vehicle loads:Theory and experimental validation[J].Journal of Sound and Vibration,1994,170(1):51-78.
[19]田仲初,杜嘉骅.车辆变速行驶状态下的车-桥耦合振动研究[J].公路与汽车,2011(6):1-4.
[20]汪家正.钢-混组合箱梁的车桥耦合振动影响分析[J].桥隧工程,2011:1-6.
[21]裴强.高墩大跨桥梁车桥祸合振动行车安全性与舒适性评价方法[D].[硕士学位论文].西安:长安大学,2011:9-11.
[22]柴小鹏.公路斜拉桥车桥耦合振动分析[D].[硕士学位论文].哈尔滨:哈尔滨工业大学,2011:1-12.
[23]肖艳平,沈火明.连续梁车桥耦合振动方法比较及特征分析[M].中国交通土建工程学术论文集,2006:1-5.
[24]韩万水,王涛.基于模型修正梁格法的车桥耦合振动分析系统[J].中国公路学报,2011,24(5):1-4.
[25]李永乐,向活跃.双车交会过程的风-车-桥耦合振动研究[J].土木工程学报,2011,44(12):1-6.
[26]杜宪亭,夏禾,余竹.车桥耦合动力分析中地震动输入模式的研究[J].中国铁道学报,2011,32(6):1-3.
[27]孔树清.公路钢箱梁车桥耦合振动的精细化有限元分析[D].[硕士学位论文].宁波:宁波大学,2011:4-11.
[28]薛军平.车桥耦合振动模型方程的建立及动力响应分析[D].[硕士学位论文].天津:天津大学,2011:6-10.
[29]姚玲森,项海帆.桥梁工程[M].北京:人民交通出版社,2008,75-84.
[30]刘福寿.基于车桥耦合振动的混凝土简支梁桥动力特性研究[D].[硕士学位论文].长春:吉林大学,2011:4-11.
[31]宋一帆.公路桥梁动力学[M].北京:人民交通出版社,1999,74-94.
[32]李鸿晶,王通,廖旭.关于Newmark-β法机理的一种解释[J].地震工程与工程振动,2011,2(31):1-2.
[33]龚纯,王正林.MATLAB语言常用算法程序集[M].北京:电子工业出版社,2008:167-187.
[34]宋叶志,贾东永. MATLAB数值分析与应用[M].北京:机械工业出版社,2009:387-392.
[35]徐涛.数值计算方法[M].长春:吉林科学技术出版社,1996:337-347.
[36]徐士良.数值分析与算法[M].北京:机械工业出版社,2009
[37]王国荣,俞耀明,徐兆亮.数值分析[M].北京:机械工业出版社,2010,430-548.
[38]吴兆金,王国英,范红军.数值分析[M].北京:人民邮电出版社,2010:305-312.
[39]马明书.龙哥-库塔法的级数与阶数[J].河南机专学报(自然科学版),1994:2(2):1-3.
[40]叶见曙,李国平.结构设计原理[M].北京:人民交通出版社,1996:222-338.
[41]熊学玉,预应力结构原理与设计[M].北京:中国建筑工业出版社,2004:120-128.
[42] M. Saiidi, B. Douglas, S. Feng. Prestress ForceEffect on Vibration Frequency of ConcreteBridges[J]. Journal of Structure Engineering,1994,120(7):2233-2241.
[43]张魁元,赵建华.大学数学——微积分（下册）[M].北京:高等教育出版社,2004:312-344.
[44]陈亚勇. MATLAB信号处理详解[M].北京:人民邮电出版社,2001:36-43.