高墩大跨预应力混凝土梁桥振动频率实用计算方法
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摘要
桥梁的自振特性在桥梁的动力分析中占有十分重要的地位,他是桥梁一切动力分析的基础。目前对于等截面的梁式桥可以得到精确的解析解,但对于变截面的梁式桥则主要是运用数值分析的方法求解。最常用的数值分析方法主要包括有限差分法和有限元法。数值分析方法虽能够得到较精确的分析结果,但其耗时较长,不利于工程技术人员对桥梁结构的快速判断。同时,影响车桥耦合振动的主要是桥梁的一阶竖向振动频率。因此,本文旨在研究变截面梁式桥的自振特性,为这类桥梁的动力分析提供参考,并给出这类桥梁基频以及一阶竖向振动频率的快速计算公式,方便工程技术人员的实际应用。因此,研究变截面梁式桥的自振特性具有重要的理论意义与工程实用价值。
本文以陕西某变截面连续梁、连续刚构、刚构—连续组合体系桥梁为依托工程,考虑了跨径变化、跨数和截面尺寸变化、桥墩墩高和桥墩截面尺寸变化,对于刚构—连续组合体系桥梁还考虑了桥跨结构形式的各种组合,在综合考虑了以上各参数的情况下,以结构设计原理为理论依据,构造了大量的桥梁模型进行模态分析,并分析了以上各参数影响桥梁自振特性的规律。对于变截面连续梁,以桥梁总长与中跨跨径的比值、跨中截面惯性矩与面积之比和支点截面惯性矩与面积之比的比值为参数；对于连续刚构,在考虑以上参数的基础上还考虑了主梁质量和桥墩质量的比值以及墩高与中跨跨径的比值；刚构—连续组合体系桥梁在连续刚构的基础上考虑了桥跨结构形式改变的影响；通过回归分析,首次给出了以上三种桥梁的基频以及一阶竖向振动频率的计算公式,并进行了算例验证。
其研究结论可供该类桥梁的设计参考,为后续的动力分析提供了理论参考,也方便了工程技术人员的实际运用。
Nature vibration properties of bridge which is the foundation of all dynamic analysis of the bridge occupies very important position in bridge's dynamic analysis. At present the non-equal beam bridge can get accurate analytic solution, but to variable cross-section beam bridge is mainly on the numerical analysis method to solve. The most commonly used numerical analysis method includes the finite difference method and finite element method. Numerical analysis method can be got more precise analysis results, but it makes against engineering and technical personnel's rapid judgment of bridge structure because of the time-consuming longer. Meanwhile, the main impact to coupled vibration of the bridge is the first vertical vibration frequency. Therefore, this thesis aims to study the nature vibration properties of variable cross-section beam bridge and provides reference for the dynamic analysis of this kind of bridge. The thesis also gives the fast calculation formula of the bridge's fundamental frequency and first vertical vibration frequency to convenient the practical application of engineering and technical personnel. So the research of nature vibration characteristics of variable cross-section of the beam type bridge has important theoretical significance and practical value.
In this thesis, based on a variable section continuous beam, continuous rigid frame, and rigid frame- continuous composite bridge project in Shaanxi. The factors is considered, such as the span changes, the number of spans, cross-section size and the number of changes in height and pier section size changes. The various combinations forms of bridges are also considered in the structure for the rigid frame- continuous composite bridge. On the case of above parameters, structural design principles as the theoretical basis and a large number of bridges models, modal analysis and the laws of effect to natural vibration characteristics are carried out. For the variable cross-section beam, the bridge span length, the ratios of spans, cross sectional moment of inertia, ratio of cross sectional inertia moment and area and ratio of pivot inertia moment and area are considered as parameters. For the continuous frame bridge, on the basis of considering the above parameters, the ratios of piers' quality and the main girder's quality and the ratios of piers heights and middle cross-spans are also considered. For rigid frame-continuous composite system, besides the factors of continuous rigid frame bridge, the impact of bridge structure style changes are introduced, too. By the regression analysis, the fundamental frequency formulas of the above three bridges and first vertical vibration frequency are given for the first time, and numerical example is also carried out.
The conclusion of the study can be take reference for the design of such bridges and for the subsequent dynamic analysis, and also facilitates the practical application of engineering and technical personnel.
本文以陕西某变截面连续梁、连续刚构、刚构—连续组合体系桥梁为依托工程,考虑了跨径变化、跨数和截面尺寸变化、桥墩墩高和桥墩截面尺寸变化,对于刚构—连续组合体系桥梁还考虑了桥跨结构形式的各种组合,在综合考虑了以上各参数的情况下,以结构设计原理为理论依据,构造了大量的桥梁模型进行模态分析,并分析了以上各参数影响桥梁自振特性的规律。对于变截面连续梁,以桥梁总长与中跨跨径的比值、跨中截面惯性矩与面积之比和支点截面惯性矩与面积之比的比值为参数；对于连续刚构,在考虑以上参数的基础上还考虑了主梁质量和桥墩质量的比值以及墩高与中跨跨径的比值；刚构—连续组合体系桥梁在连续刚构的基础上考虑了桥跨结构形式改变的影响；通过回归分析,首次给出了以上三种桥梁的基频以及一阶竖向振动频率的计算公式,并进行了算例验证。
其研究结论可供该类桥梁的设计参考,为后续的动力分析提供了理论参考,也方便了工程技术人员的实际运用。
Nature vibration properties of bridge which is the foundation of all dynamic analysis of the bridge occupies very important position in bridge's dynamic analysis. At present the non-equal beam bridge can get accurate analytic solution, but to variable cross-section beam bridge is mainly on the numerical analysis method to solve. The most commonly used numerical analysis method includes the finite difference method and finite element method. Numerical analysis method can be got more precise analysis results, but it makes against engineering and technical personnel's rapid judgment of bridge structure because of the time-consuming longer. Meanwhile, the main impact to coupled vibration of the bridge is the first vertical vibration frequency. Therefore, this thesis aims to study the nature vibration properties of variable cross-section beam bridge and provides reference for the dynamic analysis of this kind of bridge. The thesis also gives the fast calculation formula of the bridge's fundamental frequency and first vertical vibration frequency to convenient the practical application of engineering and technical personnel. So the research of nature vibration characteristics of variable cross-section of the beam type bridge has important theoretical significance and practical value.
In this thesis, based on a variable section continuous beam, continuous rigid frame, and rigid frame- continuous composite bridge project in Shaanxi. The factors is considered, such as the span changes, the number of spans, cross-section size and the number of changes in height and pier section size changes. The various combinations forms of bridges are also considered in the structure for the rigid frame- continuous composite bridge. On the case of above parameters, structural design principles as the theoretical basis and a large number of bridges models, modal analysis and the laws of effect to natural vibration characteristics are carried out. For the variable cross-section beam, the bridge span length, the ratios of spans, cross sectional moment of inertia, ratio of cross sectional inertia moment and area and ratio of pivot inertia moment and area are considered as parameters. For the continuous frame bridge, on the basis of considering the above parameters, the ratios of piers' quality and the main girder's quality and the ratios of piers heights and middle cross-spans are also considered. For rigid frame-continuous composite system, besides the factors of continuous rigid frame bridge, the impact of bridge structure style changes are introduced, too. By the regression analysis, the fundamental frequency formulas of the above three bridges and first vertical vibration frequency are given for the first time, and numerical example is also carried out.
The conclusion of the study can be take reference for the design of such bridges and for the subsequent dynamic analysis, and also facilitates the practical application of engineering and technical personnel.
引文
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[3]宋一凡,贺拴海.《弯桥结构动力性能评估分析理论与方法研究》的研究报告.长安大学,2008
[4]周勇军,赵小星,贺拴海,宋一凡.弯钢箱梁桥的动力分析及模态试验.郑州大学学报：工学版,2005,26(4)：20-24
[5]周勇军,贺拴海,宋一凡,赵小星.基于锤击法的弯连续刚构模型桥动力试验.振动、测试与诊断,2007,27(3)：212-215
[6]Stokes G G.Discussions of a Differential Equation Related to the Breaking of Railway Bridges [J].Trans, Cambridge Phil. Soc.V 8.Part5,1896:12-16
[7]Chatterjee P K. Datta T K et al. Vibration of continues bridges under moving vehicles [J].Journal of Sound Vibration.1994,169(5):619-632
[8]Kolousek V etal.Civil Engineering Structures Subjected to Dynamic Load [M].SVTL, Bratislava,1967:54-58
[9]Andersen L, Nielsen S R K, Iwankiewicz R. Vehicle moving along an infinite beam with random surface irregularities on a Kelvin foundation[J].Journal of AppliedMechanics, 2002:69-75
[10]Kawatani M, Kobayashi Y, Takamori K. Non-stationary random analysis with coupling vibration of bending and torsion of simple girder-bridge under moving vehicle [J]. Structural Engineering Earthquake Engineering JSCE,1998,15(1):107-114
[11]Marchesiello S, Fasana A, Garibaldi L, et al. Dynamic of multi-span continuous straight bridges subject to multi-degrees of freedom moving vehicle excitation[J]. Journal of Sound and Vibration,1999,224(3):541-561
[12]Wang T L, Huang D Z. Cable-stayed bridge vibration due to road surface roughness [J]. Journal of Structural Engineering ASCE 1992,188(5):1354-1373
[13]A.Wiriyachai,K.H.Chu,V.K.Garg,Bridge Impact due to Wheel and Track Irregularities [J] Journal of Engineering Mechanics Division,Vol.108,No.4,1982
[14]A.Wiriyachai, K.H.Chu, V.K.Garg, Impact Study by Various Bridge Models[J]. Earthquake Engineering and Structual Dynamics, Vol.10, No.1,1982
[15]Bhatti M.H.:Vertical and Lateral Dynamics Response of Railway Bridges due to Nonlinear Vehicle and Track Irregulates,Ph.D. Thesis [J].Illinois Institute of Technology, Chicago,Illinois,1982
[16]Wang T.L., et al. Dynamics Response of Highway Tracks duo to Road Surface Roughness [J],Journal of Computers and Structures,1993,49(6)
[17]Wang T.L.,Impact and Fatigue in Open-deck Steel Truss and Ballasted Prestressed Concrete Railway Bridge,Ph.D. Thesis [J], Illinois Institute of Technology, Chicago Illinois,1984
[18]Wang T.L.Impact in a Railway Truss Bridge [J], Journal of Computers and Structures, 1993,49(6)
[19]Wang T.L,M.shahawy.Impact in Highway Prestressed Concrete Bridges [C]. Computers and Structures Vol.44, No.3,1992
[20]Olsson M.:On the Foundational Moving Load Problems[J]. Journal of Sound and Vibration,1991,145(2)
[21]Tanabe M.Yamada Y.:Model Method for Interaction of Train and Bridge [J]. Journal of Computers and Structures,1987,27(1)
[22]Bogaert Van:Dynamics Response of Trains Crossing Large Span Double-track Bridges [J]. Journal of Constructional Steel Research,1993,24(1)
[23]Green M.F., Cebon D.Dynamics Response of Highway Bridges to Heavy Vehicles Loads: Theory and Experimental Validation [J]. Journal of Sound and Vibration,1994,170(1)
[24]Piotr o, Yozo F. Interaction of Nonconservative 1DContinuum and Moving MDOF Oscillator[J]. J EngrgMesh, ASCE,2001,127(11):1 082-1088
[25]Wang T L, Huang D Z, Mohsen S. Dynamic Re-sponse of Multigirder Bridge[J]. J Struct Engrg, ASCE,1992,118(8):2 222-2238
[26]周勇军,赵小星,贺拴海,宋一凡.弯钢箱梁桥的动力分析及模态试验[J].郑州大学学报(工学版),2005,vo126,No.4
[27]周勇军,赵小星,贺拴海,宋一凡.连续梁桥模态分析与试验[J].长安大学学报(自然科学版),2007,vo127,No.3
[28]宋一凡,贺拴海.公路桥梁冲击系数的影响因素分析[J].西安公路交通大学学报,2001,vo1.2
[29]王飞,曹传林,方志.基于能量原理的双肢薄壁高墩稳定计算[J].中外公路,2006,vo126,No.1
[30]宋一凡,贺拴海.基于能量原理的框架桥墩地震力分析[J].长安大学学报(自然科学版),2002,vo122,No.1
[31]彭献,游福贺.车桥耦合系统固有频率的研究[J].动力与控制学报,2010,vo18,No.3
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