摘要
桥梁作为重要的社会基础设施,是抗振防灾研究的重要对象。尤其是大跨度的悬索桥,由于其特殊的重要地位,其车桥耦合动力特性更是我们需要重点研究的课题。
近年来,随着世界经济的发展、技术的进步,高速铁路已经成为世界上最经济、最高效的运输系统。随着车辆行驶速度的提高,车辆与桥梁之间的动力相互作用问题更加的突出,车桥耦合动力相互作用对桥梁及车辆的影响越来越大。之前也有很多学者对这个问题进行了研究,给出了很多的解决方法,但是大都计算复杂,对各种桥型不具有通用性。因此,建立一套通用性好、精度高且使用方便的计算程序具有重大意义。
本文针对目前其它计算方法的不足,在总结和吸收国内外前人研究成果的基础上,针对大跨度悬索桥在移动车辆作用下的车桥耦合振动问题进行了研究。给出了系统的求解车桥耦合振动问题的处理方法,并且对大跨度悬索桥的静力及成桥状态计算给出了详细的计算方法,并编制了相关的程序。本文主要研究内容包括:
(1)对大跨度悬索桥的静力计算问题进行了讨论。本文基于挠度理论对悬索桥的静力计算方法进行了推导,在推导过程中考虑了活载二阶非线性项的影响,并验证了算法的正确性。在文中,对加劲梁在主塔处铰接和连续时受温度荷载的影响情况进行了对比研究。
(2)给出了大跨度悬索桥成桥状态的精细化非线性有限元计算方法。本文首先对目前存在的几种确定成桥状态的解析方法进行了回顾,随后推导了基于非线性悬链线索单元的非线性有限元法的计算程式,并给出了详细的计算过程。在文中,采用多个经典算例验证了算法的有效性,并对某跨长江悬索桥的成桥状态进行了计算分析。
(3)对简支梁的经典车桥耦合振动理论进行了回顾。对简支梁在移动力、移动质量、移动单轴车辆、移动双轴车辆作用下的解析计算方法进行了回顾。
(4)对车辆和桥梁动力模型的建立方法进行了详细的研究。文中首先对车辆的基本要素进行了介绍,特别是对刚性连接的处理进行了说明,给出了任意复杂车辆模型的建立方法,并建立了双轴车辆和四轴车辆的动力模型。文中还对大跨度悬索桥动力模型的建立进行了说明。
(5)基于随机理论,给出了路面平整度的模拟方法。文中对几种常见的路面平整度的功率谱密度进行了介绍,给出了基于谐波叠加法模拟路面平整度的计算方法。文中对空间频率范围的取值、取样周期的大小及取样时间步长的确定进行了说明,并给出了详细的计算步骤。最后对几种常见等级路面的路面平整度进行了模拟,并对模拟路面平整度的功率谱与理论功率谱进行了对比验证。
(6)推导了车桥耦合单元,建立了车桥耦合振动的计算方法。本文推导了一般车辆作用下车桥耦合单元,对车桥耦合方程的建立及求解进行了详细的说明。文中还给出了移动质量、移动单轴车辆、移动双轴车辆及移动四轴车辆作用下的车桥耦合单元的影响矩阵。最后验证了本文方法的有效性并对某跨长江悬索桥在移动卡车、移动列车作用下的动力响应进行了求解。
(7)给出了地震作用下的车桥耦合振动问题的计算方法。本文对地震作用下的车桥耦合振动方程进行了推导,并对某跨长江悬索桥在地震作用下的车桥耦合振动问题进行了研究。
As the important infrastructure, bridge is the important subject investigated of the vibration reduction and disaster resistance. Since the long span suspension bridges play an important role, the dynamic characteristics of the coupling interaction between vehicle and bridge is an important research subject needs to pay more attention.
Recently, with the development of the world economy and technical advancement, the high speed railway becomes the most economic and the most efficiency transport system in the world. With the increasing of the running speed of the vehicles, the VBI problem (the coupling interaction problem between the vehicles and bridges) becomes more serious. In the past, great deal research on the VBI problem was conducted and many solution methods were provided. But most of the solution methods are very complicated and don’t have versatility for various bridge types. So it has great significance to develop a program, which has good versatility and high precision.
In this dissertation, considering the shortage of the other methods, the VBI problem of the long span suspension bridges under moving vehicles was studied based on the summary of general study of the predecessor’s research experience in China and abroad in this field. A method was provided to deal with the VBI problem, and detailed calculating methods were provided to calculate the static characteristics and determine the target configurations under dead loads for the long span suspension bridges. The main research work is as follows:
1. The static calculation problem of long span suspension bridges was discussed. In this dissertation, the static calculation method of suspension bridges based on the deflection theory was derived. The second order nonlinear term of the live load was considered in this paper, and the validity was verified. Finally, the comparative study of stiffening girders continuous or hinged at the pylons under temperature load was made.
2. The refined nonlinear finite element method was provided to determine the target configurations under dead loads for the long span suspension bridges. In this dissertation, several analytic methods of determining the target configurations were reviewed firstly, and then nonlinear finite element method based on the nonlinear catenary cable element were derived. The detailed calculating procedure was provided. In this paper, several classical examples were adopted to verify the validity of this method, and the target configuration of a suspension bridge crossing the Changjiang River was studied.
3. The classical VBI theories for simply supported beam were reviewed. The analytic calculation methods were reviewed for simply supported beam under moving force, moving mass, moving single axle vehicle and moving double axle vehicle.
4. Detailed research on modeling the vehicle and the bridge was made. Firstly, the fundamental elements of vehicles were introduced. Especially, the method dealing with the rigid connections was illuminated. And the modeling method for arbitrary complex vehicle was provided. The dynamic models were built for double axle vehicle and four-axis vehicle. The method building the dynamic model of long span suspension bridges was also introduced.
5. The simulation method for road roughness was provided based on the stochastic theory. In this dissertation, several common power spectral density expressions for road roughness were introduced, and the simulation method was provided based on the harmonic superposition. The method to determine the range of spatial frequency, the sampling period and the sampling time step was introduced. At last, simulation was made for several common grade of road pavement, and the power spectrum estimation was compared with the theoretical power spectrum.
6. The VBI element was derived, and a method calculating the VBI characteristics was built. The VBI element subjected to moving general vehicles was derived. The method of establishing the VBI equations and solution procedure were detailed introduced. In this dissertation, the influence matrices of VBI element under moving mass, moving single axle vehicle, moving double axle vehicle and moving four-axis vehicle. At last, the validity of this method was verified, and the dynamic response of a suspension bridge crossing the Changjiang River under moving trailer vehicle and train was solved.
7. A method of solving VBI problem under seismic action was provided. In this dissertation, the vibration differential equations of the VBI problem were derived, and the VBI problem of a suspension bridge crossing the Changjiang River under seismic action was studied.
引文
[1].何发礼.高速铁路中小跨度曲线梁桥车桥耦合振动研究[D].西南交通大学博士学位论文,1999
[2]. Willis, R., Appendix to the Report of the Commissioners Appointed to Inquire into the Application of Iron to Railway Structures[R]. Stationary Office, London, England, 1849.
[3]. Willis, R., Preliminary essay to the appendix B.: Experiments for determining the effects produced by causing weights to travel over bars with different velocities[R]. GREY G. et al.: Report of the Commissioners Appointed to Inquire into the Application of Iron to Railway Structures. W. Clowes and Sons, London, 1849.
[4]. Stokes, G., Discussion of a differential equation relating to the breaking of railway bridges[J]. Transactions of the Cambridge Philosophical Society, 1849. 8(5): 707-735.
[5]. Zimmermann, H., Die Schwingungen eines Tr gers mit bewegter Last[M]. 1896: W. Ernst.
[6]. Krylov A.N., Mathematical Collection of Papers of the Academy of Sciences[M], Matematicheskil sbornik Akademii Nauk, Peterburg 1905.
[7]. Timoshenko, S., Forced vibration of prismatic bars[J]. Izvestiya Kievskogo politekhnicheskogo instituta, 1908: 163-203.
[8]. Lowan, A., LIV. On transverse oscillations of beams under the action of moving variable loads[J]. Philosophical Magazine Series 7, 1935. 19(127): 708-715.
[9]. Bondar N.G., Dynamic Calculations of Beams Subjected to a Moving Load. Issledovaniya po terrii sooruzhenii, Stroiizdat, Moscow, 1954,11,23.
[10]. Timoshenko, S., On the forced vibration of bridges[J]. Philosophical Magazine, 1922. 6(43): 1018.
[11]. Saller H., Einfluss bewegter Last auf Eisenbahnoberbau und Brucken[M]. Kreidels Verlag, Berlin 1921.
[12]. Jeffcott H. H., On the Vibration of Beams under the Actions of Moving Loads[J]. Philosophical Magazine, 1929;48:66-97.
[13]. Steuding H., Die Schwingungen von Tragern bei bewegten Lasten[J]. Archive of Applied Mechanics, 1934;5:275-305.
[14]. Schallenkamp A., Schwingungen von Tragern bei betwegten Lasten[J]. Archive of Applied Mechanics, 1937;8:182-198.
[15]. Muchnikov V. M., Some Methods of Comuputing Vibration of Elastic Systems Subjected to Moving Loads[M], Gosstroiizdat, Moscow, 1953.
[16]. Ryazanova M. YA., Vibration of Beams Produced by the Action of Load Moving on Them[J].Dopovidi AN URSR, 1958;20(2):157-161.
[17]. Naleskiewicz J., On the Dynamics of Bridge Girders[M]. Archiwum mechaniki stosowanej, 1953;5:517-544.
[18]. Bolotin V. V., Problem of Bridge Vibration under the Action of a Moving Load[J]. Izvestiya AN SSSR, Mekhanika I mashinostroenie, 1961;4:109-115.
[19]. Inglis C. E., A Mathematical Treatise on Vibration in Railway Bridges[M]. The University Press,Cambridge,1934.
[20]. Chilver A.H., A Note on the Mise-Kunii Theory of Bridge Vibration[J]. Quarterly Journal of Mechanics and Applied Mathematics,1956;9(2):207-211.
[21]. Miss K., Kunii S., A theory for the Forced Vibrations of a Railway Bridge under the Action of Moving Loads[J]. Quarterly Journal of Mechanics and Applied Mathematics, 1956;9(2):195-206.
[22]. Odman S.T.A., Differential Equation for Calculation of Vibrations Produced in Load-Bearing Structures by Moving Load[J]. 3rd Congr. Intern. Assoc. Bridge Structural Engng., Liege, 1948:669-680.
[23]. Kolousek V., Dynamics of Civil Engineering Structures. Part I-General Problems[M], 2rd; Part II- Continuous Beams and Frame Systems[M],2rd; Part III-Selected Topics(in Czech.) SNTL[M], Prague1967,1956,1961.
[24]. Stanisic MM., Hardin JC., On the response of beams to an arbitrary number of concentrated moving masses[J]. Journal of the Franklin Institut, 1969,287:115–123.
[25]. Ting EC., Genin J., Ginsberg JH., A general algorithm for the moving mass problem[J]. Journal of Sound Vibration, 1974,33(1):49–58.
[26]. Sadiku S., Leipholz HHE., On the dynamics of elastic systems with moving concentrated masses[J]. Archive of Applied Mechanics, 1987,57:223–242.
[27]. Akin JE., Mofid M., Numerical solution for response of beams with moving mass[J]. Journal of Structures Engineering, ASCE, 1989,115(1):120–131.
[28]. Hillerborg A., Dynamic Influences of Smoothly Running Loads on Simply Supported Girders[M]. Kungl. Tekn. Hogskolan, Stockholm , 1951.
[29]. Biggs J. M., Suer H. S., Louw J. M., Vibration on Simple-Span Highway Bridges[J]. Transactions of the American Society of Civil Engineers, 1959;124:291-318.
[30]. Tung T.P., Goodman L.E., Chen T.Y., Newmark N.M., Highway-Bridge Impact Problems[J]. Highway Research Board Bull., 1956;124:111-134.
[31]. Tan CP, Shore S. Response of horizontally curved bridges to moving load[J]. Journal of the Structural Division, ASCE,1968,94(9):2135–2151.
[32]. Genin J, Ginsberg JH, Ting EC. A complete formulation of inertial effects in theguideway–vehicle interaction problem[J]. Journal of Sound and Vibration, 1975,38(1):15–26.
[33]. Blejwas TE, Feng CC, Ayre RS. Dynamic interaction of moving vehicles and structures[J]. Journal of Sound and Vibration , 1979,67(4):513–521.
[34]. Wen P.R. Dynamic response of beams traversed by two-axle loads[J]. Journal of Engineering Mechanics, ASCE,1960,86(EM5):91-111
[35]. Fryba L. Vibration of solids and structures under moving loads[M]. Groningen (The Netherland): Noordhoff International Publishing 1972.
[36]. Fryba L. Dynamics of Railway B ridges[M ]. London, T homas Telford, 1996
[37]. Hiral A. , Ito M., Dynamic effects produced by trains upon suspension bridges[J]. Symposium on suspension bridges, Lisbon, 1966.
[38]. Hiral A. , Ito M., Response of suspension bridges to moving vehicles[J]. Journal of the Fauculty of Engineering, University of Tokyo. 1967.
[39]. Hayashikawa T., Watanabe N., Suspension bridge response to moving loads[J]. The Journal of Engineering Mechanics, ASCE, 1982;108(EM6) .
[40]. Dodds C.J., Robson J.D., The description of road surface roughness[J]. Journal of Sound and Vibration. 1973,31(2):175-183.
[41]. Snyder J.E., Wormley D.N., Dynamic interactions between vehicles and elevated, flexible randomly irregular guideways[J]. Journal of Dynamic Systems, Measurement and Control. 1977,99(1):22-23.
[42]. Schneider H.J., Elf H.P., Kolle P. Modeling of traveling-loads and time-dependant masses with Adina[J]. Computer and Structures, 1983,17:5-6.
[43]. Padovan J., Paramodilok O., Generalized solution of time dependent traveling load problem via moving finite element scheme[J]. Journal of Sound and Vibration.1983,91(2).
[44]. Hino J., Yoshimura T., Konishi K., A finite element method prediction of the vibration of a bridge subjected to a moving vehicle load[J]. Journal of Sound and Vibration,1984,96 (1).
[45]. Olsson M., Finite element model co-ordinate analysis of structures subjected to moving loads[J]. Journal of Sound and Vibration,1985,99 (1).
[46]. Hino J., Yoshimura T., Vibration analysis of non-linear beams subjected to a moving load using the finite element method[J]. Journal of Sound and Vibration,1985,100(4).
[47].松浦章夫.高速铁路における车辆と桥桁の动的相互作用[R].铁道技术研究资料, 1974, 31 (5) : 14-17.
[48].松浦章夫.高速铁路桥梁の动力问题の研究[R].日本土木学会论文报告集, 1976. 12,No. 256: 35-47.
[49].松浦章夫.二轴货车走行性における长大吊桥の折に角限度[R].铁道技术研究报告, 1978,1806,1-44
[50].松浦章夫.本州四国联络桥の列车走行に关する研究[R].铁道技术研究报告, 1970.
[51]. Chu K H,Railway-bridge impact: simplified train and bridge model [J]. Structural Engineering, ASCE, 1979,105(9):1823-1844.
[52]. Chu K H, Dynamic interaction of railway train and bridge [J]. Vehicle System Dynamics,1980, 9(4):207-236.
[53]. Wiriyachai A, Chu K H, Garg V K., Bridge impact due wheel and track irregularities [J]. Engineering Mechanics Division, ASCE,1982,108(4):648-665.
[54]. Wiriyachai A, Chu K H, Garg V K., Impact study by various bridge models[J]. Earthquake Engineering & structural Dynamics1982, 10(1):31-45.
[55]. Bhatti M. H., Vertical and Lateral Dynamic Response of Railwai Bridges due to Nonlinear Vehicle and Track Irrgularities[D]. Illinois Institute of technology, Chicago, Illinois, 1982.
[56]. Wang T. L., Dynamic Response of Highway Tracks due to Road Surface Roughness[J], Journal of Computers and Structures, 1993,49(6):1055-1067.
[57]. Wang T. L., Impact in a Railway Truss Bridge[J], Journal of Computers and Structures, 1993,49(6):1045-1054.
[58]. Wang T. L., Shahswy M., Impact in Highway Prestressed Concrete Bridges[J], Journal of Computers and Structures, 1992,44(3):525-534.
[59]. Wang T. L., Ramp/Bridge Interface in Railway Prestressed Concrete Bridges[J], Journal of Structures Engineering, 1990,116(6):1648-1659.
[60]. Wang T. L., Impact and Fatigue in Open-deck Steel Truss and Ballasted Prestressed Concrete Railway Bridges[D]. Illinois Institute of technology, Chicago, Illinois, 1984.
[61]. Wang T. L., Chu K. H., Railway Bridge/Vehicle Interaction Studies with New Vehicle Model[J], Journal of Structural Engineering,1991,117(7),2099-2116.
[62]. Diana G., A Numerical Method to Define the Dynamic Behavior of a Train Running on a Deformable Structure[J], MECCANICA, Special Issue,1988,27-42.
[63]. Diana G., Dynamic Interaction between Railway Vehicles and Track[R]. Report Dip. Di. Meccanica Politecnico di Milano,1986.
[64]. Diana G., Cheli F., Dynamic Interaction of Railway Systems with Large Bridges[J], Vehicle System Dynamics,1989,18(1-3):71-106.
[65]. Olsson M., Finite Element Model Coordinate Analysis of Structures Subjected to Moving Loads[J], Journal of Sound and Vibration,1985,99(1):1-12.
[66]. Olsson M., On the Foundational Moving Load Problems[J], Journal of Sound and Vibration, 1991,145(2):299-307.
[67]. Tanabe M., Yamada Y., model Method for Interaction of Train and Bridge[J], Journal of Computers and Structures, 1987,27(1):119-127.
[68]. Bogaert Van, Dynamic Response of Trains Crossing Large Span Double-track Bridges[J], Journal of Constructional Steel Research, 1993,24(1):57-74.
[69]. Green M. F., Cebon D., Dynamic Response of Highway Bridges to Heavy Vehicles Loads: Theory and Experimental Validation[J], Journal of Sound and Vibration, 1994,170(1):51-78.
[70]. Green M. F., Effects of Vehicle Suspension Design on Dynamics of Highway Bridges[J], Journal of Structural Engineering, ASCE, 1995,121(2):272-282.
[71]. Hwang ES, Nowak AS. Simulation of dynamic load for bridges[J]. Journal of Structural Engineering, ASCE 1991;117(5):1413–1434.
[72]. Yang F, Fonder GA. An iterative solution method for dynamic response of bridge–vehicle systems[J]. Earthquake Engineering and Structural Dynamics , 1996,25:195–215.
[73]. Yang Y. B., Yau JD. Vehicle–bridge interactions and applications to high speed rail bridges[J]. Proc Natl Sci Coun ROC (A)1998;22(2):214–224.
[74]. Garg VK, Dukkipati RV., Dynamics of railway vehicle systems[M]. New York: Academic Press, 1984.
[75]. Yang Y. B., Lin B. H., Vehicle–bridge Interaction Analysis by Dynamic CondenstionMethod[J], Journal of Structural Engineering, ASCE, 1995,121(11)1636-1643.
[76]. Yang Y. B., Yau J. D., Vehicle–bridge Interaction Element for Dynamic Analysis[J], Journal of Structural Engineering, ASCE, 1997,123(11)1512-1518.
[77]. Yang Y. B., Impact Formulas for Vehicle Moving over Simple and Continuous Beams[J], Journal of Structural Engineering, ASCE, 1995,121(11)1644-1650.
[78]. Yang Y. B., Yau JD, Hsu LC. Vibration of simple beams due to trains moving at high speeds[J]. Journal of Structural Engineering, ASCE, 1997,19(11):936-944.
[79]. Yang Y. B., Yean-Seng Wu. A versatile element for analyzing vehice-bridge interaction response[J]. Engineering Structres, 2001,23:452-469.
[80]. Wang T. L., Huang DZ, Cable-stayed bridge vibration due to road surface roughness[J], Journal of Structural Engineering, ASCE, 1992,118(5):1354-1373.
[81]. Yang Y.M., Pan J.Y, Cheng Q.G, Theoretical and experimental studies of the dynamic response of long span railway bridge[J]. China Railway Science, Beijing, 1995,16(4):1-15.
[82]. Kawatani M., Kobayashi Y., Takamori K., Non-stationary random analysis with coupling vibration of bending and torsion of simple girder-bridge under moving vehicles[J]. Structural Engineering/Earthquake Engineering, JSCE, 1998,15(1):107-114.
[83]. Guo X.R., Zhen Q.Y., Space vibration analysis of the time-dependent system of long span railway bridges and train under wind load[J]. Proceedings of Workshop on Research and Monitoring of Long Span Bridges, Hong Kong, April, 2000:40-45.
[84]. Cheng Y.S.,. Au F.T.K, Cheung Y.K., Vibration of railway bridges under a moving train by using bridge-track-vehicle element [J]. Engineering Structures 2001;23:1597-1606.
[85]. Ju S.H., Wang Y.M., Time-dependent absorbing boundary conditions for elastic wave propagation[J]. International Journal for Numerical Methods in Engineering, 2001,50(9):2159–2174.
[86]. Ju S.H., Finite element analyses of wave propagations due to high-speed train across bridges[J], International Journal for Numerical Method in Engineering,2002,54(9):1391-1408.
[87]. Ju S.H., Lin H.T., Numerical investigation of a steel arch bridge and interaction with high-speed trains[J]. Engineering Structures, 2003,25(2):241–250.
[88]. Ju S.H., Lin H.T., Analysis of train-induced vibrations and vibration reduction schemes above and below critical Rayleigh speeds by finite element method[J], Soil Dynamics and Earthquake Engineering, 2004,24:993-1002.
[89]. Ju S.H., 3D Finite element analyses of wave barriers for reduction of train-induced vibrations[J], Journal of Geotechnical and Geoenvironmental Engineering, ASCE,2004,130(7):740-748.
[90]. Ju S.H., Lin H.T., Analysis of train-induced vibrations and vibration reduction schemes above and below critical Rayleigh speeds by finite element method[J], Soil Dynamics and Earthquake Engineering,2004,24(12):993-1002.
[91]. Ju S.H., Lin H.T., Hsueh C.C., Wang S.L., A simple finite element model for vibration analyses induced by moving vehicles[J]. International Journal for Numerical Methods in Engineering, 2006,68:1232-1256.
[92]. Ju S.H., Lin H.T., A finite element model of vehicle-bridge interaction considering braking and acceleration[J]. Journal of Sound and Vibration, 2007,303:46-57.
[93]. Ju S.H., Lin H.T., Chen T.K., Studying characteristics of train-induced ground vibrationsadjacent to an elevated railway by field experiments[J], Journal of Geotechnical and Geoenvironmental Engineering, 2007, 133(10): 1302-1307.
[94]. Chen Y.J., Ju S.H., Ni S.H., Shen Y.J., Prediction methodology for ground vibration induced by passing trains on bridge structures[J]. Journal of Sound and Vibration, 2007,302:806-820.
[95]. Ju S.H., Finite element analysis of structure-borne vibration from high-speed train[J], Soil Dynamics and Earthquake Engineering, 2007,27(3):259-273.
[96]. Ju S.H., Lin H.T., Experimentally investigating finite element accuracy for ground vibrations induced by high-speed trains[J], Engineering Structures, 2008,30:733-746.
[97]. Ju S.H., Lin H.T., Huang J.Y., Dominant frequencies of train-induced vibrations[J]. Journal of Sound and Vibration, 2009,319:247-259.
[98]. Raid Karoumi, Response of cable-stayed and suspension bridges to moving vehicles[D]. Royal Institute of Technology Department of Structural Engineering. TRITA-BKN, Bulletin,1998.
[99]. Green M.F., Cebon D., Dynamic interaction between heavy vehicles and highway bridges[J]. Computers and Structures. 1997,62(2):253-264.
[100]. Rieker J. R. , Lin Y.H., Trethewey M.W., Discretization considerations in moving load finite element beam models[J]. Finite Elements in Analysis and Design, 1996,21:129-144.
[101]. Henchi K., Fafard M., Talbot M., Dhatt G., An efficient algorithm for dynamic analysis of bridges under moving vehicles using a coupled modal and physical components approach[J]. Journal of Sound and Vibration, 1998,212(4):663-683.
[102]. Yang F.H., Fonder GA, Dynamic response of cable-stayed bridge under moving loads[J]. Journal of Engineering Mechanics, ASCE, 1998,124(7):741-747.
[103]. Zheng D.Y., Cheung Y.K., Au FTK, Cheng Y.S, Vibration of multispan non-uniform beams under moving loads by using modified beam vibration functions[J]. Journal of Sound and Vibration, 1998,212(3):455-467.
[104]. Cheng Y.S., Au FTK, Cheung Y.K., Zheng D.Y., On the separation between moving vehicles and bridge[J]. Journal of Sound and Vibration. 1999,222(5):781-801.
[105]. Cheung Y.K., Au FTK, Zheng D.Y., Cheng Y.S., Vibration of multispan non-uniform bridges under moving vehicles and trains by using modified beam vibration functions[J]. Journal of Sound and Vibration, 1999,228(3):611-628.
[106]. Marchesiello S., Fasana A., Garibaldi L., Piombo BAD, Dynamics 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.
[107]. Au FTK, Wang J.J, Cheung Y.K., Impact study of cable-stayed bridge under railway traffic using various models[J]. Journal of Sound and Vibration, 2001,240(3):467-481.
[108]. Au FTK, Wang J.J, Cheung Y.K., Impact study of cable-stayed railway bridges with random rail irregularities[J]. Engineering Structures, 2002,24:529-541.
[109]. Cheung Y.K., Au FTK, Cheng Y.S., Zheng D.Y., On the separation between moving vehicles and bridge[J]. Journal of Sound and Vibration, 1999,222(5):781-801.
[110]. Lin YH,Trethewey MW.Finite element analysis of elastic beams subjected to moving dynamic loads[J].Journal of Sound and Vibration 1990;136:323-342.
[111]. Huang D, Wang TL.Impact analysis of cable-stayed bridges[J].Computers and Structures 1992,43(5):897-908.
[112]. Huang DZ, Wang TL, Shahawy M.Impact studies of multigirder concrete bridges[J]. Journal of Structural Engineering, 1993,119(8):2387-402.
[113]. P.K.Chatterjee,T.K.Datta, C.S.Surana. Vibration of continous bridges under moving vehicles[J]. Journal of Sound and Vibration, 1994,169:619-632.
[114]. Zibdeh H S. Stochastic vibration of an elastic beam due to random moving loads and deterministic axial forces[J].Engineering Structures,1995,17(7):530-535.
[115]. Zibdeh H S, Rechwitz R. Moving loads on beams with general boundary conditions[J].Journal of Sound and Vibration,1996,195(1):85-102.
[116]. Xu X, Xu W, Genin J.A nonlinear moving mass problem[J]. Journal of Sound and Vibration,1997,204(3):495-504.
[117]. Huang DZ, Wang TL. Vibration of highway steel bridge with longitudinal grads[J]. Computer and Structures 1998,69:235-245.
[118]. D.Y. Zheng, Y.K. Cheung, F.T.K.Au, Y.S.Cheng. Vibration of multi-span non-uniform beams under moving loads byusing modified beam vibration function[J], Journal of Sound and Vibration.(1998)212(3),445-467.
[119]. Wang R T. Vibration of multi-span Timoshenko beams to a moving force[J].Journal of Sound and Vibration,1998,207(5):731-742.
[120]. Foda M A, Abduljabbar Z.A dynamic green function formulation for the response of a beam structure to moving mass[J].Journal of Sound and Vibration,1998,210(3):295-306.
[121]. Tan G H, Brameld G H, Thambiratnam D P, Development of an analytical model for treating bridge vehicle interaction[J]. Engineering Structres,1998,20(1/2):250-260.
[122]. Wu J.S., Shih P.Y., Dynamic responses of railway and carriage under the high-speed moving loads[J]. Journal of Sound and Vibration, 2000,236(1):61-87.
[123]. Qi-Lin Zhang,A.Vrouwenvede, J.Wardenier. Numerical simulation of train-bridge interactive dynamics[J].Computers and Structures,2001,79:1059-1075.
[124]. F.T.K.Au, Y.S.Cheng, Y.K.Cheung. Effects of random road surface roughness and long-term deflection of prestressed concrete girder and cable-stayed bridges on impact due to moving vehicles[J]. Computer and Structures,79(2001),853-872.
[125]. ZHU X.Q., LAW S.S.. Dynamic load on continuous multi-lane bridge deck from moving vehicles[J]. Journal of Sound and Vibration,2002,251(4):697-716.
[126]. Xu Y.L., Guo W.H., Dynamic analysis of coupled road vehicle and cable-stayed bridge systems under turbulent wind[J]. Engineering Structure, 2003,25:473-486.
[127]. Almutairi N.B., Hassan M.F., Abdel-Rohman M., Terro M., Control of suspension bridge nonlinear vibrations due to moving loads[J]. Journal of Engineering Mechanics, ASCE, 2006,132(6):659-666.
[128]. Xiang T.Y, Zhao R.D., Xu T.F., Relibaility evaluation of vehicle-bridge dynamic interaction. Journal of Structural Engineering[J], ASCE, 2007,133(8):1092-1999.
[129]. Michal Majka. Effects of speed, load and damping on the dynamic response of railway bridges and vehicles [J]. Computers and Structures 2008; 86:556-572.
[130].李国豪.桁梁桥的扭转、稳定和振动[M].北京:人民交通出版社,1975.
[131].李国豪.桥梁结构稳定与振动[M].北京:中国铁道出版社,1992.
[132].陈英俊,车辆荷载下桥梁振动理论的演进[J],桥梁建设, 1975,2:21-36.
[133].胡人礼.普通桥梁结构振动[M].北京:中国铁道出版社,1988.
[134].胡人礼.桥梁力学[M].北京:中国铁道出版社,1999.
[135].何度心.列车动载[J].地震工程与工程振动. 1988,8(4):78-98.
[136].何度心.桥梁振动研究[M].北京:地震出版社,1989.
[137].程庆国、许慰平,大跨度铁路斜拉桥列车走行性探讨[J],全国桥梁结构学术大会论文集,武汉,1992:41-51.
[138].程庆国、潘家英,大跨度铁路斜拉桥竖向刚度分析[J],全国桥梁结构学术大会论文集,武汉,1992:1163-1168.
[139].张煅、柯在田,既有线提速至160km/h桥梁评估的研究[J],中国铁道科学,1996,17(1):9-20.
[140].张健峰,大跨度铁路钢斜拉桥刚度问题的研究[D],硕士学位论文,铁道科学研究院,1981.
[141].李小珍、强士中等,高速铁路—大跨度钢斜拉桥空间耦合振动响应研究[J],桥梁建设,1998,5,65-68.
[142].李小珍、强士中,京沪高速南京越江钢斜拉桥车桥耦合振动分析[J],西南交通大学学报,1999,34(2),153-157.
[143].李小珍、王玉良、强士中,大跨度连续拱桁组合钢桥空间振动分析[J],振动与冲击,1999,18(4):35-39.
[144].郝超、强士中、马栋君,移动荷载作用下桥梁的振动控制[J],国外桥梁,1999,3:38-42.
[145].黄维平、强士中,大跨度悬索桥环境振动的双向TMD控制[J],地震工程与工程振动,1999,19(1):100-103.
[146].沈锐利,列车过桥时桁梁桥的空间振动分析[D],硕士学位论文,西南交通大学,1987.
[147].沈锐利,高速铁路桥梁与车辆耦合振动研究[D],博士学位论文,西南交通大学,1998.
[148].何发礼,高速铁路中小跨度曲线梁桥车桥耦合振动研究[D],博士学位论文,西南交通大学,1999.
[149].何发礼,李乔,曲率和超高对曲线梁桥车桥耦合振动的影响[J],桥梁建设,1999,3:5-7.
[150].曾庆元等,桁梁行车空间振动计算的桁段有限元法[J],桥梁建设,1985,4:1-16.
[151].曾庆元、杨平,形成矩阵的“对号入座”法则与桁梁空间分析的桁段有限元法[J],铁道学报,1986,8(2):48-58.
[152].曾庆元、郭向荣,列车桥梁时变系统振动分析理论及应用[M],中国铁道出版社,1999.
[153].曾庆元、骆宁安等,桥上列车横向摇摆力的初步研究[J],桥梁建设,1989,2:28-36.
[154].曾庆元,关于铁路桥梁的刚度问题[J],长沙铁道学院学报,1991,9(3):1-15.
[155].曾庆元等,列车—桥梁时变系统的横向振动分析[J],铁道学报,1991,13(2):38-46.
[156].郭文华、郭向荣等,大跨度斜拉桥空间振动计算分析[J],振动与冲击,1998,17(1):30-33.
[157].曹雪琴,列车通过时桥梁结构竖向振动分析[J],上海铁道学院学报,1981,2(3):1-15.
[158].曹雪琴,钢桁梁桥横向振动[J],中国铁道出版社,1991.
[159].曹雪琴、陈晓,轮轨蛇行引起桥梁横向振动随机分析[J],铁道学报,1986,8(1),89-97.
[160].曹雪琴、刘必胜、吴鹏贤,桥梁结构动力分析[M],中国铁道出版社,1987.
[161].曹雪琴、顾萍,沪宁线限速钢梁桥提速试验与分析[J],上海铁道科技,2000,3:14-16.
[162].曹雪琴等,列车过桥箱型钢梁空间振动分析[J],上海铁道学院学报,1982,3(3):17-35.
[163].马坤全、曹雪琴、朱金龙,列车通过抢修高墩横向振动随机分析[J],铁道学报,1998,2:88-94.
[164].夏禾,陈英俊,车—梁—墩体系动力相互作用分析[J],土木工程学报,1992,25(2),3-12.
[165].夏禾等,风和列车荷载共同作用下刚梁柔拱组合系桥的动力响应研究[J],全国桥梁学术大会论文集,同济大学出版社,1992:1063-1070.
[166].夏禾,陈英俊,风和列车荷载同时作用下车桥系统的动力可靠性[J],土木工程学报,1994,27(2),14-21.
[167].夏禾、阎贵平,列车—斜拉桥系统在风载作用下的动力响应[J],北方交通大学学报,1995,19(2):131-136.
[168].夏禾、陈英俊,列车提速情况下铁路双线简直钢桁梁动力响应分析[J],铁道学报,1996,18(5):75-82.
[169].夏禾等,轻轨列车和高架桥梁系统的动力响应分析[J],北方交通大学学报,1994,18(1):1-8.
[170].夏禾等,高速铁路轨道动力分析与结构模式[J],北方交通大学学报,1996,20(2),192-199.
[171].夏禾等,铁路斜拉桥的地震响应特性研究[J],北方交通大学学报,1995,19(2):137-142.
[172].夏禾,高速铁路连续梁桥动力响应分析[J],北方交通大学学报,1997,21(4):399-404.
[173].夏禾,支座位移对桥上高速运行列车安全的影响[J],工程力学增刊,1997,295-300.
[174].夏禾,列车过桥时高架墩的动力响应及其对车辆运行稳定性的影响[D],硕士学位论文,北方交通大学,1984.
[175].夏禾,钢板梁桥横向振动加固及其试验分析[J],工程力学增刊,1998,473-478.
[176]. Xia He, et al, Computer simulation for dynamics of railway track structures[J], Proc. 4th Annual Railway Transportation Conference, Dec. 13-14, Tehran, Iran, 169-176.
[177]. Xia He, Chen Yingjun, Dynamic analysis of steel truss brides under moving train loads[J]. Advances in Structural Engineering, 1995:48-54.
[178]. Xia He, et al, Dynamic analysis of train-bridge system under random excitations[J], Proc. 4th SSD’98, Notre Dame, USA, 1998:535-542.
[179]. Xia He, Chen Yingjun, Dynamic analysis of vehicle-track-bridge system[J], Bridges into the 21st Century, Proc. HKCEC, Hong Kong, 1995:1142-1147.
[180]. Xia He, et al, Dynamic interaction of train and a flexible arch stiffened steel truss bridge during earthquake[J]. Proc. JSSC-4, Tokyo, Japan, 1992:763-770.
[181]. Xia He, Chen Yingjun, Dynamic reliability of train-bridge system under wind action by stochastic extreme analysis[J], Proc. EASEC-4, Seoul, Korea, 1993:2063-2068.
[182]. Xia He, et al, Dynamic analysis of train-bridge system and its application in steel girder reinforcement[J], Journal of Computers and Structures, 2001,79:1851-1860.
[183]. Xia He, Xu Y.L., et al, Dynamic interaction of long suspension bridges with running trains[J], Journal of Sound and Vibration, 2000,237(2):263-280.
[184].雷俊卿、郑明珠、徐恭义,悬索桥设计[M],北京:人民交通出版社,2001.
[185].周孟波.悬索桥手册[M],北京:人民交通出版社,2003.
[186]. Brotton D M. A general computer program for the solution of suspension bridge problems[J]. The Structural Engineer,1966,44(5):161-167.
[187]. Saafan S A. Theoretical analysis of suspension bridges[J]. Proc. ASCE,1966,92(4):1-11.
[188]. Gregor P. Wollmann. Preliminary analysis of suspension bridges[J]. Journal of Bridge Engineering, 2001, 6(4),227-233.
[189]. John H. Mathews, Kurtis D. Fink.数值方法(MATLAB版)[M],北京,电子工业出版社,2002.
[190]. Kim H.K., Lee M.J., Analysis of target configurations under dead loads for cable-supported bridges[J]. Computers and Structures, 2001,79:2681-2692.
[191]. Kim H.K., Lee M.J., Chang S.P., Determination of hanger installation procedure for a self-anchored suspension bridge[J], Engineering Structures, 2006,28:959-976.
[192].潘永仁.悬索桥结构非线性分析理论与方法[M],北京:人民交通出版社,2004.
[193].贺栓海.桥梁结构理论与计算方法[M],北京:人民交通出版社,2003.
[194].史建三.悬索桥大缆架设计算的索长分析法[J],桥梁建设,1993,4,30-37.
[195].张哲.混凝土自锚式悬索桥[M]],北京:人民交通出版社,2005.
[196].狄谨,武隽.自锚式悬索桥主缆线形计算方法[J].交通运输工程学报,2004,4(3).
[197].小西一郎(日).钢桥(第五分册)[M],北京:人民铁道出版社,1980.
[198].肖海波.悬索桥主缆成桥线形精确分析[J].中国市政工程,2003,4(104).
[199].肖汝城,项海帆.大跨径悬索桥结构分析理论及其专用程序系统的研究[J].中国公路学报,1998.
[200].罗喜恒、肖汝城、项海帆.空间缆索悬索桥的主缆线形分析[J],同济大学学报,2004,32(10):1349-1354.
[201].铁道部大桥工程局桥梁科学研究所,悬索桥[M],科学技术文献出版社,1996.
[202].向锦武,罗绍详,陈鸿天.悬索结构振动分析的悬链线索元法[J].工程力学,1999,16(3): 130-134.
[203]. A H.Peyrot,A M.Goulois.Analysis of cable structures[J].Computers and Structures,1979,10:805-813.
[204]. Ali HM,Abdel-Ghaffar AM.Modeling the nonlinear seismic behavior of cable-stayed bridges with passive control bearings[J].Computers and Structures,1995,54:461-92.
[205]. Karoumi R.Some modelling aspects in the nonlinear finite element analysis of cable supported bridges[J].Computers and Structures,1999,71:397-412.
[206]. Jin Cheng , Ru-Cheng Xiao , Hai-Fan Xiang , Jian-Jing Jiang.NASAB: a finite element software for the nonlinear aerostatic stability analysis of cable-supported bridges[J].Advancesin Engineering Software, 2003,34 : 287-296.
[207].王建国,逄焕平,李雪峰.悬索桥线形分析的悬链线单元法[J].应用力学学报,2008,25(4):627-631.
[208]. O’Brien, Francis AJ.Cable movements under two dimensional loads[J].J Struct Engng , ASCE , 1964, 90 (ST3) : 89-123.
[209]. Michalos J., Birnstiel C.Movement of a cable due to changed in loading[J]. ASCE , 1960, 86 (ST12) : 23-38.
[210]. Jayaraman HB. , Knudson WC. , A curved element for the analysis of a cable structures[J].Computers and Structures,1981,14:325-333.
[211]. A. M S.Freire,J.H.O. Negrao,A.V. Lopes.Geometrical nonlinearities on the static analysis of highly flexible steel cable-stayed bridges[J] . Computers and Structures,2006,84:2128-2140.
[212].沈锐利.悬索桥主缆系统设计及架设计算方法研究[J].土木工程学报,1996,29(2): 3-9.
[213].夏禾.车桥与结构动力相互作用[M].科学出版社,2002.
[214].李广慧.车辆—无碴轨道—桥梁系统振动特性及其应用[M].黄河水利出版社,2007
[215]. EI-Madany M.M.,Design optimization of truck suspensions using covariance analysis[J]. Computers and structures,1988,28(2):241-246.
[216]. Fafard M., Bennur M., Savard M. A general multi-axle vehicle model to study the bridge-vehicle interaction [J]. Engineering Computations, 1996, 14(5): 491-508.
[217]. Hani H. Nassif, Ming Liu, Oguz Ertekin. Model validation for bridge-road-vehicle dynamic interaction system [J]. Journal of Bridge Engineering, 2003, Vol. 8, No. 2: 112-120.
[218]. Hwang E., Nowak A. Simulation of dynamie load for bridges [J]. Journal of structure Engineering, ASCE, 1991, 117(5) .
[219]. Harris, N., E. OBrien, and A. Gonzalez, Reduction of bridge dynamic amplification through adjustment of vehicle suspension damping[J]. Journal of Sound and Vibration, 2007. 302(3): 471-485.
[220]. Cebon D. Handbook of Vehicle-Road Interaction [M]. Swets&Zeitlinger, 1999.
[221]. R.克拉夫,J.彭津,结构动力学[M],第2版,北京:高等教育出版社,2006.
[222].王勖成,邵敏.有限单元法基本原理和数值方法[M].1997第二版,92-97.
[223]. ANSYS Structural Analysis Guide[M], Ansys, Houston, Pennsylvania ANSYS , 1998.
[224]. Structural Analysis, Release 5.3[M]. Ansys, Houston, Pennsylvania, 1996.
[225]. D.E. Newland, An Introduction to Random Vibration and Spectral Analysis[M], 2nd ed., Longman, New York, NY, 1984.
[226]. W.Q. Zhu, Random Vibration[M], Academic Press, Beijing, China, 1992.
[227]. Honda, H., Y. Kajikawa, and T. Kobori, Spectra of road surface roughness on bridges[J].Journal of the Structural Division, 1982. 108(9): 1956-1966.
[228]. GB/T 7031-1986.车辆振动输入路面平度表示方法.汽车国家标准汇编[S].
[229]. ISO 2631. Mechanical vibration and shock-evaluation of human exposure to whole-body vibration[S].
[230]. C.J. Dodds, The laboratory simulation of vehicle service stress[J], Journal of Engineering for Industry, ASME 2,1974. 96(2). 391–398.
[231]. M. Shinozuka, Digital simulation of random processes and its applications[J], Journal of Sound and Vibration. 25 (1972) 111–128.
[232]. G.I. Schueiler, M. Shinozuka, Stochastic Methods in Structural Dynamics[J], Martinus Nijhoff Publishers, 1987.
[233]. M. Shinozuka, Digital simulation of random processes in engineering mechanics with the aid of FFT technique[J], in stochastic problems in mechanics, in: S.T. Ariaratnam, H.H.E. Leipholtz (Eds.), University of Waterloo Press, Waterloo, 1974.
[234]. W.Schiehlen,B.Hu. Spectral simulation and shock absorber identification[J],International Journal of Non-Linear Mechanics, 2003(38):161-171
[235]. I.M. Smith,D.V. Griffiths. Programming the finite element method(Third Edition)[M],北京:电子工业出版社,2003.9
[236]. Iwnick S., Manchester benchmarks for rail vehicle simulation[J]. Vehicle System Dynamics, 1998;30:295-313
[237].范立础,胡世德、叶爱君.大跨度桥梁抗震设计[M],北京:人民交通出版社,2001,4