摘要
横向风作用下高速列车在桥上运行时，由于列车风的作用，在列车头尾部必然产生比较明显的三维流动，同时列车中部流场也会因列车运动而受到一定的影响。为研究列车风对车桥耦合振动的影响，建立了同时考虑列车风和横向风作用及轨道不平顺影响的车桥耦合振动分析模型。
本文从以下几个方面对该分析模型进行了详细的研究：
1、利用大型商业流体计算软件FLUENT，采用多重参考系法计算德国ICE高速列车在铁路桥上运行时流场的稳态解。研究表明：列车风对车桥系统流场的影响主要体现在列车头部的排挤作用，列车尾部的拖曳作用，列车尾部存在一个较强的旋涡，对列车尾部的影响区域更大更强，对列车中部流场的影响基本可以忽略。列车风对列车的阻力、横向力、升力、摇头力矩影响较大。列车风的作用使得整个列车产生一种向上提升和向横风向摇头的作用。列车风对头尾车附近区域桥梁的气动力有比较明显的影响。
2、在轮轨三维非线性接触几何关系上，考虑了桥梁振动对蠕滑率、轨道空间位置的影响，并引入了沈氏理论对轮轨接触蠕滑力的非线性修正。
3、建立了综合考虑横向静风、列车风、轨道不平顺的车桥耦合振动分析模型，实现了在每一迭代时间步准确计算轮轨接触几何参数，提出了轮轨接触点的绝对空间位置和接触力唯一的车桥系统分组迭代收敛准则。在每一迭代步计算每节车辆的响应时采用车辆加速度残差范数与加速度范数之比控制迭代收敛。
4、以德国高速铁路标准简支梁桥为例，研究了列车风对高速铁路中小跨简支梁桥车桥耦合振动响应的影响，并采用轮轨接触点在车轮、轨头上的横向位置时程曲线进行了研究。分析表明：列车风对车桥耦合振动的影响主要体现在车辆的安全性上，列车风对桥梁振动的影响完全可以忽略。虽然列车风对车辆的轮重减载率、脱轨系数、横向水平力有一定程度的影响，但车辆振动的各项指标均远小于控制指标，因此从这个意义上看可以不考虑列车风对简支梁桥车桥耦合振动的影响。
5、以日本新干线上的屋代南桥为例，研究了列车风对大跨度桥梁车桥耦合振动响应的影响，并采用轮轨接触点在车轮、轨头上的横向位置时程曲线进行了研究。分析表明：列车风对车桥耦合振动的影响主要体现在头尾车的安全性上，列车风对桥梁振动的影响基本可以忽略。列车风显著增大了头尾车的轮重减载率、脱轨系数、轮轨横向水平力。提高桥梁的竖向刚度可以明显减小车辆的竖向加速度、竖向Sperling指标和桥梁的竖向位移、竖向加速度，对车辆和桥梁的横向振动基本没有影响，体现了车桥耦合振动中竖向和横向振动的弱耦合特性。
Three-dimensional flow will be appeared near the front and rear of the high-speed train when it is running on the bridge under the cross wind and train induced wind, also the flowfield near the middle part of the train will be affected at some degree. An analysis model of coupling vibration of vehicle and bridge was established to study the train induced wind influence, in comprehensively considering of cross wind, train induced wind and rail irregularities.
In this paper, the main research work is carried out to study this analysis model as follows:
1. Steady flowfields around the vehicle and bridge when German high-speed train ICE travelling on the railway bridge were obtained based on MRF(multiple reference frame) method by the commercial computational fluid dynamics(CFD) software FLUENT . The present study shows that the effect of train induced wind to the vehicle-bridge system is mainly revealed in the pushing effect near the front of the train, the dragging effect near the rear of the train, a strong vortex is formed following the train. The train induced wind has more influence on zone near the rear of the train, and has little effect to the flowfield near the middle part of the train. In general,the train induced wind has clear influence on the drag force, lateral force, lift force and yaw moment of the train. The whole effect of the train induced wind makes the train to move up and yaw toward the cross wind direction. The train induced wind has evident infulence on the aerodynamic forces of the bridge near the first and end vehicle.
2. The bridge vibration effect to the creepage and the space position of track was considered in three dimensional wheel/rail contact geometry. Also the non-linear Shen-Hedrick-Elkins theory was applied to modify the wheel/rail contact creep-forces.
3. The analysis model of the vehicle-bridge coupling vibration was developed by comprehensively considering the cross wind, the train induced wind, rail irregularity. And the wheel/rail contact geometric parameters were accurately calculated at each time step iteration. The new improved iteration convergence criterion is that the absolute space position and contact force are unique in the seperated iterative procedure of the vehicle-bridge system.At the same time, iteration accuracy and integration convergency were controlled using the ratio of residual acceleration norms and acceleration norms of vehicle for computing the vibration of each vehicle at every iteration step.
4. A German high speed railway standard simply supported beam bridge was used as an example to study the train induced wind influence on the vehicle-bridge vibration of the simply supported small- and middle-span beam bridge. Also the lateral position time history of the wheel/rail contact on the wheel tread and rail head was investigated. The result shows that the train induced wind has some influence on the vehicle safty and has very little influenc on the bridge vibration.Although the train induced wind has some infulence on the reduction rate for wheel load, the derailment coefficient, and the lateral force of the vehicle.but all vibration index of the vehicle are very small compared to the design index. So we can neglect the train induced wind influence on the coupling vibration of vehicle and simplified bridge.
5. Taking the south Yashiro bridge in Japanese Shinkansen Line as an example to study the influence of the train induced wind on the vehicle-bridge vibration of long-span bridge. Also the lateral position time history of the wheel/rail contact on the wheel tread and rail head was investigated. The result shows that the train induced wind has evident influence on the safty of the first and last car,and has little influence on the bridge vibration. The train induced wind obviously increases the reduction rate for wheel load, the derailment coefficient, lateral force for the first and the last car. Increasing the bridge vetical stiffness can obviously decrease the vertical acceration,the vertical Sperling index of the vehicle and the vertical displacement,the veritcal accerlation of the bridge.but has very little effect to the lateral vibration of vehicle and bridge. And this reflects the rather weak coupling property of the vertical and lateral vibration in the vehicle-bridge vibration.
引文
[1] 王其昌主编．高速铁路土木工程．成都：西南交通大学出版社，1999．11
[2] 铁道部第三勘察设计院主编．京沪高速铁路设计暂行规定(上册)．北京：中国铁道出版社，2003．3
[3] 严国敏．试谈“部分斜拉桥”——日本屋代南桥、屋代北桥、小田原港桥．国外桥梁．1996，(1)：47-50
[4] 堀江笃，土屋恂，广田和羲．宫崎试验线列车风·自然风试验．铁研报告．1983，1249(10)：65-70
[5] 堀江笃，本间则男．宫崎试验线列车风·自然风试验．铁研报告．1984，1281(11)：29-33
[6] Mackrodt P A(德)，Steinheuer J(德)，Stoffers G(德)．Ⅱ型轮轨试验机车车辆空气动力学最佳形状的发展．李燕译，空气动力学和噪声，1996年：64-79
[7] ORE C149专业委员会．高速列车通过隧道产生的问题．黄弈锦译，空气动力学和噪声，1996年：91-128
[8] 王厚雄，何德昭，徐鹤寿．准高速东风型列车风速度场特性初探．中国铁道科学．1993，14(2)：100-110
[9] 王厚雄，何德昭，徐鹤寿．列车风作用下人体气动特性．第四届全国风工程及工业空气动力学会议论文集．1994，11：375-380
[10] 田红旗，梁习锋．准高速列车交会压力波试验研究．铁道学报．1998，20(4)：39-42
[11] 井门敦志、饭田雅宣和前田达夫．列车头部尾部形状最佳化的风洞试验．空气动力学和噪声，1996年：190-196
[12] 孙彤，孙翔译．采用高新技术的德国铁路ICE高速列车．成都：西南交通大学出版社，1992：50-52
[13] Fox T A, Henson D A. The prediction of the magnitudes of pressure transients generated by a train entering a single tunnel. Proc. Inst. Civ. Eng.. 1971, 49:53-69
[14] 吴德康译．对超高速列车在隧道内运行时压力变化的实验研究．隧道译丛．1994，(5)：1-9
[15] Raoul Jerome C. Train for the 21st century. Rail International. 1994, (4): 2-8
[16] Baker C J. Train aerodynamic forces and moments from moving model experiments. Journal of Wind Engineering and Industrial Aerodynamics. 1986, 24(3):227-251
[17] Cooper R. Tests on a 1/5th scale APT-P in the MIRA wind tunnel. British Rail Research Division Technical Memorandum TMAERO 28,1978
[18] Cooper R. Wind tunnel tests on a 1/25th scale APT-P model. British Rail Research Division Technical Memorandum TMAERO 43, 1982
[19] Baker C J. Ground vehicles in high cross winds. Part Ⅰ: steady aerodynamic forces. Journal of Fluids and Structures. 1991, (5):69-90
[20] Baker C J. Ground vehicles in high cross winds. Part Ⅱ: unsteady aerodynamic forces. Journal of Fluids and Structures.1991, (5):91—111
[21] Baker C J. Ground vehicles in high cross winds. Part Ⅲ:The interaction of aerodynamic forces and the vehicle system. Journal of Fluids and Structures. 1991, (5):221-241
[22] Baker C J, Dalley S J, Johnson T, Quinn A, Wright N G. The Slipstream and wake of a high-speed train. Proceeding of Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit. 2001, 215(2):83-99
[23] 陈南翼，张健．高速列车空气阻力试验研究．铁道学报．1998，20(5)：40-46
[24] 马启文，张松．准高速列车气动性能试验研究．西南交通大学学报．1997，32(3)：266-270
[25] 周瑜平．列车风洞试验研究探索．第四届全国风工程及工业空气动力学学术会议论文集，1994，11：369-374
[26] 田红旗，高广军．270km·h~(-1)高速列车气动性能研究．中国铁道科学．2003，24(2)：14-18
[27] 田红旗．列车交会空气压力波研究及应用．铁道科学与工程学报．2004，1(1)：83-89
[28] Copley J M. Three-dimensional flow around railway train. Journal of Wind Engineering and Industrial Aerodynamics.1987, 26(1): 21-52
[29] Chiu T W. Two-dimensional second-order vortex panel method for the flow in a cross-wind over a train and other two-dimensional bluff bodies. Journal of Wind Engineering and Industrial Aerodynamics. 1991, 37(1): 43-64
[30] Chiu T W. Prediction of the aerodynamic loads on a railway train in a cross-wind at large yaw angles using an integrated two-and threedimensional source/vortex panel method. Journal of Wind Engineering and Industrial Aerodynamics. 1995, 57(1): 19-39
[31] Chiu T W, Squire L C. Experimental study of the flow over a train in a crosswind at large yaw angles up to 90°. Journal of Wind Engineering and Industrial Aerodynamics.1992, 45(1): 47-74
[32] Reinhardt-Piechowiak A, Ducruet C. Inviscid fluid flow around high-speed trains passing by in open air. Proceeding of Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit. 1999, 213: 105-116
[33] 饭田雅宣，吉田康夫，铃木昌弘．铁道的气动力学模拟．马大炜译，空气动力学和噪声．1996：51-55
[34] Aieta S, Tabbal A, Mestreau E, Montmayeur N, Masbernat F, Wolfhugel Y F, Dumas J C. CFD aerodynamics of the French high speed train. SAE Technical Paper Series, 1992: 85-99
[35] Khier W, Breuer M, Durst F. Flow structure around trains under side wind conditions: a numerical study. Computers & Fluids. 2000, 29(2): 179-195
[36] 雷波．明线上高速列车风和会车压力波的研究．成都：西南交通大学博士学位论文．1995．5
[37] 雷波，刘应清．明线上高速列车会车压力波的数值模拟．西南交通大学学报．1995，30(3)：295-301
[38] 雷波，刘应清．列车风作用下人体气动力的计算分析．铁道学报．1999，21(6)：20-23
[39] 张小钢．高速列车湍流绕流三维数值模拟研究．成都：西南交通大学博士学位论文．1995．4
[40] 张小钢．高速列车优化外形的数值分析．西南交通大学学报．1996，31(3)：256-261
[41] 张小钢，刘应清．高速列车湍流绕流三维数值模拟研究．西南交通大学学报．1996，31(3)：262-266
[42] 张小钢，刘应清．具有地面效应的高速列车湍流绕流数值模拟研究．西南交通大学学报．1997，32(2)：150-153
[43] 张小钢，刘应清，赵海恒．高速列车经过路边建筑物时的非定常湍流绕流数值模拟研究．铁道学报．1998，20(2)：87-92
[44] 梅元贵．高速铁路隧道压力波数值模拟研究．成都：西南交通大学博士学位论文．1997．11
[45] 梅元贵，赵海恒，刘应清．高速铁路隧道压力波数值分析．西南交通大学学报．1995，30(6)：667-672
[46] 李人宪．列车三维紊态外流场的数值模拟研究．成都：西南交通大学博士学位论文．1998．9
[47] 李人宪，刘应清．高速列车紊流外流场的数值模拟研究．应用力学学报．2001，18(1)：6-13
[48] 杨忠超．基于EBE策略的列车三维紊态外流场有限元法并行计研究．成都：西南交通大学博士学位论文．2002．4
[49] 武青海，周虹伟，朱勇更．高速列车湍流流场数值仿真计算探讨．铁道学报．2002，24(3)：99-103
[50] 刘尚培，项海帆，谢霁明译．风对结构的作用——风工程导论．上海：同济大学出版社，1987
[51] 项海帆等．公路桥梁抗风设计指南．北京：人民交通出版社，1996
[52] 李国豪．桥梁结构稳定与振动．北京：中国铁道出版社，1992
[53] 张相庭．结构风压和风振计算．上海：同济大学出版社，1985
[54] 张相庭．工程抗风设计计算手册．上海：同济大学出版社，1998
[55] 陈英俊，于希哲．风荷载计算．北京：中国铁道出版社，1998
[56] 向海帆．桥梁空气动力学的未来．国际学术动态．1998，(10)：73-75
[57] Walther J H. Discrete Vortex Method for Two-dimensional Flow past Bodies of Arbitrary Shape Undergoing Prescribed Rotary and Translational Motion. Ph. D. Thesis. Department of Fluid Mechanics, Technical University of Denmark, September 1994
[58] Walther Jens Honoré, Larsen Allan. Two dimensional discrete vortex method for application to bluff body aerodynamics. Journal of Wind Engineering and Industrial Aerodynamics. 1997, 67&68: 183-193
[59] Larsen Allan, Walther Jens H. Aeroelastic analysis of bridge girder sections based on discrete vortex simulation. Journal of Wind Engineering and Industrial Aerodynamics.1997, 67468: 253-265
[60] Larsen Allan. Advances in aeroelastic analyses of suspension and cable-stayed bridges. Journal of Wind Engineering and Industrial Aerodynamics.1998, 74-76: 73-90
[61] Larsen Allan, Walther Jens H. Discrete vortex simulation of flow around generic bridge deck sections. Journal of Wind Engineering and Industrial Aerodynamics.1998, 77&78: 591-602
[62] Morgenthal Guido, McRobie Allan. A comparative study of numerical methods for fluid- structure interaction analysis in long-span bridge design. Wind and Structures.2002, 5 (2-4): 101-114.
[63] Taylor I, Vezza M. Aeroelastic stability analysis of a bridge deck with added vanes using a discrete vortex method. Wind and Structures. 2002, 5 (2-4): 277-290.
[64] Fujiwara A, Kataoka H, Ito M. Numerical simulation of flow field around an oscillating bridge using finite difference method. Journal of Wind Engineering and Industrial Aerodynamics.1993, 46-47: 567-575
[65] Kuroda Shinichi. Numerical simulation of flow around a box girder of a long span suspension bridge. Journal of Wind Engineering and Industrial Aerodynamics.1997, 67&68: 239-252
[66] De Foy B. Unsteady incompressible flow solver with optimised operators. Ph.D. Thesis, Cambridge University, Department of Engineering, Cambridge, England, 1998
[67] Bruno L, Khris S, Marcillat J. Numerical simulation of the effect of section details and partial streamlining on the aerodynamics of bridge decks. Wind and Structures.2001, 4(4): 315-332.
[68] Vairo Giuseppe. A numerical model for wind loads simulation on long-span bridges. Simulation Modelling Practice and Theory. 2003, 11(5-6): 315-351
[69] Mendes P A, Branco F A. Numerical wind studies for the Vasco da Gama Bridge, Portugal. Structural Engineering International, 1998,8 (2): 124-128.
[70] Selvam R Panneer, Govindaswamy S, Bosch H. Aeroelastic analysis of bridges using FEM and moving grids. Wind and Structures, An International Journal. 2002, 5(2-4): 257-266.
[71] Karniadakis G, Sherwin S J. Spectral/hp Element Methods for CFD. Oxford University Press, Oxford, 1999.
[72] Li L, Sherwin S J, Bearman P W. A moving frame of reference algorithm for fluid/structure interaction of rotating and translating bodies. International Journal for Numerical Methods in Fluids. 2002, 38(2): 187-206.
[73] Robertson I, Sherwin S J, Bearman P W. Flutter instability prediction techniques for bridge deck sections. International Journal for Numerical Methods in Fluids.2003, 43 (10-11): 1239-1256.
[74] Robertson I, Li L, Sherwin S J, Bearman P W. A numerical study of rotational and transverse galloping rectangular bodies. Journal of Fluids and Structures. 2003, 17(5): 681-699.
[75] Robertson I, Sherwin S, Bearman P. Prediction of rotational instabilities of rectangular and semi-circular leading edge sections. Flow, Turbulence and Combustion.2003, 71(1-4): 93-103
[76] Selvam R P, Tarini M J, Larsen A. Computer modelling of flow around bridges using LES and FEM. Journal of Wind Engineering and Industrial Aerodynamics. 1998, 77&78: 643-651
[77] Brar P S. Numerical calculation of bluff body flutter derivatives via computational fluid dynamics. Ph.D. Thesis, The John Hopkins University, Baltimore, MD, USA, 1997.
[78] Timoshenko. 工程中的振动问题.胡人礼译,北京：中国铁道出版社,1978
[79] Timoshenko S P. Forced vibration of prismatic bars. Izvestiya Kievskogo Politekhnicheeskogo Institute, 1908
[80] Timoshenko S P. On the forced vibration of bridges. Philosoph Magazine, 1922, Ser.6
[81] Inglis C E. A mathematical treatise on vibration in railway bridges. Cambridge, 1934
[82] Schallenkamp A. Schwingungen von tragern bei bewegten laster. Ingenieur Archiv, 1937, 8: 182-198
[83] Mise K, Kunii S. A theory for the forced vibrations of a railway bridge under the action of moving loads. Quartley Journal of Mech. and Applied Math.. 1956, 9
[84] Wen P R. Dynamic response of beams traversed by two-axle loads. Journal of Engineering Mechanics, ASCE.1960, 86(EM5): 91-111
[85] Symonds P S, Neal B G. Travelling loads on rigid-plastic beams. Journal of Engineering Mechanics, ASCE.1960, 86(EM1): 79-89
[86] Schlack Alois L, Raske Theodore F. Resonance of beams due to cyclic moving loads. Journal of Engineering Mechanics, ASCE. 1966, 92(EM6):175-184
[87] Adams G G, Bogy D B. Steady solutions for moving loads on elastic beams with end-sided constrains. Journal of Applied Mechanics, Transactions of ASME.1975, 42 Ser E(4): 800-804
[88] Beljwas T E, Feng C C, Ayre R S. Dynamic interaction of moving vehicles and structures. Journal of Sound and Vibration.1979, 67(4): 513-521
[89] Hayashikawa Toshiro, Watanabe Noboru. Dynamic behavior of continuous beams with moving loads. Journal of Engineering Mechanics, ASCE.1981, 107(1): 229-246
[90] Genin J, Ting E C, Vafa Z. Curved bridge response to a moving vehicle. Journal of Sound and Vibration.1982, 81(4): 469-475
[91] Fryba L. Non-stationary response of a beam to a moving random force. Journal of Sound and Vibration.1976, 46(3): 323-338
[92] Hayashikawa Toshiro, Watanabe N. Suspension bridge response to moving loads. Journal of Engineering Mechanics Division, ASCE. 1982, 108(EM6): 1051-1066
[93] Snyder J E III, Wormley D N. Dynamic interactions between vehciles and elevated, flexible randomly irregular guideways. Journal of Dynamic Systems, Measurement and Control Transactions of the ASME. 1977, Ser G 99(1): 23-33
[94] Gupta R K, Traill-Nash R W. Bridge dynamic loading due to surface irregularities and braking of vehicle. Earthquake Engineering & Structural Dynamics. 1980, 8(2): 83-96
[95] Palamas J, Coussy O, Bamberger Y. Effects of surface irregularities upon the dynamic response of bridges under suspended moving loads. Journal of Sound and Vibration. 1985, 99(2): 235-245
[96] Fryba L. Dynamic interaction of vehicle with tracks and roads. Vehicle System Dynamics.1987, 16(3): 129-138
[97] Schneider H -J, Elf H P, Koelle P. Modelling of travelling-loads and time-dependent masses with Adina. Computer and Structures. 1983, 17(5-6): 749-755
[98] Padovan J, Paramodilok O. Generalized solution of time dependent travelling load problem via moving finite element scheme. Journal of Sound and Vibration. 1983, 91(2): 195-209
[99] Hino J, Yoshimura T, Konishi K, Ananthanarayana N. Finite element method prediction of the vibration of a bridge subjected to a moving vehicle load. Journal of Sound and Vibration. 1984, 96(1): 45-53
[100] Olsson M. Finite element modal co-ordinate analysis of structures subjected to moving loads. Journal of Sound and Vibration. 1985, 99(1): 1-12
[101] Hino T, Yoshimura T, Ananthanarayana N. Vibration analysis of non-linear beams subjected to a moving load using the finite element method. Journal of Sound and Vibration.1985, 100(4): 477-491
[102] Chu K H, Garg V K, Wiriyachai A. Dynamic interaction of railway train and bridges. Vehicle System Dynamics.1980, 9(4): 207-236
[103] Wiriyachai A, Chu Kaugh Han, Garg V K. Impact study by various bridge models. Earthquake Engineering & Structural Dynamics. 1982, 10(1): 31-45
[104] Bhatti M H, Garg V K, Chu K H. Dynamic Interaction between freight train and steel bridge. Journal of Dynamic Systems, Measurement and control Transactions ASME.1985, 107(1): 60-66
[105] Chu Kuang-Han, Garg Vijay K, Bhatti Majeed H. Impact in truss bridge due to freight trains. Journal of Engineering Mechanics.1985, 111(2): 159-174
[106] Wang T L. Impact and fatigue in open-deck steel truss and ballasted prestressed concrete railway bridges. Ph.D. thesis. , Illinois Institue of Technology, Chicago, Illinois, 1984
[107] Wang Ton-Lo. Ramp/Bridge interface in railway prestressed concrete bridge. Journal of Structural Engineering.1990, 166(6): 1648-1659
[108] Wang Ton-Lon, Garg Vi jay K, Chu Kuang-Han. Railway bridge/vehicle interaction studies with new vehicle model. Journal of Structural Engineering. 1991, 117(7): 2099-2116
[109] Tanabe Makoto, Yamada Yoshiaki, Wakui Hajime. Modal methods for interaction of train and bridge. Computer and Structures. 1986, 27(1): 119-127
[110] Diana G, Cheli F. Dynamic interaction of railway systems with large bridges. Vehicle System Dynamics. 1989, 18(1): 71-106
[111] Olsson M. On the fundamental moving load problems. Journal of Sound and Vibration.1991, 145(2): 299-307
[112] Van Bogaert Ph. Dynamic response of trains crossing large span doubletrack bridges. Journal of Constructional Steel Research. 1993, 24(1): 57-74
[113] Green M F, Cebon D. Dynamic response of highway bridges to heavy vehicle loads: theory and experimental validation. Journal of Sound and Vibration. 1994, 170(1): 51-78
[114] Green Mark F, Cebon David, Cole David J. Effects of vehicle suspension design on dynamics of highway bridges. Journal of Structural Engineering. 1995, 121(2): 272-282
[115] 曾庆元．田志奇，杨毅，杨平．桁梁行车空间振动计算的桁段有限元法．桥梁建设．1985，(4)：1-17
[116] 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．铁道学报．1986，8(2)：48-59
[117] 杨平．列车对桥梁的蛇行激扰初探．土木工程学报．1987，20(2)：46-54
[118] 杨毅，曾庆元．列车桥梁时变振动系统模态综合法．振动与冲击．1988，(1)：1-9
[119] 杨平．铁路桥梁行车振动分析的等效输入法．长沙铁道学院学报．1989，7(1)：99-102
[120] 曾庆元，杨毅，骆宁安，江锋，张麒．列车-桥梁时变系统的横向振动分析．铁道学报．1991，13(2)：38-45
[121] 曾庆元，骆宁安，江锋．桥上列车横向摇摆力的初步研究．桥梁建设．1990，(1)：28-36
[122] 陈淮．上承式桁梁桥列车横向摇摆力的计算结果分析．长沙铁道学院学报．1991，9(3)：42-51
[123] 朱汉华．列车-桥梁时变系统振动能量随机分析理论．长沙铁道学院博士学位论文．1992．1
[124] 朱汉华、曾庆元．列车-桥梁时变系统振动能量随机分析理论方法．长沙铁道学院学报．1994，12(4)：6-10．
[125] 王荣辉，郭向荣，曾庆元．高速列车构架人工蛇行波的随机模拟方法．长沙铁道学院学报．1995，13(2)：1-7．
[126] 王荣辉，曾庆元，郭向荣．朱汉华．高速列车构架人工蛇行波V-σ曲线关系的 确定．长沙铁道学院学报．1996，14(1)：13-19．
[127] 王荣辉，郭向荣，曾庆元．高速列车-钢桁梁桥系统横向振动随机分析．铁道学报．1996，18(1)：90-95．
[128] 王荣辉，郭向荣，曾庆元．准高速列车——钢筋混凝土连续梁桥横向车振随机分析．桥梁建设．1996，(1)：23-27．
[129] 郭向荣，曾庆元．高速铁路多跨简支梁桥横向振动随机分析．长沙铁道学院学报．1997，15(1)：1-9．
[130] 张麒．曾庆元．钢桁梁桥横向刚度控制指标的探讨．桥梁建设．1998，(1)：1-4．
[131] 郭向荣，曾庆元．高速铁路简支钢桁梁桥横向刚度限值研究．长沙铁道学院学报．1998，16(2)：1-6．
[132] 张麒，曾庆元．铁路钢桁梁桥横向刚度的随机分析．长沙铁道学院学报．1998，16(2)：7-10．
[133] 郭文华，郭向荣，曾庆元．京沪高速铁路南京长江大桥斜拉桥方案车桥系统振动分析．土木工程学报．1999，32(3)：23-27．
[134] 郭向荣，曾庆元．高速铁路多Π形预应力混凝土梁桥动力特性及列车走行性分析．铁道学报．2000，22(1)：72-78．
[135] 郭向荣，陈淮，曾庆元．铁路连续钢桁梁桥横向刚度限值分析．桥梁建设．2000，(1)：13-16．
[136] 郭向荣，曾庆元．京沪高速铁路南京长江斜拉桥方案行车临界风速分析．铁道学报．2001，23(5)：75-80．
[137] 郭向荣，刘庆艳，曾庆元．高速铁路大跨度钢桥横向刚度限值分析．中国铁道科学．2001，22(5)：29-33．
[138] 曾庆元，向俊，娄平．车桥及车轨时变系统横向振动计算中的根本问题与列车脱轨能量随机分析理论，中国铁道科学．2002，23(1)：1-10．
[139] 向俊，曾庆元，娄平．再论列车脱轨能量随机分析．中国铁道科学．2002，23(2)：26-32．
[140] 陈淮．曾庆元．桥上列车横向摇摆力的随机分析．桥梁建设．2002，(2)：1-5．
[141] 曹雪琴．列车通过时桥梁结构竖向振动分析．上海铁道学院学报．1981，2(3)：1-15
[142] 曹雪琴，吴鹏贤．桁梁桥横向振动实测资料的概率统计分析．桥梁建设．1983，(3)：43-51
[143] 曹雪琴．桁梁桥横向刚度的设计检算．桥梁建设．1985，(3)：37-45
[144] 曹雪琴，陈晓．轮轨蛇行引起桥梁横向振动随机分析．铁道学报．1986，8(1)：89-97
[145] 曹雪琴．钢桁梁桥横向振动．北京：中国铁道出版社，1991
[146] 曹雪琴．车速提高至140km/h对既有桥跨结构的影响分析．铁道学报．1991，13(3)：97-103
[147] 顾萍，朱金龙．提速客车通过限速钢桥的试验和动力分析．中国铁道科学．2002． 23(2)：80-85
[148] 凌知民，曹雪琴，项海帆．铁路高墩连续梁桥车桥耦合振动响应分析．铁道学报．2002，24(5)：98-102
[149] 王刚．高速铁路三塔斜拉桥车桥动力分析．上海铁道大学学报．1999，20(10)：11-15
[150] 许慰平．大跨度铁路桥梁车桥耦合振动研究．北京：铁道科学研究院博士学位论文．1988
[151] 孙建林．大跨度斜拉桥横向振动特性分析．北京：铁道科学研究院博士学位论文．1988
[152] 杨岳民．大跨度铁路桥梁车桥动力响应理论分析及试验研究．北京：铁道科学研究院博士学位论文．1995．8
[153] 杨岳民，潘家英，陈庆国．大跨度铁路桥梁车桥动力响应理论分析及试验研究．中国铁道科学．1995，16(4)：1-15
[154] 王春贵．大跨度铁路斜拉桥车激空间振动线性及非线性分析．北京：铁道科学研究院博士学位论文．1996
[155] 张格明．中高速条件下车线桥动力分析模型与轨道不平顺影响．北京：铁道科学研究院博士学位论文．2001
[156] 高芒芒．高速铁路列车—线路—桥梁耦合振动及列车走行性研究．北京：铁道科学研究院博士学位论文．2001
[157] 高芒芒，李永强，许兆军，潘家英．高速列车作用下的芜湖长江大桥车桥耦合振动分析．中国铁道科学．2001，22(5)：34-40
[158] 张煅，柯在田，邓蓉，谢毅．既有线提速至160km/h桥梁评估的研究．中国铁道科学．1996，17(1)：9-20
[159] 杨宜谦，张煅，周宏业，孙宁．用调频质量阻尼器抑制铁路桥梁竖向共振的研究．中国铁道科学．1998，19(1)：12-18
[160] 夏禾，陈英俊．车—梁—墩体系动力相互作用分析．土木工程学报．1992，25(2)：3-12
[161] 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．土木工程学报．1994，27(2)：14-21
[162] 夏禾，阎贵平．列车—斜拉桥系统在风荷载作用下的动力响应．北方交通大学学报．1995，19(2)：131-136
[163] Xia He, Xu Y L, Chan T H T. Dynamic interaction of long suspension bridges with running trains. Journal of Sound and Vibration. 2000, 237(2): 263-280
[164] Xia H, De Roeck G, Zhang H R, Zhang N. Dynamic anlysis of train-bridge system and its application in steel girder reinforcement. Computers and Structures. 2001, 79(20-21): 1851-1860
[165] 夏禾．车辆与结构动力相互作用．北京：科学出版社，2002
[166] 夏禾，徐幼麟，阎全胜．大跨度悬索桥在风与列车荷载同时作用下的动力响应分析．铁道学报．2002，24(4)：83-91
[167] 夏禾，张楠，张鸿儒，DE ROECK Guido．300km/h高速铁路PC槽型梁动力试验研究．工程力学．2003，20(6)：99-105
[168] 阎贵平，夏禾．列车与刚梁柔拱组合体系的地震响应分析．北方交通大学学报．1994，18(1)：9-16
[169] 阎贵平，夏禾．铁路斜拉桥的地震响应特性分析．北方交通大学学报．1995，19(2)：137-142
[170] 张楠，夏禾，DE ROECK Guido．高速铁路铰接式列车车桥系统动力响应分析．工程力学．2004，21(2)：46-53，9
[171] 袁向荣．考虑约束扭转效应时桥梁的振动分析．成都：西南交通大学博士学位论文．1992．11
[172] 葛玉梅，袁向荣．机车-桁架桥耦合振动研究．西南交通大学学报．1998，33(2)：138-142
[173] 葛玉梅．斜拉桥在考虑风效应时的车-桥耦合振动．成都：西南交通大学博士学位论文．2001．3
[174] 葛玉梅，周述华，李龙安．斜拉桥在考虑风效应时的车-桥耦合振动．西南交通大学学报．2001，36(4)：369-373
[175] 葛玉梅，李永乐，何向东．作用在车-桥系统上风荷载的风洞试验研究．西南交通大学学报．2001，36(6)：612-616
[176] 沈锐利．高速铁路线上简支梁桥车桥共振问题初探．西南交通大学学报．1995，30(3)：275-282．
[177] 沈锐利．高速铁路简支梁桥竖向振动响应研究．中国铁道科学．1996，17(3)：24-34
[178] 沈锐利．高速铁路桥梁与车辆耦合振动研究．成都：西南交通大学博士学位论文．1998．10
[179] 宁晓骏．高速铁路列车~桥梁~基础空间耦合振动研究．成都：西南交通大学博士学位论文．1998．5
[180] 宁晓骏，何发礼，强士中．车桥耦合振动研究中轮轨接触几何非线性的考虑．桥梁建设．1999，(2)：8-10
[181] 宁晓骏，李小珍，强士中．高速铁路桥墩横向刚度的初步研究．西南交通大学学报．2000，35(1)：11-13
[182] 李小珍，强士中，沈锐利．高速列车-大跨度钢斜拉桥空间耦合振动响应研究．桥梁建设．1998，(4)：65-68
[183] 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．西南交通大学学报．1999，34(2)：153-157
[184] 李小珍，王应良，强士中．大跨度连续拱桁组合钢桥空间振动分析．振动与冲击．1999，18(4)：35-39，91
[185] 李小珍．高速铁路列车-桥梁系统耦合振动理论及应用研究．成都：西南交通大学博士学位论文．2000．5
[186] 李小珍，蔡婧，强士中．芜湖长江大桥斜拉桥的车桥耦合振动分析．铁道学 报．2001，23(2)：70-75
[187] 李永乐．风—车—桥系统非线性空间耦合振动研究．成都：西南交通大学博士学位论文．2003．8
[188] 李永乐，廖海黎，强士中．车桥系统气动特性的节段模型风洞试验研究．铁道学报．2004，26(3)：71-75
[189] 李永乐，强士中，廖海黎．风—车—桥系统空间耦合振动研究．土木工程学报．2005，38(7)：61-64，70
[190] 李永乐，强士中，廖海黎．考虑车辆位置影响的风-车-桥系统耦合振动研究．桥梁建设．2004，(3)：1-4
[191] 单德山．高速铁路曲线梁桥车桥耦合振动分析及大跨度曲线梁桥设计研究．西南交通大学博士学位论文．1999．6
[192] 单德山，李乔．车桥耦合振动数值模拟及软件实现．西南交通大学学报．1999．34(6)：663—667
[193] 单德山，李乔，蒋永林．Dynamic Response of Curved-Beam under Moving Load．Journal of Southwest Jiaotong University．1999，7(2)：163-172
[194] 单德山，李乔．移动荷载列作用下简支曲线梁的振动响应．铁道学报．2001，23(3)：99-103
[195] 单德山，李乔．曲率半径对曲线连续梁桥车桥耦合振动的影响．桥梁建设．2004，(6)：1-3，16
[196] 单德山．李乔．曲线弯梁桥振动分析方法．土木工程学报．2005，38(10)：61-65，87
[197] 何发礼．高速铁路中小跨度曲线梁桥车桥耦合振动研究．西南交通大学博士学位论文．1999．3
[198] 何发礼，李乔．曲率和超高对曲线梁桥车桥耦合振动的影响．桥梁建设．1999，(3)：5-7
[199] 何发礼，李乔．高速铁路中小跨度曲线梁的弯桥直作．铁道学报．2000，22(4)：113-116
[200] 何发礼，李乔．曲率和超高对曲线梁桥耦合振动的影响．桥梁建设．1999，(3)：5-7
[201] Yang Yeong-Bin, Lin Bing-Houng. Vehicle-bridge interaction analysis by dynamic condensation method. Journal of Structural Engineering.1995, 121 (11): 1636-1643
[202] Yang Yeong-Bin, Liao Shu-Shyan, Lin Bing-Houng. Impact formulas for vehicles moving over simple and continuous beams. Journal of Structural Engineering. 1995, 121(11): 1644-1650
[203] Yang Yeong Bin, Yau Jong-Dar. Vehicle-bridge interaction element for dynamic analysis. Journal of Structural Engineering. 1997, 123(11): 1512-1518
[204] Yang Yeong-Bin, Yau Jong-Dar, Hsu Lin-Ching. Vibration of simple beams due to trains moving at high speeds. Engineering Structures.1997, 19(11): 936-944
[205] Wu Yean-Seng, Yang Yeong-Bin. Steady-state response and riding comfort of trains moving over a series of simply supported bridges. Engineering Structures. 2003, 25(2): 251-265
[206] Xu Y L, Zhang N, Xia H. Vibration of coupled train and cable-stayed bridge systems in cross winds[J]. Engineering Structures. 2004, 26(10): 1389-1406.
[207] Li Yong-le, Qiang Shi-zhong, Liao Hai-li,Xu Y L. Dynamics of wind-rail vehicle-bridge systems[J]. Journal of Wind Engineering and Industrial Aerodynamics. 2005, 930: 483-507
[208] Tanaka H, Davenport A G. Response of taut strip models to turbulent wind. Journal of Engineering Mechanics, ASCE. 1982, 108: 33-49
[209] Jones W P, Launder B E. The prediction of laminarization with two equation model of turbulence. Int. J. Heat and Mass Transfer. 1972, 15: 301-314
[210] Yakhot Victor, Orszag Steven A. Renormaliztion group analysis of turbulence Ⅰ. Basic theory. Journal of Scientific Computing. 1986, 1(1): 3-5
[211] Speziale G G, Thangam S. Analysis of an RNG based turbulence model for seperated flows. International Journal of Engineering Science. 1992, 30(10): 1379-1388
[212] K Yakhot V, Orszag S A, Thangam S, Gatski T B, Speziale C G. Development of turbulence models for shear flows by a double expansion technique. Physics of Fluids A. 1992, 4(7): 1510-1520
[213] Smith L M, Reynolds W C. On the Yakhot-Orszag-renormalzation group method for deriving trubulence statistics and models. Physics of Fluids A (Fluid Dynamics). 1992, 4(2): 364-390
[214] Nagano Yasutaka, Itazu Yoshibiro. Renormalization group theory for turbulence: Assessment of the Yakhot-Orszag-Smith theory. Fluid Dynamics Research.1997, 20(1-6): 157-172
[215] 李玲．轴流压气机机匣处理的数值模拟与实验研究．北京：北京航空航天大学博士学位论文．1998
[216] 李玲，李玉梁．应用基于RNG方法的湍流模型数值模拟钝体绕流的湍流流动．水科学进展．2000，11(4)：357-361
[217] 王辉，沉水福，唐锦春．低层坡屋面群体建筑表面风压的数值模拟．工程力学．2003，20(6)：135-140，64
[218] Smith L M, Woodraff S L. Renormalization-group analysis of turbulence. An. Rev. Fluid Mech, 1998, 30: 275-310
[219] Suh Sang-Ho, Roh Hyung-Woon, Kim Ha-Rim, Lee Kwang-Yerl, Kim Kyu-Suk. Application of Computational techniques for studies of wind pressure coeffcients around an odd-geometrical building. Journal of Wind Engineering and Industrial Aerodynamics. 1997, 67-68: 659-670
[220] Murakami S. Current status and future trends in computational wind engineering. Journal of Wind Engineering and Industrial Aerodynamics. 1997, 67-68: 3-34
[221] 刘导治．计算流体力学基础．北京：北京航空航天大学出版社，1989．3
[222] 李炜．黏性流体的混合有限分析解法．北京：科学出版社，2000．1
[223] Barth T J, Jespersen D. The design and application of upwind schemes on unstructured meshes. Technical Report AIAA-89-0366, AIAA 27th Aerospace Sciences Meeting, Reno, Nevada, 1989
[224] Hutchinson B R, Raithby G D. Multigrid Method Based on the additive Correction Strategy. Numerical Heat Transfer.1986, 9(5): 511-537
[225] Patankar S V. Namerical Heat Transfer and Fluid Flow. Hemsphere, Washington, D. C., 1980
[226] Rhie C M, Chow W L. Numerical study of the turbulent flow past an airfoil with trailing edge separation. AIAA Journal.1983, 21(11): 1525-1532
[227] Luo J Y, Issa R I, Gosman A D. Prediction of impeller induced flows in mixing vessels using multiple frames of reference [A]. IChemE Symp, 1994, ser 136 [C]: 549-556
[228] Sehyun Shin, Chang Hyukjae, Athavale Mahesh. Numerical investigation of the pump flow in an automotive torque converter. SAE 1999 Transactions, Section 6, 108(part2): 1967-1977
[229] Luo J Y, Gosman A D, Issa R I, Middleton J C, Fitzgerald M K. Full flow field computation of mixing in baffled stirred vessels. Chemical Engineering Research & Design.1993, 71 (A3): 342-344.
[230] Launder B E, Spalding D B. The Numerical Computation of Turbulent Flows. Computer Methods in Applied Mechanics and Engineering. 1974, 3(2): 269-289
[231] 李正农，楼梦麟，宋锦忠，庞加斌．渡槽槽体结构风载体形系数的风洞试验研究．水利学报．2000，9：15-19
[232] 李正农，吴红华，楼梦麟．湍流对于渡槽槽体结构风载体形系数的影响．第六届全国风工程及工业空气动力学学术会议论文集，北京，2002：55-60
[233] Baker C J, Dalley S J, Johnson T, Quinn A, Wright N G. The slipstream and wake of a high-speed train. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit.2001, 215(2): 83-99
[234] Ghia U, Ghia K N, Shin C T. High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method. Journal of Computational Physics.1982, 48(3): 387-411
[235] Schreiber R, Keller H B. Driven cavity flows by efficient numerical techniques. Journal of Computational Physics.1983, 49(2): 310-333
[236] Gatski T B, Grosch C E, Rose M E. A numerical study of the two-dimensional Navier-Stokes equations in vorticity-velocity variables. Journal of Computational Physics. 1982, 48(1): 1-22
[237] Chen C J, Chen H C. Finite analytic numerical method for unsteady two-dimensional Navier-Stokes equations. Journal of Computational Physics. 1984, 53(2): 209-226
[238] Gupta M M, Manohar R P, Noble B. Nature of viscous flows near sharp corners. Computers and Fluids. 1981, 9(4): 379-388
[239] Goodrich J W, Gustafson K, Halasi K. Hopf bifurcation in the driven cavity. Journal of Computational Physics. 1990, 90(1): 219-261
[240] Shen J. Hopf bifurcation of the unsteady regularized driven cavity flow. Journal of Computational Physics. 1991, 95(1): 228-245
[241] Auteri F, Parolini N, Quartapelle L. Numerical investigation on the stability of singular driven cavity flow. Journal of Computational Physics. 2002, 183(1): 1-25
[242] 罗林．轨道随机干扰函数．中国铁道科学．1982，3(1)：1-7
[243] Vijay K．Garg，Rao V．Dukkipati．铁道车辆系统动力学．沈利人译，成都：西南交通大学出版社，1998．9
[244] 德国联邦铁路慕尼黑研究中心．城间特快列车ICE技术任务书(Lastenheft IC-Express)．周本宽、熊火耀、罗世辉、刘思宁、章音、金炜东译，铁道部科学 技术司、西南交通大学编，1993．3
[245] 雷晓燕．轨道力学与工程新方法．北京：中国铁道出版社，2002．8：38-53
[246] 翟婉明．车辆——轨道耦合动力学．北京：中国铁道出版社，1997
[247] 长沙铁道学院随机振动研究室．关于机车车辆/轨道系统随机激励函数的研究．长沙铁道学院学报．1985，(2)：1-36
[248] 铁道部科学研究院铁道建筑研究所．我国干线轨道不平顺功率谱的研究．TY-125，北京：铁道部科学研究院，1999
[249] 许慰平．大跨度铁路桥梁车桥空间耦合振动研究．北京：铁道科学研究院，1989
[250] 陈果，翟婉明，左洪福．仿真计算比较我国干线谱与国外典型轨道谱．铁道学报．2001，23(3)：82-87
[251] 曹雪琴等．桥梁结构动力分析．北京：中国铁道出版社，1987
[252] 徐绍鑫．随机振动．北京：高等教育出版社，1990．5
[253] 陈果，翟婉明．铁路轨道不平顺随机过程的数值模拟．西南交通大学学报．1999，34(2)：138-142
[254] 严隽耄，王开文．任意形轮轨接触关系的计算．铁道车辆．1984，22(2)：24-28
[255] 王开文．车轮接触点迹线及轮轨接触几何参数的计算．西南交通大学学报．1984，19(1)：89-99
[256] 王福天．车辆系统动力学．北京：中国铁道出版社，1994年
[257] 张孝珂，刘新明，刘煜，任玉君．LM型车辆车轮磨耗形踏面．铁道车辆．1984，(11)：1-7
[258] 李光明．快速重载轨道技术手册．北京：中国铁道出版社，1999．9
[259] 严隽耄，王开文．锥形及磨耗形踏面轮对的空间轮轨接触几何约束特点．铁道学报．1985，7(2)：9-17
[260] Shen Z Y (沈志云),Hedrick J E,Elkins J A. A comparison of alternative creep force models for rail vehicle dynamic analysis. Proceedings of 8th IAVSD Symposium, MIT, Cambridge, 1983: 591-605
[261] 李成辉．轨道结构振动理论及应用研究．成都：西南交通大学博士学位论文，1996
[262] 石洞，石志源，黄东洲．桥梁结构电算．第2版．上海：同济大学出版社，1989
[263] 铁道部科学研究院铁建所．广深准高速铁路运营线试验报告之三——桥梁动载试验报告．北京，1995
[264] 铁道部科学研究院等．200km/h电动旅客列车组环线及广深线试验研究报告．北京，2000
[265] 曾宇清．车桥(轨)耦合振动系统仿真中的基本问题、解决办法及其应用范围．中国铁道科学．2002，23(4)：12-17
[266] GB 5599-85，铁道车辆动力学性能评定和试验鉴定规范，1985
[267] TB/T 2360-93，铁道机车动力学性能试验鉴定方法及评定标准，1993
[268] 95J01-L，高速试验列车动力车强度及动力学性能规范，1995
[269] 95J01-M，高速试验列车客车强度及动力学规范，1995
[270] 铁道部科学研究院机辆所译．既有线铁路运营提速试验手册·解释．国外高速列车译文集，1997
[271] 铁道部科学研究院译．脱轨研究专集．铁路行车安全泽文集，1998
[272] 詹斐生．平稳性指标的历史回顾(上)．铁道机车车辆．1994，(4)：43-52
[273] 詹斐生．平稳性指标的历史回顾(中)．铁道机车车辆．1995，(1)：39-51
[274] 詹斐生．平稳性指标的历史回顾(下)．铁道机车车辆．1995，(2)：19-21，62
[275] 铁运函[2004]120号．铁路桥梁检定规范．北京：中国铁道出版社，2004
[276] 严国敏．现代斜拉桥．成都：西南交通大学出版社，1996
[277] 铁道部第三勘测设计院主编．铁路桥涵设计基本规范(TBl0002．1-99)．北京：中国铁道出版社，2000
[278] 严隽耄．车辆工程．第二版．北京：中国铁道出版社，2004
