摘要
客运专线和高速铁路的大规模兴建和列车速度的不断提高,以及越来越多的超大跨度跨海大桥的建设,为建立车桥耦合振动的精细化数值仿真模型提出了必然的需求。现有的车辆与桥梁的耦合振动研究中,在建立车辆动力学模型时,主要采用传统动力学分析方法拉格朗日第二类方程或牛顿-欧拉方程导出位置与姿态坐标的运动微分方程。随着铁路科学技术的发展,研究的车辆动力学模型越来越复杂,同时从车桥耦合振动研究中车辆分析模型的发展趋势看,需要进一步抽象和细化车辆动力学各元件对象模型,特别是考虑悬挂非线性问题,用手工符号推导动力学方程将面临相当繁重的代数和微分运算,并且非常容易出错,为此,不得不将系统作许多强制性的简化,降低自由度,但这样做很难揭示复杂的动力学性态,也很难满足精细化仿真的要求,使用多体系统动力学方法进行程式化的建模成为一种必然的选择。对桥梁进行有限元模拟时,一般采用空间杆系有限元法,而高速铁路桥梁的截面形状多为空心箱形截面,为了更准确的考虑梁体在高速列车作用下的空间挠曲以及扭转变形的特点,需要采用空间板壳单元模拟梁体。对于采用摩擦桩基础的桥梁,建立桥梁动力学模型需要同时考虑梁体—桥墩—桩基础—桩土相互作用的共同影响。
随着计算机技术、有限元分析理论与多体系统动力学的发展,车辆—桥梁各子系统的精细化仿真分析及系统链接的实现成为了可能,车辆的动力学行为可以使用多体系统动力学方法进行分析,桥梁等弹性结构则使用有限元方法进行分析,然后将两个子系统在轮轨接触面离散的信息点上进行数据交换实现联合仿真。将多体系统动力学软件SIMPACK与有限元软件ANSYS结合起来,为车桥耦合振动的联合仿真分析构建了平台。
本文首先介绍了多体系统动力学的基本理论,利用多体系统动力学方法建立了车辆三维空间精细化仿真模型,充分考虑了模型中的各种非线性因素,除了轮轨接触几何关系,轮轨蠕滑力计算非线性特性外,还充分考虑了机构参数中的各种非线性因素,并计算了车辆的线性临界速度和非线性临界速度。介绍了桥梁动力模型的有限元法、动力子结构技术的实现以及求解自振特性的原理。
其次,针对弹性轮轨接触和约束轮轨接触,分别建立了多体系统中轮轨接触的运动方程,分析了轮轨接触点的求解方法及两种接触时法向力的求解原理。根据轮轨运动学关系,详细推导了Kalker简化理论—FASTSIM算法的实现过程。在分析多体系统动力学和有限元方法耦合集成的基础上,建立了多体系统和有限元数据交换过程的计算流程,并介绍了基于BDF的DASSL算法。以高速铁路简支梁桥为例,进行了车桥耦合振动仿真分析,证明了方法的可行性和有效性。
最后,以客运专线大跨度连续梁桥和琼州海峡跨海工程超大跨度斜拉桥方案为研究对象,建立了车桥耦合振动三维精细化仿真模型。采用基于多体系统动力学和有限元法的联合仿真技术,进行了动车组列车通过桥梁时的仿真研究。
针对大跨度连续梁桥,建立了同时考虑梁部、桥墩、桩基础和桩土相互作用的完整的桥梁动力学模型。对弹性轮轨接触和约束轮轨接触从理论上进行比较,并对两种接触时的车桥耦合振动响应进行了对比分析,研究了轮轨接触对车桥耦合振动的影响,分析了其适用性；对单线行车、双向对开以及两列车以不同车速双向对开时的车桥耦合振动仿真结果进行了对比分析；从比较秦沈线轨道谱、德国低干扰及德国高干扰谱三种谱功率谱密度和时间样本幅值的差异并结合三种谱时的车桥耦合振动动力参数的对比分析,探明了秦沈客运专线轨道谱与德国轨道谱之差异,探究了不平顺谱波长成分对车桥动力参数的影响；分析了阻尼比对桥梁动力响应的影响。
针对琼州海峡跨海工程斜拉桥方案,采用空间板壳和杆系混合单元有限元法建立了斜拉桥动力分析模型。仿真计算了列车以不同车速单线行车和双向对开通过该大跨度斜拉桥的空间耦合振动响应,检算该方案桥是否具有足够的横向、竖向刚度及良好的运营平稳性。
With the large-scale construction of passenger dedicated railway and high-speed railway, continuous improvement of train speed, and construction of more and more crossing-channel bridges, to establish refined numerical simulation model for coupled vibration between vehicle and bridge become an inevitable demand. In existing studies of coupled vibration for vehicle-bridge system, differential motion equations of coordinates of position and attitude are derived by traditional kinetics analysis method the second kind Lagrange equation and Newton-Euler equation when establishing vehicle dynamics model. With the development of railway science technology, the vehicle dynamics models foe study become more complex. On the other hand, the component object models of vehicle dynamics need to be futher abstracted and refined, especially nonlinear problems of suspension should be considered. Therefore heavy algebra and differential operations will be confronted with when deriving dynamic equations by manual symbols, and errors may be encountered easily. To this end, many mandatory simplifications have to be done for the system, and degrees of freedom are reduced. As a result, it is difficult to reveal the complex dynamic behaviour, and it is hard to meet the requirement of refined simulation. So it is an inevitable choice to establish programming model by multi-dynamics approach. The bridge dynamic model usually is established by Space bar finite element method. Because the cross-section shape of high-speed railway bridges is mostly hollow box section, space shell element is used to simulate girder to more accurately consider space deflection and torsion of girder under high-speed train. For the bridges with friction pile foundation, the girder-pier-pile foundation-interaction between pile and soil are all should be considered when establishing dynamic models.
With the development of computer technology, finite element analysis theory and multi-body system dynamics, refined simulation of each subsystem for vehicle-bridge system and link of systems may be realized. Dynamic behavio of vehicle can be analyzed by multi-body system dynamics method, and flexible structure (such as bridge) can be analyzed by finite element method, and then the co-simulation of two subsystems (vehicle and bridge) is performed by the interfacing data exchange at discrete communication points. The co-simulation platform for coupled vibration between vehicle and bridge is constructed by integration of multi-body system dynamics software SIMPACK and finite element software ANSYS.
Firstly, basic theories of multi-body system dynamics are intrduced. The refined three-demensional space vehicle model is set up by multi-body system dynamics method, and the multiple non-linear properties including all kinds of non-linear factors of mechanism parameters besides wheel/rail contact geometry and creep forces are considered. Linear and non-linear critical speeds are calculated. Finite element method of dynamic model of the bridge, dynamic substructure technology and principle of solving vibration characteristic are intrduced.
Secondly, the motion equations are established in multi-body system for elastic wheel/rail contact and constraint wheel/rail contact, solving method of wheel/rail contact point and wheel/rail normal force are analyzed. According to wheel/rail kinematic relation, the realization process of Kaller simplified theory-FASTIM algorithm is detailedly derived. Based on coupled integration of multi-body system dynamics and finite element method, calculation process of exchange data between multi-body system dynamics and finite element is set up, and DASSL algorithm based on BDF is introduced. Taking a simply supported beam bridge on high-speed railway as example, coupled vibration between vehicle and bridge is simulated. Feasibility and validity of the method are confirmed.
Finally, taking a long-span continuous beam bridge on passenger dedicated railway and super-large cable-stayed bridge scheme of crossing-channel project over Qiongzhou strait as study objects, the 3D refined simulation models of coupled vibration between vehicle and bridge are established. The simulation reaearchs are completed when the motor train runs through the bridges by co-simulation techonology based on multi-body system dynamics and finite element method.
For long-span continuous beam bridge, whole dynamic model of the bridge is established, and girder, bridge pier, pile foundation and pile-soil interaction are all considered simulately. The impact of wheel/rail contact on coupled vibration between vehicle and bridge and applicability of wheel/rail contact are studied by comparing theory difference of two wheel/rail contact (elastic contact and constraint contact) and resultes of simulation analysis of coupled vibration between vehicle and bridge. The simulation resultes of coupled vibration are compared and analyzed when only a motor train passes the bridge and when two trains pass bridge with the opposite direction at equal or uneqal speed. By comparison and analysis of PSD, time-sample amplitude of three kindes spectrums (QS track spectrum, German railway spectrum of high irregularity and low irregularity) and dynamic parameters of coupled vibration for vehicle-bridge system, the difference of track spectrum of QS passenger railway line and typical track spectrum abroad is proved, and the impact of wavelength components of the irregularity spectrums on dynamic parameters of vehicle-bridge system is explored. Impact of damping ration on dynamic response of the bridge is analyzed.
For super-large cable-stayed bridge scheme of crossing-channel project over Qiongzhou strait, the dynamic analysis model of cable-stayed bridge is established by use of space bar-shell hybrid finite element method. The space vibration responses are calculated by co-simulation based on multi-body system dynamics and finite element method when the train runs through the long span cable-stayed bridge at different speeds in order to test if the bridge has the sufficient lateral or vertical rigidity and the operation stability is fine.
引文
[1]钱立新.世界高速铁路技术[M].北京：中国铁道出版社,2003
[2]钱仲侯.高速铁路[M].北京：中国铁道出版社,1999
[3]高家驹,王文仓.高速铁路与广深准高速铁路概论[M].北京：中国铁道出版社,1994.6
[4]孙翔编译.世界各国的高速铁路[M].成都：西南交通大学出版社,1992
[5]李小珍,高速铁路列车-桥梁系统耦合振动理论及应用研究[D].成都：西南交通大学土木工程学院,2000
[6]郑健,中国高速铁路桥梁[M].北京：高等教育出版社,2008
[7]Timoshenko著,胡人礼译.工程中的振动问题[M].北京：中国铁道出版社,1978
[8]Timoshenko S P. Forced vibration of prismatic bars. Izvestiya Kievskogo Politekhnicheeskogo Institute,1908
[9]Timoshenko S P. On the forced vibration of bridges [J], Philosoph Magazine,1922, Ser.6
[10]Inglis C E. A mathematical treatise on vibration in railway bridges [M].Cambridge, 1934
[11]Schallenkamp A. Schwingungen von tragern bei bewegten laster [J]. Ingenieur Archiv, 1937,8:182-198
[12]Mise K, Kunii S. A theory for the forced vibration of a railway bridge under the action of moving loads [J]. Quartley Journal of Mech. and Applied Math.1956,9
[13]Wen P R. Dynamic response of beams traversed by two-axle loads [J]. Jounal of Engineering Mechanics, ASCE.1960,86(EM5):91-111
[14]Symonds P S, Neal B G. Travelling loads on rigid-plastic beams [J]. Journal of Engineering Mechanics, ASCE.1960,86(EM1):79-89
[15]Schlack Alois L, Raske Theodore F. Resonance of beams due to cyclic moving loads [J]. Journal of Engineering Mechanics, ASCE.1966,92(EM6):175-184
[16]Ting E C, Ginsberg J H. A general algorithm for moving mass problems [J]. Journal
of Sound and Vibration.1974,33(1):49-58
[17]Adams G G, Bogy D B. Steady solutions for moving loads on elastic beams with end-sided constrains [J] Journal of Applied Mechanics, Transaction of ASME.1975,42 Ser E(4):800-804
[18]Blejwas T E, Feng C C. Ayre R S. Dynamic interaction of moving vehicles and structures [J].Jounal of Sound and Vibration.1979,67(4):513-521
[19]Hayashikawa Toshiro, Watanabe Noboru. Dynamic behavior of continuous beams with moving loads [J]. Journal of Engineering Mechanics, ASCE.1981, 107(1):229-246
[20]Genin J, Ting E C, Vafa Z. curved bridge response to a moving vehicle [J]. Journal of Sound and Vibration.1982,81(4):469-475
[21]Fryba L. Non-stationary response of a beam to a moving random force [J]. Journal of Sound and Vibration.1976,46(3):323-338
[22]Hiral A, Ito M. Dynamic effects produced by trains upon suspension bridges [J]. Symposium on suspension bridges, Lisbon,1966
[23]Hiral A, Ito M. Response of suspension bridges to moving vehicles [J]. Journal of the Faculty of Engineering, University of Tokyo.1967,XXIX(1)
[24]Hayashikawa Toshiro, Watanabe N. Suspension bridge response to moving loads [J]. Journal of Engineering Mechanics Division,ASCE.1982,108(EM6):1051-1066
[25]Dodds C J, Robson J D. The description of road surface road surface roughness [J]. Journal of Sound and Vibration.1973,31 (2):175-183
[26]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):23-33
[27]Gupta R K, Traill-Nash R W. Bridge dynamic loading due to surface irregularities and braking of vehicle [J]. Earthquake Engineering and Structure Dynamics.1980,8:83-96
[28]Palamas J, Coussy O, Bamberger Y. Effects of surface irregularities upon the dynamic response of bridges under suspended moving loads [J]. Journal of Sound and Vibration.1985,99(2):235-245
[29]Fryba L, Dynamic interaction of vehicle with tracks and roads [J]. Vehicle System Dynamics.1987,16(3):129-138
[30]Schneider H J, Elf H P, Koelle P. Modelling of traveling-loads and time-dependent masses with Adina [J]. Computer and Structure.1983,17:5-6
[31]Padovan J, Paramodilok O. Generalized solution of time dependent traveling load problem via moving finite element scheme [J]. Joumal of Sound and Vibration.1983,91 (2):195-209
[32]Hino J, Yoshimura T, Konishhi K, Ananthanarayana N. 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):45-53
[33]Olsson M. Finite element modal co-ordinate analysis of structures subjected to moving loads [J]. Journal of Sound and Vibration.1985,99(1):1-12
[34]Hino T, Yoshimura T, Ananthanarayana N. 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):477-491
[35]Chu K H, Garg V K. Railway-bridge impact:simplified train and bridge model [J]. Journal of Structural Division,ASCE.1979,105(ST9):1823-1844
[36]Wiriyachai A, Chu K H, Garg V K. Impact study by various bridge models [J]. Earthquake Engineering & Structural Dynamics.1982,10(1); 31-45
[37]Bhatti M H, Garg V K., Chu K H. Dynamic Interaction between freight train and steel bridge [J]. Journal of Dynamic Systems, Measurement and control Transactions ASME.1985,107(1):60-66
[38]Chu K H, Garg V K, Bhatti M H. Impact in truss bridge due to freight trains [J]. Journal of Engineering Mechanics.1985,111(2):159-174
[39]Wang T L. Impact and fatigue in open-deck steel truss and ballasted prestressed concrete railway bridges [D]. Ph.D thesis. Illinois Institue of Technology, Chicago, Illinois,1984
[40]Wang Ton-Lo. Ramp/Bridge interface in railway prestressed concrete bridge [J]. Journal of Structure Engineering.1990,166(6):1648-1689
[41]Wang Ton-Lon, Garg Vijay K, Chu Kuang-Han. Railway bridge/vehicle interaction studies with new vehicle model [J]. Journal of structure Engineering.1991,117(7):2099-2116
[42]Tanabe Makoto, Yamada Yoshiaki, Wakui Hajime. Modal methods for interaction of train and bridge [J]. Computer and Structure.1986,27(1):119-127
[43]Diana G, Cheli F. Dynamic interaction of railway systems with large bridges [J].
Vehicle System Dynamics.1989,18(1):71-106
[44]Olsson M. On the fundamental moving load problems [J]. Journal of Sound and Vibration.1991,145(2):299-307
[45]Bogaert V. Dynamic response of trains crossing large span double-track bridges [J]. Journal of Constructional Steel Research.1993,24(1):57-74
[46]Green M F, Cebon D. Dynamic reponse of highway bridges to heavy vehicle loads: theoy and experimental validation [J]. Journal of Sound and Vibration.1994,170(1):51-78
[47]Green M F, Cebon D, Cole D J. Effects of vehicle suspension design on dynamics of highway bridges [J]. Journal of structural Engineering.1995,121(2):272-282
[48]Yang Y B, Lin B H. Vehicle-bridge interaction analysis by dynamic condensation method [J]. Journal of Structural Engineering,ASCE.1995,121(11):1636-1643
[49]Yang Y B, Liao S S, Lin B H. Impact formulas for vehicle moving over simple and continuous beams [J]. Journal of Structural Engineering. ASCE.1995,121(11)1644-1650
[50]Yang Y B, Yau J D. Vehicle-bridge interaction element for dynamic analysis [J]. Journal of Structural Engineering Structures.1997,123(11):1512-1518
[51]Yang Y B, Yau J D, Hsu L C. Vibration of simple beams due to trains moving at high speed [J]. Engineering Structure.1997,19(11):936-944
[52]程庆国,许慰平.大跨度铁路斜拉桥列车走行性探讨.全国桥梁结构学术大会论文集,武汉,1992,41-51
[53]程庆国,潘家英.大跨度铁路斜拉桥竖向刚度分析.全国桥梁结构学术大会论文集,武汉,1992,1163-1168
[54]许慰平.大跨度铁路桥梁车桥空间耦合振动研究[D].北京：铁道科学研究院,1988
[55]孙建林.大跨度铁路桥梁车桥空间耦合振动研究[D].北京：铁道科学研究院,1988
[56]杨岳民.大跨度铁路桥梁车桥动力响应理论分析及实验研究[D].铁道部科学研究院博士学位论文,1995
[57]王贵春.大跨度铁路斜拉桥车激空间振动线性及非线性分析[D].北京：铁道科学研究院,1996
[58]柯在田,陈新中,张煅.准高速铁路线上桥梁动力性能研究[J].铁道建筑.1991,(S1)：62-69
[59]张煅,柯在田,邓蓉,等.既有线提速至160km／h桥梁评估的研究[J].中国铁道科学.1996,(1)：9-20
[60]邓蓉,张煅.中小跨度钢板梁桥在提速中的振动性能研究[J].中国铁路.1997,(1)：30-34
[61]谢毅,严普强,张煅,等.准高速行车下铁路桥梁振动特性的试验研究[J].振动与冲击.1998,17(1)：53-57
[62]刘汉夫,杨孚衡,张煅.对铁路上承式钢板梁横摆振动的剖析[J].中国铁路.1999,(5)： 29-32
[63]高岩,张煅.高速铁路中小跨度桥梁竖、横向刚度限值及合理分布的研究[J].铁道建筑技术.2000(4)：11-14
[64]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[D].北京：铁道部科学研究院,2001
[65]万家.高速列车—无碴轨道—桥梁耦合系统动力学性能仿真研究[D].北京：铁道科学研究院,2005
[66]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
[67]夏禾,陈英俊.车—梁—墩体系动力相互作用分析.土木工程学报[J],1992,25(2)：3-12
[68]夏禾,陈英俊等.风和列车荷载共同作用下刚梁柔拱组合桥的动力响应分析.92’全国桥梁结构学术大会论文,武汉,1063-1070
[69]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度[J].土木工程学报,1994,27(2)：131-136
[70]夏禾,闫贵平.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
[71]夏禾,陈英俊,张煅,等.列车提速情况下铁路双线简支钢桁梁动力响应分析[J].铁道学报,1996,18(5)：75-82
[72]王庆波,汪胜,许克宾,等.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)：400-403
[73]张楠,夏禾.地震对多跨简支梁桥上列车运行安全的影响[J].世界地震工程,2001,17(4)： 93-99
[74]张楠.高速铁路铰接式列车的车桥动力耦合问题的理论分析与试验研究[D].北京：北方交通大学,2002
[75]韩艳,夏禾,郭薇薇.斜拉桥在地震与列车荷载同时作用下的动力响应分析[J].工程力学,2006,23(1)：93-98,68
[76]郭薇薇,夏禾,徐幼麟.风荷载作用下大跨度悬索桥的动力响应及列车运行安全分析[J].工程力学,2006,23(2)：103-110
[77]郭薇薇,夏禾.风荷载作用下大跨度桥梁的动力响应及行车安全性分析[J].中国铁道科学,2006,27(2)：137-139
[78]夏禾,郭薇薇,张楠.车桥系统共振机理和共振条件分析[J].铁道学报,2006,28(5)： 53-58
[79]夏禾.车辆与结构动力相互作用[M].北京：科学出版社,2002
[80]夏禾,张楠.车辆与结构动力相互作用(第二版)[M].北京：科学出版社,2005
[81]曾庆元,田志奇,杨毅,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
[82]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,1986,892)：48-58
[83]曾庆元,郭向荣.列车桥梁时变系统振动分析理论及应用[M].北京：中国铁道出版社,1999
[84]曾庆元,骆宁安,江锋.桥上列车横向摇摆力的初步研究[J].桥梁建设,1990,(1)：28-36
[85]曾庆元.关于铁路桥梁的刚度问题[J].铁道科学与工程学报,1991,9(3)：1-15
[86]曾庆元,杨毅,骆宁安,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
[87]曾庆元.弹性系统动力学总势能不变值原理[J].华中理工大学学报,2000,28(1)：1-3
[88]张麒,曾庆元.钢桁梁桥横向刚度控制指标的探讨[J].桥梁建设,1998(1)：1-4
[89]张麒,曾庆元.焦支复线洛阳黄河大桥横向刚度分析[J].桥梁建设,2000,(4)：14-16
[90]郭文华,郭向荣,曾庆元.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
[91]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[J].土木工程学报,1999,32(3)：23-27
[92]郭向荣,曾庆元.高速铁路结合梁桥与列车系统振动分析模型[J].华中理工大学学报,2000,28(3)：60-62
[93]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[J].铁道学报,2000,22(1)：72-78
[94]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[J].铁道学报,2001,23(5)：75-80
[95]郭向荣,曾庆元.高速铁路简支钢桁梁桥横向刚度限值研究[J].长沙铁道学院学报,16(2)：1-6
[96]郭向荣,陈淮,曾庆元.铁路连续钢桁梁桥横向刚度限值分析[J].桥梁建设,2000,(1)：13-16
[97]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[J].中国铁道科学,2001,22(5)：30-33
[98]向俊,曾庆元,周智辉.桥上列车脱轨的力学机理、能量随机分析理论及其应用[J].铁道学报,2004,26(2)：97-104
[99]周智辉,曾庆元.桥上列车脱轨计算分析[J].中国铁道科学,2004,25(4)：46-49
[100]向俊,赫丹,左一舟,等.京山线滦河老桥上货物列车脱轨分析[J].交通运输工程学报,2004,4(3)：16-19
[101]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
[102]曹雪琴.钢桁梁桥横向振动[M].北京：中国铁道出版社,1991
[103]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
[104]曹雪琴,刘必胜,吴鹏贤.桥梁结构动力分析[M].北京：中国铁道出版社,1987
[105]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
[106]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,1998,20(1)： 88-94
[107]王刚,曹雪琴.高速铁路大跨度斜拉桥车桥动力分析[J].上海铁道大学学报,2000,21、(8)：7-11
[108]曹雪琴,吴定俊,罗蔚文,等.铁路桥梁刚度检定标准总报告[R].上海铁道大学,1999
[109]沈锐利.列车过桥时桁梁桥的空间振动分析[D],成都：西南交通大学硕士学位论文,1987
[110]沈锐利.高速铁路桥梁与车辆耦合振动研究[D],西南交通大学土木工程学院,1998
[111]沈锐利.高速铁路简支梁桥竖向振动响应研究[J].中国铁道科学.1996,(3)
[112]沈锐利.高速铁路线上简支梁桥车桥共振问题初探[J].西南交通大学学报.1995,(3)
[113]葛玉梅,袁向荣.机车—桁架桥梁耦合振动研究[J].西南交通大学学报.1998,(2)
[114]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[D].成都：西南交通大学土木工程学院,1999
[115]单德山,李乔.车桥耦合振动数值模拟及软件实现[J].西南交通大学学报.1999,34(6)：663-667
[116]单德山,李乔.移动荷载列作用下简支曲线梁的振动响应[J].铁道学报.2001,23(3)：99-103
[117]单德山,李乔.铁路曲线连续梁桥车桥耦合振动研究[J].振动与冲击.2005,24(4)：62-77
[118]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[J].桥梁建设.2004(6)：1-3,16
[119]何发礼.高速铁路中小跨度曲线梁桥车桥耦合振动研究[D],成都：西南交通大学土木工程学院,1999
[120]何发礼,李乔.曲率和超高对曲线连续梁桥车桥耦合振动的影响[J].桥梁建设.1999,(3)：5-7
[121]何发礼,李乔.高速铁路中小跨度曲线梁的弯桥直作[J].铁道学报.2000,22(4)：113-116
[122]李小珍,马文彬,强士中.车桥系统耦合振动分析的数值解法[J].振动与冲击.2002,21(3)：21-25
[123]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[J].桥梁建设.1998,(4)：65-68
[124]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
[125]李小珍,喻璐,强士中.不同主梁竖曲线下大跨度斜拉桥的车桥耦合振动分析[J].振动与冲击.2003,22(2)：43-46
[126]李小珍,强士中.大跨度公铁两用斜拉桥车桥动力分析[J].振动与冲击.2003,22(1)： 6-19
[127]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[J], 桥梁建设,1999,2,8-10
[128]宁晓骏,李小珍,强士中.高速铁路桥墩横向刚度的初步研究[J],西南交通大学学报,2000,35(1),11-13
[129]宁晓骏.高速铁路列车—桥梁—基础空间耦合振动研究[D],成都：西南交通大学土木工程学院,1998
[130]宁晓骏,叶燎原.高速铁路中桥梁跨径布置与共振关系的探讨[J],振动与冲击,2000,19(3)
[131]李永乐,强士中,廖海黎.风速场模型对风—车—桥系统耦合振动特性影响研究[J].空气动力学学报.2006,24(1)：131-136
[132]李永乐.风—车—桥系统非线性空间耦合振动研究[D].西南交通大学土木工程学院,2003
[133]晋智斌.车—线—桥耦合系统及车—桥随机振动[D].成都：西南交通大学土木工程学院,2007
[134]林玉森.地震作用下高速铁路桥上列车走行性研究[D].成都：西南交通大学土木工程学院,2007
[135]黄林.列车风与自然风联合作用下的车—桥耦合振动分析[D].成都：西南交通大学土木工程学院,2007
[136]蔡成标.高速铁路列车—线路—桥梁耦合振动理论及应用研究[D].成都：西南交通大学牵引动力重点实验室,2004
[137]王福天.车辆系统动力学[M].北京：中国铁道出版社,1994
[138]V K Garg.铁道车辆系统动力学[M].沈利人译.成都：西南交通大学出版社,1998
[139]张定贤.机车车辆轨道系统动力学[M].北京：中国铁道出版社,1996
[140]张军,姜克斌,胡业平.车桥耦合动力学系统模态综合分析[J].解放军理工大学学报,2003,4(1)：67-70
[141]王元丰,许士杰.桥梁在车辆作用下空间动力响应的研究[J].中国公路学报,2000,13(4)：37-41
[142]王潮海,王宗林.车桥耦合振动分析的模态综合方法[J].公路交通科技,2006,23(12)：76-80,90
[143]李小珍,张黎明,张洁.公路桥梁与车辆耦合振动研究现状与发展趋势[J].工程力学,2008,25(3)：230-240
[144]Roberson R E, Schwertassek R. Dynamics of multibody systems [M]. Berlin:Spring
Verlag,1988
[145]Huston R L. Multibody dynamics — modeling and analysis methods [J]. J of Appl.mech,1991,44(3):109-117
[146]Schichlen W. Recent development in multibody systems dynamics [J]. Journal of Mechanical Science and Techonology,2005,19(1):227-236
[147]Haug E J. Computer aided kinematics and dynamics of mechanical systems. Auyn and Bacon, Necdham Heights, Mass achusetts 02194,1989
[148]刘延柱,洪嘉振,杨海兴.多刚体系统动力学[M].北京：高等教育出版社,1989.
[149]休斯敦R L.多体系统动力学(上册)[M].刘又午译.天津：天津大学出版社,1987
[150]休斯敦R L.多体系统动力学(下册)[M].刘又午译.天津：天津大学出版社,1991
[151]J维滕伯格.多刚体系统动力学[M].谢传锋译.北京：北京航空学院出版社,1986
[152]袁士杰,吕哲勤.多刚体系统动力学[M].北京：北京理工大学出版社,1992
[153]洪嘉振.计算多体系统动力学[M].北京：高等教育出版社,1999
[154]Bianch G, Schiehlen W. Dynamics of multibody system [M].Berlin: Spring-Verlag,1986
[155]Agrawal O P, Shabana A A. Application of deformable body mean axes to flexible multibody system dynamics [J]. Computer Methods in Applied Mechanics and Engineering,1986,56:217-245
[156]Cavin R K, Dusto A R. Hamilton's Principle:finite-element methods and flexible body dynamics [J]. AIAA Journal,1977,15(2):1684-1690
[157]Change C W, Shanana A A. Hybrid control of flexible multibody systems [J]. Computers and Structures,1987,25(6):831-844
[158]黄文虎,邵成勋.多柔体系统动力学[M].北京：科学出版社,1996
[159]陆佑方.柔性多体系统动力学[M].北京：高等教育出版社,1999
[160]贺启庸,倪纯双,王卫东.多体系统动力学与车辆动力学[J].铁道车辆,1995,33(1)：38-42
[161]倪纯双,贺启庸,洪嘉振.铁路车辆多体动力学综述[J].中国铁道科学,17(4)：1-11
[162]Jaschinski A. Contributions to railway vehicle analysis and design. Scientific Report DLR,1992, (12):33-47
[163]陈泽深,王成国.铁道车辆动力学与控制[M].北京：中国铁道出版社,2004
[164]Schiehlen,W.Multi body Systems Handbook.Springer:Berlin,1990
[165]Kortum,W.Sharp,R.S.Multibody Computer Codes in Vehicle System Dynamics [J], volume 22 of Supplement to Vehicle System Dynamics,1993
[166]Dietz, S, Netter, H.Fatigue Life Predictions by coupling finite element and multibody systems calculation. In Proceedings of DETC'97 ASME Design Engineering Technical Conferences, Sacramento, USA,1997
[167]Veitl, A.and Kortum, W. Pantograph/Catenary Dynamics and Control. In The Dynamics of Vehicles on Roads and Tracks,15th IAVSD-Symposium, Budapest, Hungary,1997.
[168]缪炳荣,方向华,傅秀通.SIMPACK动力学分析基础教程[M].成都：西南交通大学出版社,2008
[169]陈潇凯,林逸,施国标,等.多体系统动力学软件在汽车工程中应用的新进展[J].计算机仿真,22(6)：201-204
[170]缪炳荣.应用SIMPACK对复杂机车多体系统建模与分析方法的研究.机械科学与技术[J],2006,25(7)：813-816
[171]GB 5599-85.铁道车辆动力学性能评定和试验鉴定规范[S],1985
[172]TB／T 2360-93.铁道机车动力学性能试验鉴定方法及评定标准[S],1993
[173]95J01-L,高速试验列车动力车强度及动力学性能规范[S],1995
[174]95J01-M,高速试验列车动力客车强度及动力学规范[S],1995
[175]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
[176]铁道部科学研究院译.脱轨研究专集.铁路行车安全译文集,1998
[177]詹斐生.平稳性指标的历史回顾(上)[J].铁道机车车辆.1994,(4)：43-52
[178]詹斐生.平稳性指标的历史回顾(中)[J].铁道机车车辆.1995,(1)：39-51
[179]詹斐生.平稳性指标的历史回顾(下)[J].铁道机车车辆.1995,(2)：19-21,62
[180]王勖成,邵敏.有限单元法基本原理和数值方法[M].北京：清华大学出版社,19978
[181]朱伯芳.有限单元法原理及应用[M].北京：中国水利水电出版社,1998
[182]丁浩江,何福保.弹性及塑性力学中的有限单元法[M].北京：机械工业出版社,1989
[183]吴鸿庆,任侠.结构有限元分析[M].北京：中国铁道出版社,2000
[184]殷学纲,陈淮,蹇开林.结构振动分析的了结构方法[M].北京：中国铁道出版社,1991
[185]楼梦麟.结构动力力分析的子结构方法[M].上海：同济大学出版社,1997
[186]王文亮,杜作润.结构振动与动态子结构方法[M].上海：复旦大学出版社,1985
[187]GUYAN R J. Reduction of stiffness and mass matrices [J].American Institute of Aeronautics and Astronautics Journal,1965,13(2):1133-1145
[188]铁道部第三勘察设计院主编.铁路桥涵设计基本规范(TB10002.1-2005)[S].北京：中国铁道出版社,2005
[189]铁道部第三勘察设计院主编.新建时速300-350km／h客运专线铁路设计暂行规定(上册)[S].北京：中国铁道出版社,2007
[190]铁运函[2004]120号.铁路桥梁检定规范[S].北京：中国铁道出版社,2004
[191]德国联邦铁路城际特别快车ICE技术任务书.铁道部科技司,西南交通大学,1993
[192]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.长沙铁道学院雪白.1985,(2)：1-36
[193]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
[194]钱雪军.轨道不平顺的时域模拟法[J].铁道学报.2000,22(4)：94-98
[195]陈果,翟婉明.铁路轨道不平顺随机过程的数值模拟[J].西南交通大学学报,1999,34(2)：138-142
[196]曾宇清,王卫东,贺启庸.车辆激励谱的时频转换复现技术[J].中国铁道科学,1996,17(4)：26-32
[197]王元丰,王颖,王东军.铁路轨道不平顺模拟的一种新方法[J].铁道学报,1997,19(6)：110-115
[198]Gunter Schupp, Christoph Weidemann. Modelling the contact between wheel and rail whthin multibody system simulation [J]. Vehicle System Dynamics,2004,41(5):349-364
[199]马卫华.轮对纵向振动及其相关动力学影响研究[D].成都：西南交通大学牵引动力重点实验室,2007
[200]Arnold M. Netter H. Wear profiles and the dynamical simulation of wheel/rail systems. Progress in Industrial Mathematics at ECMI'96:77-84
[201]Netter H, Schupp G. New aspects of contact modeling and validation within multibody system simulation of railway vehicles, the Dynamics of Vehicles on Roads and Tracks,15thIAVSD-Symposium,1997:246-249
[202]Hiroaki Ishida, Kenji Ueki. A new continuous measuring method of wheel/rail
forces.QR of RTRI.1994(2)
[203]Schupp G. Different contact models for wheel-rail systems:a comparison. Interal Report IB515-96-22,DLR German Aerospace Center, Institute of Aeroelasticity, Vehicle System Dynamics Group, Germany
[204]SIMREF:8.5 Wheel Rail Pre-processors\SIMREF:8.5.1 Introduction\SIMREF:8.5.4 The General Contact Pre-processor.2003
[205]Oskar Wallrapp. Reviw of past developments in multibody system d-ynamics-from FADYNA to SIMPACK [J]. Vehicle System Dynamics,2004,41(5):339-348
[206]J.P.Pascal, G.Sauvage.New method for reducing the Multicontact wheel/rail problem to one eauivalent contact patch [J]. Vehicle System Dynamics,1994(3):473-488
[207]Schupp, G., Jaschinski, A. Virtual Prototyping:the future way of designing railway vehicles. Journal of Vehicle Design. Simulation and Prototyping in Vehicle DeSsign and Development:1999,22(1/2):93-115
[208]Kalker J J. A fast algorithm for the simplified theory of rolling contact [J]. Vehicle System Dynamics,1982,11:1-13
[209]Kalker J J. A simplified theory for Non-Hertzian contact [M]. In:Proc 8th IAVSD-Symp, Cambridge, USA, Swets & Zeitlinger,1983
[210]Kalker J J. Simplified theory of rolling contact, Delft Progress Report, Delft University Press, Netherlands,1972,1-10
[211]金学松.轮轨蠕滑理论及其试验研究[M].成都：西南交通大学出版社,2006
[212]Shabana AA.Dynamics of multibody systems [M]. Cambridge,Cambridge University Press,1998
[213]Dietz s, Hippmann G, Schupp G. Interaction of vehicles and flexible tracks by co-simulation of multibody vehicle systems and finite element track models [J]. Vehicle System Dynamics Supplement,2003:37 (sup.):372-384.
[214]Wallrapp O. Flexible bodies in multibody system codes [J]. Vehicle System Dynamics,1998,(30):237-256
[215]Arnold M. Simulation algorithms in vehicle system dynamics. Luther-university Halle, Department of Mathematics and Computer Science. Technical Report(27),2004
[216]陈宪麦,杨凤春,吴旺青,等.秦沈客运专线轨道谱评判方法的研究[J].铁道学报,2006,28(4)：84-88