高架桥系统环境振动评价与减振分析
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摘要
随着国民经济的飞速发展，铁路、地铁和城市轨道交通系统也在全国进入建设高潮，与此同时列车运行产生的振动对环境的影响也越来越大，已到了必须重视的地步。但是，目前国内对沿线环境振动的评价、预测方法仍以现场实测和经验公式为主，误差较大，缺乏系统的研究和定量的分析方法，因此不能在建设前有效地指导设计与施工。为了正确评价轨道沿线环境的振动，有必要深入研究列车荷载作用下地基土的动力响应。
本文以列车荷载作用下的轨道、高架桥和地基为研究对象，分析了轨道交通荷载作用下地基土的响应，得到振动在地基土中的传播特性。对振动较大的轨道沿线采用了两种不同的减振措施，并对减振效果进行分析比较。
本文主要研究了以下几个方面的问题：
1、综述了已有的轨道模型以及各种模型适用的研究范围。在此基础上选取Euler梁模型以及Timoshenko梁模型进行分析。从计算结果看，在研究高速移动荷载作用下轨道系统的动力响应这种特定情况下，本文提出的模型与计算方法是合理的。
2、考虑到地基振动对建筑物产生的直接影响，本文对移动荷载引起的地基响应作了详细的研究。由于地质条件的复杂性，将地基看成是层状的，并且每层都是均匀弹性的，通过解三维弹性体的波动方程(Navier方程)得到地基在移动荷载作用下的波数-频域的解，再通过快速Fourier逆变换(FFT)求得空间-时间域的解。基于分层法的解析算法，得到了在不同点以及在同一点但不同地质条件下的时程分析曲线、加速度变化曲线和传递函数反应谱，结果表明，地基土在x、y、z三个方向的响应都是随时间变化的，并且伴随有明显的波动现象产生；对于相同地质条件的不同观察点，距离荷载作用线越远的地方振幅越小，即振动具有明显的衰减性。
3、关于轻轨列车荷载作用下的地基土的振动分析，本文考虑到轻轨的结构形式一般为高架桥，与普通铁路和地铁不同，因此，本文对这一问题进行了专门研究。高架桥系统对周围环境的影响是通过高架桥的柱子而产生的，其特征是荷载位置不变，但大小随时间变化。对这一问题的计算，只需能够求得列车
武汉理工大学博士学位论文
荷载作用下桥墩的时程曲线，则现有的有限元软件ANSYS己能较好地求解。
因此在计算轻轨列车荷载作用下地基土的响应时，本文运用ANSYS软件进行
模拟，在振动较大的地方采用设置阻波区(WIB，wave Impeding Block)和隔
振沟两种减振措施，同时对减振效果进行分析比较，得到了较为理想的结果。
通过本文的研究成果表明，轻轨的振动分析可以服务于轻轨工程的可行性研究、
设计与施工，为政府决策部门提供依据，对轨道系统运行时产生的环境振动较
敏感的建筑物采取合理的隔振与减振措施进行指导，并对减振效果进行预评价。
最后，在全面总结论文工作的基础上，提出本课题尚待深入研究的若干问题。
With the rapid development of the national economy, the construction of railway, subway and urban rail-viaduct system have been reached a new climax in present period. At the same time, the influence of the vibration caused by the moving vehicles on the near environment has been increased and paid close attention to. Up to now, the methods used for the evaluation and forecasting of the environmental vibration along the whole railway have still been the field survey and some empirical formulas which will result in certain errors, the systematic study and the quantificational analysis on this problem have not been performed in our country. So it is impossible to instruct the design and construction of rail transportation effectively. In order to evaluate the vibration along railway correctly, it is necessary to lucubrate the dynamic response of ground bearing the moving loads of vehicle.
In this paper, regarding the rail, viaduct and ground as study objects, the response of ground under the moving loads on rails are analyzed in detail and the propagation characteristic of vibration in the ground are concluded. In addition, two kinds of vibration-decreasing measures are applied on the rail lines with big vibration, and the effects of decreasing vibration are also analyzed comparatively.
The main study includes the following aspects.
1. Introducing some rail models in existence and their respective research direction in point. Considering our purpose is studying the dynamic response of ground under the speedy moving loads, the Euler beam model and Tirnoshenko beam model are selected here to be rail models. In this particular condition that studying the dynamic response of rail system under the speedy moving loads, it has been already proved by the calculation results that the rail models and calculating methods applied in this problem are rational.
2. Taking account of the direct effect of ground vibration on buildings, the ground responses caused by the moving loads is studied in detail. Because of the complication of ground condition, the ground is regarded as continuous layers and each layer of soil is defined as a uniform and elastic object. By solving the wave equation (Navier Equation) of three-dimensional elastic object, the results of ground
under moving loads in wave number ?frequency field are obtained, then through the rapid Fourier reverse transform, the results in space-time field are obtained. Based on the resolving algorithm of continuous-layer method, the time order analyzing curves, acceleration curves and the response spectra of transfer function at the different points of the ground and at the same point on the different ground conditions are gained. It demonstrates that the responses of ground in x, y and z axial directions all change by time, and the obvious wave propagation appears in ground. For different observing points on the same ground condition, at more distant points from the load line, the less swings are found, that is to say, vibration possesses the obvious characteristic of attenuation.
3. The ground vibration caused by load of vehicle in light railway system is analyzed as well. Different from the common railway and subway, the viaduct is the main structural member in light railway system, which is studied in specialty in this paper. The effect of viaduct system on near environment is generated through the column of viaduct, so the characteristics of loads are that the action points do not change but the values change with time. For the modeling of this kind of problem, because the time-order curves of viaduct column bearing the loads of vehicles are expect to get, the present finite element analysis software ?ANSYS can be used to solve it quite well. So ANSYS is applied here to calculate the response of ground under moving loads in light railway system. At the locations with the big vibration, two measures for vibration-diminishing ?Wave Impeding Block and Open Drain for Isolating Vibration are constructed, and the effective of vibration-diminishing is analyzed
本文以列车荷载作用下的轨道、高架桥和地基为研究对象，分析了轨道交通荷载作用下地基土的响应，得到振动在地基土中的传播特性。对振动较大的轨道沿线采用了两种不同的减振措施，并对减振效果进行分析比较。
本文主要研究了以下几个方面的问题：
1、综述了已有的轨道模型以及各种模型适用的研究范围。在此基础上选取Euler梁模型以及Timoshenko梁模型进行分析。从计算结果看，在研究高速移动荷载作用下轨道系统的动力响应这种特定情况下，本文提出的模型与计算方法是合理的。
2、考虑到地基振动对建筑物产生的直接影响，本文对移动荷载引起的地基响应作了详细的研究。由于地质条件的复杂性，将地基看成是层状的，并且每层都是均匀弹性的，通过解三维弹性体的波动方程(Navier方程)得到地基在移动荷载作用下的波数-频域的解，再通过快速Fourier逆变换(FFT)求得空间-时间域的解。基于分层法的解析算法，得到了在不同点以及在同一点但不同地质条件下的时程分析曲线、加速度变化曲线和传递函数反应谱，结果表明，地基土在x、y、z三个方向的响应都是随时间变化的，并且伴随有明显的波动现象产生；对于相同地质条件的不同观察点，距离荷载作用线越远的地方振幅越小，即振动具有明显的衰减性。
3、关于轻轨列车荷载作用下的地基土的振动分析，本文考虑到轻轨的结构形式一般为高架桥，与普通铁路和地铁不同，因此，本文对这一问题进行了专门研究。高架桥系统对周围环境的影响是通过高架桥的柱子而产生的，其特征是荷载位置不变，但大小随时间变化。对这一问题的计算，只需能够求得列车
武汉理工大学博士学位论文
荷载作用下桥墩的时程曲线，则现有的有限元软件ANSYS己能较好地求解。
因此在计算轻轨列车荷载作用下地基土的响应时，本文运用ANSYS软件进行
模拟，在振动较大的地方采用设置阻波区(WIB，wave Impeding Block)和隔
振沟两种减振措施，同时对减振效果进行分析比较，得到了较为理想的结果。
通过本文的研究成果表明，轻轨的振动分析可以服务于轻轨工程的可行性研究、
设计与施工，为政府决策部门提供依据，对轨道系统运行时产生的环境振动较
敏感的建筑物采取合理的隔振与减振措施进行指导，并对减振效果进行预评价。
最后，在全面总结论文工作的基础上，提出本课题尚待深入研究的若干问题。
With the rapid development of the national economy, the construction of railway, subway and urban rail-viaduct system have been reached a new climax in present period. At the same time, the influence of the vibration caused by the moving vehicles on the near environment has been increased and paid close attention to. Up to now, the methods used for the evaluation and forecasting of the environmental vibration along the whole railway have still been the field survey and some empirical formulas which will result in certain errors, the systematic study and the quantificational analysis on this problem have not been performed in our country. So it is impossible to instruct the design and construction of rail transportation effectively. In order to evaluate the vibration along railway correctly, it is necessary to lucubrate the dynamic response of ground bearing the moving loads of vehicle.
In this paper, regarding the rail, viaduct and ground as study objects, the response of ground under the moving loads on rails are analyzed in detail and the propagation characteristic of vibration in the ground are concluded. In addition, two kinds of vibration-decreasing measures are applied on the rail lines with big vibration, and the effects of decreasing vibration are also analyzed comparatively.
The main study includes the following aspects.
1. Introducing some rail models in existence and their respective research direction in point. Considering our purpose is studying the dynamic response of ground under the speedy moving loads, the Euler beam model and Tirnoshenko beam model are selected here to be rail models. In this particular condition that studying the dynamic response of rail system under the speedy moving loads, it has been already proved by the calculation results that the rail models and calculating methods applied in this problem are rational.
2. Taking account of the direct effect of ground vibration on buildings, the ground responses caused by the moving loads is studied in detail. Because of the complication of ground condition, the ground is regarded as continuous layers and each layer of soil is defined as a uniform and elastic object. By solving the wave equation (Navier Equation) of three-dimensional elastic object, the results of ground
under moving loads in wave number ?frequency field are obtained, then through the rapid Fourier reverse transform, the results in space-time field are obtained. Based on the resolving algorithm of continuous-layer method, the time order analyzing curves, acceleration curves and the response spectra of transfer function at the different points of the ground and at the same point on the different ground conditions are gained. It demonstrates that the responses of ground in x, y and z axial directions all change by time, and the obvious wave propagation appears in ground. For different observing points on the same ground condition, at more distant points from the load line, the less swings are found, that is to say, vibration possesses the obvious characteristic of attenuation.
3. The ground vibration caused by load of vehicle in light railway system is analyzed as well. Different from the common railway and subway, the viaduct is the main structural member in light railway system, which is studied in specialty in this paper. The effect of viaduct system on near environment is generated through the column of viaduct, so the characteristics of loads are that the action points do not change but the values change with time. For the modeling of this kind of problem, because the time-order curves of viaduct column bearing the loads of vehicles are expect to get, the present finite element analysis software ?ANSYS can be used to solve it quite well. So ANSYS is applied here to calculate the response of ground under moving loads in light railway system. At the locations with the big vibration, two measures for vibration-diminishing ?Wave Impeding Block and Open Drain for Isolating Vibration are constructed, and the effective of vibration-diminishing is analyzed
引文
[1] Dieterman H. A. and Metrikine A. V. Steady-state displacements of a beam on an elastic half-space due to a uniformly moving constant load. European Journal of Mechanics, A/Solids, 1997, 16(2) : 295-306
[2] Dieterman H. A. and Metrikine A. V. The equivalent stiffness of a half-space interacting with a beam. Critical velocities of a moving load along the beam. European Journal of Mechanics, A/Solids, 1996, 15(1) : 67-90
[3] Kenney J. T., Pasadena J.R. Calif. Steady-State Vibrations of Beam on Elastic Foundation for Moving Load. Transactions of the ASME. Ser. E, Journal of applied mechanics, 1954, 12:359-364
[4] F. C. P. de Barros, J. E. Luco. Moving Green's Functions for a Layered Visco-Elastic Half-space. Univ. of Calf. at San Diego,La Jolla,1992
[5] Hong Hao, Thien Cheong Ang. Analytical Modeling of Traffic-Induced Ground Vibrations. J. Eng. Mech., ASCE. 1998, 124(8) : 921-928
[6] 王逢朝，夏禾，张鸿儒．地铁列车振动对邻近建筑物的影响．北方交通大学学报，1999， 23(5) ：45-48
[7] 田春芝．地铁振动对周围建筑物影响的研究概况．铁道劳动安全与环保，2000，27(1)
[8] Watts G. R. Case Studies of the Effects of Traffic Induced Vibrations on Heritage Buildings: [Technical Report]. Berkshire, Transport and road research laboratory, 1987
[9] Wilson G. P. Control of Ground Borne Noise and Vibration. J. of Sound and Vibration , 1983 ,87(2) : 339-350
[10] Kurzweil G. Ground Borne Noise and Vibration from Underground Rail Systerns. J. of Sound and Vibration , 1979, 66 (3 ): 363-370
[11] BataMilosla V. Effects on Buildings of Vibrations Caused by Traffic. J. of Buildings and Science, 1977, (6) : 221-246
[12] Hayakawa K. Reduction Effects of Ballast Matsand EPS Blocks on Ground Vibration Caused by Trainandits Evaluation. Proc. Inter Noise' 92, 1992． 233-240
[13] Degrande G. A special Finite Element Method for Wave Propagation in Dry and Saturated Poroelastic Media: [Ph.D. thesis]. Belgium: Leuven K.U., 1992
[14] Richart F.E., Woods R.D. Vibration of Soils and foundations. NewJersey: Prentice Hall, INC, Englewood Cliffs, 1987
[15] 青木一郎．铁道交通振动周边居民对影响．东京：东京都环境科学研究所年报，1994，(18)：24～30
[16] 夏禾，冯爱军，张弥．高架轻轨系统列车振动效应研究．地铁与轻轨，1992，(2)：27～33
[17] 夏禾，冯爱军，张弥．轻轨列车和高架桥梁系统的动力响应分析．北方交通大学学报，1994，18(1)：1～8
[18] 夏禾，陈英俊．车—桥—墩体系动力相互作用分析．土木工程学报，1992，25(2)：1～10
[19] Xia He. A Study of Vibration Effects of Underground Trains Upon Surrounding Environments. Advances in Structural Engineering. Beijing: Railway Publishing House,1995. 116～122
[20] 王毅．浅淡地铁振动与噪声．地铁与轻轨，1993，(2)：19～20
[21] 王毅．北京地下铁道振动对环境影响的调查与研究．地铁与轻轨，1993，(2)：21～25
[22] 潘昌实，谢正光．地铁区间隧道列车振动测试与分析．土木工程学报，1990，23(2)：21～28
[23] 潘昌实，刘维宁．隧道列车振动试验与动态分析．兰州铁道学院学报，1985，4(2)：1～21
[24] 孙家麒，振动公害浅谈．环境保护，1979，(5)：25～27
[25] 孙家麒．振动公害的治理．环境保护，1979，(6)：34～37
[26] 盛碧华．城市轨道交通高架桥上道床结构型式探讨，地铁与轻轨，1993，(2)：26～31
[27] 傅光新编泽．地铁轨道基础参数对隧道衬砌振动的影响．地铁与轻轨，1993，(2)：40～43
[28] 周才宝．地下铁道整体轨下基础．地铁与轻轨，1994，(2)：29～31
[29] 铁道部科学研究院铁道建筑研究所．广深线准高速铁路行车噪声、振动环境影响和治理措施的研究与试验：[研究报告]．北京：铁道部科学研究院，1995
[30] 铁道部科学研究院环境评价与工程中心．北京西至黄村联络线环境影响报告书：[研究报告]，北京：铁道部科学研究院，1995
[31] 茅玉泉．交通运输车辆引起的地面振动特性利衰减．建筑结构学报，1987，(1)：12～19
[32] 杨光辉．列车运行引起的地面振动衰减规律研究：[博士学位论文]．北京：北方交通大学，1998
[33] 潘昌实，谢正光．北京地铁列车振动对环境影响的探讨．隧道及地下工程学会第七届年会论文集，北京：1992．424～431
[34] 姚正伦．重庆地下轻轨列车运行地面振动效应的预测与评价．隧道及地下工程学会第七届年会论文集．北京：1992．372～379
[35] 马筠．我国铁路环境振动现状及传播规律．中国环境科学，1987，7(5)：4～7
[36] 陈实．高速铁路列车对周围环境的振动影响研究：[博士学位论文]．北京：北方交通
大学，1997
[37] 于大明．轻轨列车作用下高架桥梁系统振动及其对周边环境的影响．桥梁及结构工程学会第12届年会论文集．北京：1996．632～640
[38] 杨永斌．高速列车所引致之土壤振动分析：[研究报告]．台湾：台湾大学，1995
[39] Jiangun J. Study on Dynamic Soil Structure Interaction of Extended High Pier Bridges: [Ph.D. thesis]. Okayama Japan: Okayama Univ., 1993
[40] 雷晓燕，杜厚智．轨道结构空间自由振动分析．铁道工程学院，1998，3(1)
[41] 翟婉明．铁路轮轨冲击振动模拟与试验．计算力学学报，1999，16(1)，2
[42] 李德武．列车振动荷载的数定分析，甘肃科学学报，1998，10(2)
[43] Volgerg G. Propagation of Ground Vibrations near Railway Tracks. J. of Sound and Vibration, 1983, 87(2): 371～376
[44] Dawn T. M. Ground Vibration from Passing Trains. J. of Sound and Vibration, 1979, 66(3): 355～362
[45] Dinning M. G. Ground Vibrations From Heavy Freight Trains. Sound and Vibration, 1983, 87(2): 351～356
[46] Rucker W. Dynamic Behavior of Rigid Foundations of Arbitrary Shape on a Half-Space. Earthquake Engineering and Structural Dynamics, 1982, 66(5): 674～690
[47] Gakenhemier D.C., Miklowitz J. Transient Excitation of an Elastic Half-Space by a Point Load Travelling on the Surface. Journal of Applied Mechanics, ASME, Series E, 1969,36(3): 505～515
[48] Takemiya H. and Kellezi L. Paraseismic behavior of Wave Impending Block (WIB) measured for ground vibration reduction, 1998
[49] Hunt H., Forrest J. Floating slab track for vibration reduction: Why simple models don't work. Seventh International Congress on Sound Vibration, 2000,7
[50] Amir M. K., Christian M. Ground vibration from high-speed railway lines. International Conference on Soil-Structure Interaction in Urban Civil Engineering. 8/9., October, 1998
[51] Blanc R.H. Transient wave propagation methods for determining the viscoelastic properties of solids. Journal of Applied Mechanics, September 1993, 60:763
[52] 李德武，高峰，隧道基底结构列车振动现场测试与分析．甘肃科学学报，1999，11(1)
[53] 潘昌实．黄土隧道列车动荷载响应有限元初步数定分析研究．土木工程学报，1984，17(4)
[54] 谭复兴．轨道结构与车辆垂向耦合振动模型及轨道试验研究．铁道学报，1997．19卷增刊：115～121
[55] 刘吉源，戈新生，陈立群．轴向力作用下Timoshenko梁的横向振动．北京机械工业学院学报，2000．15(3)：56～59
[56] 潘昌实，Pande G．N．黄土隧道列车动荷载响应有限元初步数定分析研究．上木工程学报，1984，17(4)
[57] 马筠．我国铁路环境振动现状及传播规律．中国环境科学，1987，7(5)：4～7
[58] 谢伟平，徐劲，左鹏飞，移动荷载作用下轨道系的反应谱分析．工程力学增刊，2001
[59] 彭波，谢伟平，蒋沧如．移动荷载作用下地基-轨道系统的土动力分析．华中科技大学学报(城市科学版)，2003，20(2)
[60] 李德建，曾庆元，黄玉盈．准高速列车-轨道时变系统空间振动随机分析．华中理工大学学报，1998，26(4)
[61] 李成辉，万复光．轨道结构随机振动．铁道学报，1998，20(3)
[62] 谢伟平，左鹏飞，徐劲．基于分层法的土动力分析．爆破，2002，19(1)
[63] 谢伟平，胡建武，徐劲．高速移动荷载作用下的轨道—地基系统的动力响应．岩石力学与工程学报，2002，21(7)
[64] 谢伟平，于艳丽，姚春桥．高速移动荷载作用下轨道系统的振动研究．地震[程与工程振动，2002，22(2)：85～90
[65] 邱舍朝，冯爱君．浅谈轨道交通高架桥的变形控制．铁道标准没计，1998，10
[66] 张安静．轻轨高架桥整体道床无缝线路轨道设计的探讨，铁道标准设计，1995，10
[67] 张弥，夏禾，冯爰君．轻轨列车和高架桥梁系统的动力响应分析．北方交通大学学报，1994，18(1)
[68] 谢伟平，徐劲．移动荷载作用下轻轨系统的动力响应分析．武汉理工大学学报，2002
[69] 王洪生，高秀华．Timoshenko梁的对偶积分变换解法．山东建筑工程学院学报，1996．1(4)：5～12
[70] 辜小安，田春芝．地铁振动对建筑物内二次结构噪声影响预测．铁道劳动安全卫生与环保，2000，27(1)：62～64
[71] 李保德，谢伟平，李荣．交通荷载所引起的地基振动的研究．武汉理工大学学报，2001．23(3)：77～79
[72] Schwedler J. W. Discussion on iron permanent way. In: Wood, Charles: Iron permanent way Minutes of Proc. of the Instn. of Civ. Engnrs, London, 1882, 67: 95-118
[73] Winkler E. Die Lehre yon der Elastizi(?)t und Festigkeit. Prag: Verlag H. Dominikus, 1867
[74] Timoshenko S. Strengths of rail. Transactions of the Institute of Ways of Communication. St. Petersburg, Russia, 1915
[75] Timoshenko S. Method of analysis of statical and dynamical stresses in rail. Proc. Second
Int. Congress for Appl. Mech. Zurich, 1926． 407-418
[76] Timoshenko S. and Langer F. B. Stresses in railroad track. J. Appl. Mech. 1932, 54: 277-302
[77] Prud' homme. M. A. and Janin G. The stability of track laid with long welded rails. Part Ⅰ and Ⅱ Bulletin of the International Railway Congress Association, June and July/August, 1969, 88 : 460-480
[78] Prud' homme. M. A. and La Voie. Revue Generale des Chemins de Fer. 1970, 91: 56-72
[79] Kerr A. D. The stress and stability analysis of railroad tracks. J. Appl. Mech. 1974, 41: 841-848
[80] Kerr A. D. On the stress analysis of rails and ties. American Railway Engineering Association, 1976, Bulletin 659: 19-43
[81] Dorr J. Der unedliche. Federnd gebettete Balken unter dem Einflu β einer gleichiormig bewegten Last. Ing. Arch. 1943,14: 167-192
[82] Dorr J. Das Schwingungsverhalten eines federnd gebetteten, unendlich langen Balkens. Ing. Arch. 1948, 16:287-298
[83] Alexander V. P., Lawrence A. B. Response of Elastic Continum Carrying Linear Oscillator. Journal of Engineering Mechanics, 1997, 8: 878-884
[84] Takemiya H., Yuasa S. Line Side Ground Vibration Induced By High-Speed Train And Mitigation Measure. W1B. Eurodyn' 99, 1999． 7
[85] Grassie S. L. ect. The dynamic response of railway track to high frequency vertical excitation. Journal of Engineering Mechanics, Science, 1982, 24(2)
[86] Johnson E. A., Ramallo J. C., Spencer B. F. etc. Intelligent base isolation systems. Proc. of 2nd World Conf. On Struct. Control, Vol. 1, Tokyo, 1998
[87] Lefeuve G, Mesgouez D and Le Houedec. Ground vibration due to a high speed moving harmonic load. Eurodyn'99, Prague, 1999． 7
[88] Lang J. Result of rneasurements on the control of structure-borne noise from subways. Seventh International Congress on Acoustics. Budapest, 1971, 421-424
[89] Urgar E. Vibrations produced in buildings by passage of subway trains. Parameter estimation for preliminary design. Inter-noise. 1975,491-498
[90] Kurzweil G. Prediction of noise and vibration in buildings near the New York City Subway. Inter-noise. 1982,213-216．
[91] 杨桂通，张善元．弹性动力学．中国铁道出版社，1988
[92] 佐藤泰夫．弹性波动论．岩波书屋，1977
[93] Nelson J. Prediction and control of ground-borne noise and vibration from rail transittrains. UMTAMA-06-0049-83-4 Report
[94] Melke J. Noise and Vibration from underground railway lines: proposals for a prediction procedure. J.S.& Vib. 1988, 120(2): 391～406
[95] Voberg K.G. Propagation of ground Vibrations near railway tracks. J.S & vib. 1983, 87(2):371～376
[96] Wei-Ping Xie, Yan-Li Yu and Hong-Gang Sun. The vibration response of Euler beam by moving load. The Seventh International Symposium on Structural Engineering for Young Experts (ISSEYE-7). Tianjin: Science Press, 2002. 177～181
[97] Wei-Ping Xie, Hong-Gang Sun and Yan-Li Yu. The Dynamic Response of Kailway System for the Moving Load. The 5th International Conference on Vibration Engineering (ICVE' 2002). Nanjing, 2002
[98] Jenkins H. H., Stephenson J. E., Clayton G. A. etc. The effect of Track and vehicle parameters on wheel/rail vertical dynamic forces. The Railway Engineering Journal, 1974, 3,2～16
[99] Krylov V. Vibrational impact of high-speed trains. Ⅰ. Effect of track dynamics. Acoustical Society of America, 1996, 100(5):3121～3129
[100] 谢伟平，于艳丽，李红兵．高速移动荷载下轨道系统振动模拟的数值算法．武汉理工大学学报，2001，23(12)：57～60
[101] 谢伟干，于艳丽，姚春桥．轨道系统动力模型及环境振动评价．岩土力学，2002增刊
[102] 谢伟平，孙洪刚，于艳丽．轻轨系统引起的地基振动响应分析．华中科技大学学报，2002，19(4)：23～26
[103] 谢伟平，徐劲，左鹏飞．移动荷载作用下轨道系的反应谱分析．第十届全国结构工程学术会议论文集，2001．8
[104] 谢伟平，左鹏飞，孙洪刚．基于Timoshenko梁的轨道系统动力响应模拟．武汉理工大学学报，2002，24(4)
[105] 彭波，谢伟平，蒋沧如．移动荷载作作下轨道-高架桥系统的动力分析，武汉理工大学学报，2003，25(5)
[106] 谢伟平，孙洪刚，姚春桥．基于有限元法的高速列车引起土的动力分析．岩土力学，2002增刊
[107] 潘昌实，李德武，谢正光．北京地铁列车振动对环境影响的探讨．振动与冲击，1995，14(4)：29～34
[108] 赵荣欣，谢永利，章勇等．泡沫塑料—水泥土充填沟隔振性状研究．西安公路交通大
学学报，1999，18(1)：38-42
[109] 王其昌．高速铁路土木工程．成都：西南交通大学出版社，1999年
[110] 王朝逢，夏禾，吴萱．列车振动对环境及建筑物的影响分析．北方交通大学学报，1999，23(4)
[111] 夏禾，吴萱，于大明．城市轨道交通系统引起的环境振动问题．北方交通大学学报，1999，23(4)
[112] 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
[113] 雷晓燕，陈水生．高速铁路轨道结构空间动力分析．铁道学报，2000，22(5)：76～80
[114] 胡用生，陆正刚，张辉．高速列车与轨道垂向动力耦合仿真模型的开发．铁道学报，1997，19卷增刊：15～21
[115] 张玉娥，白宝鸿．高速铁路隧道列车振动响应数值分析方法．振动与冲击，2001，20(3)：91～102
[116] 翟婉明，韩卫军，蔡成标等．高速铁路板式轨道动力特性研究．铁道学报，1999，21(6)：65～69
[117] 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
[118] 李文会，卢文良，许克宾．列车移动荷载作用下曲线上桥梁的振动响应分析．石家庄铁道学院学报，2001，14(2)：43～46
[119] 蔡成标，翟婉明．机车—轨道—桥梁垂向耦合动力学分析．西南交通大学学报，1997，32(6)：628～63
[120] 刘学毅，王平．高速轨道频域响应特性分析．西南交通大学学报，2000．35(4)：35～39
[121] 合田和哉．移动加振移动载荷次元成层地盘内波动传播关研究応用．岡山大学博士论文，1997．3．
[122] 竹宫宏和，里中修平，谢伟平．高速移动加振源轨道—底盘系动的応答周边地盘振动传播[J]．土木学会论文集，2001，682(7)：299～309
[123] 竹宫宏和，合田和哉，小森大资．高速列车运行时对沿线地基振动的计算机模拟和预测土木学会论文集，1998，NO．488／I-23，11～13
[124] 古田胜．时间域积分方程式法轨道系振动解析关基础的研究．岡山大学博士论文，1998．9
[125] Kazuhisa ABE,Masaru FURUTA. Time domain integral representation for track vibration analysis. [日本]土木学会构造工学论文集，1997.43A (3)
[126] 阿部和久，古田勝．时间域积分表现式轨道振动解析法．[日本]土木学会构造
工学论文集，1997．43A：9～16
[127] 吉冈修，芦谷公稔．新干线轨道振动的产生和传播模型．[日本]物理探查，1995，48(5)：299～315
[128] 塩津吉彦．高速列车运行引起的地基振动特性研究．1998
[129] 白旗弘实，三木千寿，馆石和雄．高速移动荷载作用下桥梁振动响应的解析算法．土木学会论文集，1996，NO．549／I-37，107～114
[130] 行武宗轨．人工振动源对象传播线路振动轻减工法关研究．1998
[131] 川谷充郎，山田靖则，金哲佑，川木秀昭．道路桥交通振动三次元解析床版応答评价。桥梁振动’97论文集
[132] 冈林隆敏．桥梁振动制振·制御，桥梁振动’97论文集
[133] 川谷充郎，小林羲和，今枝拓也。道路桥交通振动使用性确率论的评价．桥梁振动’97论文集
[2] Dieterman H. A. and Metrikine A. V. The equivalent stiffness of a half-space interacting with a beam. Critical velocities of a moving load along the beam. European Journal of Mechanics, A/Solids, 1996, 15(1) : 67-90
[3] Kenney J. T., Pasadena J.R. Calif. Steady-State Vibrations of Beam on Elastic Foundation for Moving Load. Transactions of the ASME. Ser. E, Journal of applied mechanics, 1954, 12:359-364
[4] F. C. P. de Barros, J. E. Luco. Moving Green's Functions for a Layered Visco-Elastic Half-space. Univ. of Calf. at San Diego,La Jolla,1992
[5] Hong Hao, Thien Cheong Ang. Analytical Modeling of Traffic-Induced Ground Vibrations. J. Eng. Mech., ASCE. 1998, 124(8) : 921-928
[6] 王逢朝，夏禾，张鸿儒．地铁列车振动对邻近建筑物的影响．北方交通大学学报，1999， 23(5) ：45-48
[7] 田春芝．地铁振动对周围建筑物影响的研究概况．铁道劳动安全与环保，2000，27(1)
[8] Watts G. R. Case Studies of the Effects of Traffic Induced Vibrations on Heritage Buildings: [Technical Report]. Berkshire, Transport and road research laboratory, 1987
[9] Wilson G. P. Control of Ground Borne Noise and Vibration. J. of Sound and Vibration , 1983 ,87(2) : 339-350
[10] Kurzweil G. Ground Borne Noise and Vibration from Underground Rail Systerns. J. of Sound and Vibration , 1979, 66 (3 ): 363-370
[11] BataMilosla V. Effects on Buildings of Vibrations Caused by Traffic. J. of Buildings and Science, 1977, (6) : 221-246
[12] Hayakawa K. Reduction Effects of Ballast Matsand EPS Blocks on Ground Vibration Caused by Trainandits Evaluation. Proc. Inter Noise' 92, 1992． 233-240
[13] Degrande G. A special Finite Element Method for Wave Propagation in Dry and Saturated Poroelastic Media: [Ph.D. thesis]. Belgium: Leuven K.U., 1992
[14] Richart F.E., Woods R.D. Vibration of Soils and foundations. NewJersey: Prentice Hall, INC, Englewood Cliffs, 1987
[15] 青木一郎．铁道交通振动周边居民对影响．东京：东京都环境科学研究所年报，1994，(18)：24～30
[16] 夏禾，冯爱军，张弥．高架轻轨系统列车振动效应研究．地铁与轻轨，1992，(2)：27～33
[17] 夏禾，冯爱军，张弥．轻轨列车和高架桥梁系统的动力响应分析．北方交通大学学报，1994，18(1)：1～8
[18] 夏禾，陈英俊．车—桥—墩体系动力相互作用分析．土木工程学报，1992，25(2)：1～10
[19] Xia He. A Study of Vibration Effects of Underground Trains Upon Surrounding Environments. Advances in Structural Engineering. Beijing: Railway Publishing House,1995. 116～122
[20] 王毅．浅淡地铁振动与噪声．地铁与轻轨，1993，(2)：19～20
[21] 王毅．北京地下铁道振动对环境影响的调查与研究．地铁与轻轨，1993，(2)：21～25
[22] 潘昌实，谢正光．地铁区间隧道列车振动测试与分析．土木工程学报，1990，23(2)：21～28
[23] 潘昌实，刘维宁．隧道列车振动试验与动态分析．兰州铁道学院学报，1985，4(2)：1～21
[24] 孙家麒，振动公害浅谈．环境保护，1979，(5)：25～27
[25] 孙家麒．振动公害的治理．环境保护，1979，(6)：34～37
[26] 盛碧华．城市轨道交通高架桥上道床结构型式探讨，地铁与轻轨，1993，(2)：26～31
[27] 傅光新编泽．地铁轨道基础参数对隧道衬砌振动的影响．地铁与轻轨，1993，(2)：40～43
[28] 周才宝．地下铁道整体轨下基础．地铁与轻轨，1994，(2)：29～31
[29] 铁道部科学研究院铁道建筑研究所．广深线准高速铁路行车噪声、振动环境影响和治理措施的研究与试验：[研究报告]．北京：铁道部科学研究院，1995
[30] 铁道部科学研究院环境评价与工程中心．北京西至黄村联络线环境影响报告书：[研究报告]，北京：铁道部科学研究院，1995
[31] 茅玉泉．交通运输车辆引起的地面振动特性利衰减．建筑结构学报，1987，(1)：12～19
[32] 杨光辉．列车运行引起的地面振动衰减规律研究：[博士学位论文]．北京：北方交通大学，1998
[33] 潘昌实，谢正光．北京地铁列车振动对环境影响的探讨．隧道及地下工程学会第七届年会论文集，北京：1992．424～431
[34] 姚正伦．重庆地下轻轨列车运行地面振动效应的预测与评价．隧道及地下工程学会第七届年会论文集．北京：1992．372～379
[35] 马筠．我国铁路环境振动现状及传播规律．中国环境科学，1987，7(5)：4～7
[36] 陈实．高速铁路列车对周围环境的振动影响研究：[博士学位论文]．北京：北方交通
大学，1997
[37] 于大明．轻轨列车作用下高架桥梁系统振动及其对周边环境的影响．桥梁及结构工程学会第12届年会论文集．北京：1996．632～640
[38] 杨永斌．高速列车所引致之土壤振动分析：[研究报告]．台湾：台湾大学，1995
[39] Jiangun J. Study on Dynamic Soil Structure Interaction of Extended High Pier Bridges: [Ph.D. thesis]. Okayama Japan: Okayama Univ., 1993
[40] 雷晓燕，杜厚智．轨道结构空间自由振动分析．铁道工程学院，1998，3(1)
[41] 翟婉明．铁路轮轨冲击振动模拟与试验．计算力学学报，1999，16(1)，2
[42] 李德武．列车振动荷载的数定分析，甘肃科学学报，1998，10(2)
[43] Volgerg G. Propagation of Ground Vibrations near Railway Tracks. J. of Sound and Vibration, 1983, 87(2): 371～376
[44] Dawn T. M. Ground Vibration from Passing Trains. J. of Sound and Vibration, 1979, 66(3): 355～362
[45] Dinning M. G. Ground Vibrations From Heavy Freight Trains. Sound and Vibration, 1983, 87(2): 351～356
[46] Rucker W. Dynamic Behavior of Rigid Foundations of Arbitrary Shape on a Half-Space. Earthquake Engineering and Structural Dynamics, 1982, 66(5): 674～690
[47] Gakenhemier D.C., Miklowitz J. Transient Excitation of an Elastic Half-Space by a Point Load Travelling on the Surface. Journal of Applied Mechanics, ASME, Series E, 1969,36(3): 505～515
[48] Takemiya H. and Kellezi L. Paraseismic behavior of Wave Impending Block (WIB) measured for ground vibration reduction, 1998
[49] Hunt H., Forrest J. Floating slab track for vibration reduction: Why simple models don't work. Seventh International Congress on Sound Vibration, 2000,7
[50] Amir M. K., Christian M. Ground vibration from high-speed railway lines. International Conference on Soil-Structure Interaction in Urban Civil Engineering. 8/9., October, 1998
[51] Blanc R.H. Transient wave propagation methods for determining the viscoelastic properties of solids. Journal of Applied Mechanics, September 1993, 60:763
[52] 李德武，高峰，隧道基底结构列车振动现场测试与分析．甘肃科学学报，1999，11(1)
[53] 潘昌实．黄土隧道列车动荷载响应有限元初步数定分析研究．土木工程学报，1984，17(4)
[54] 谭复兴．轨道结构与车辆垂向耦合振动模型及轨道试验研究．铁道学报，1997．19卷增刊：115～121
[55] 刘吉源，戈新生，陈立群．轴向力作用下Timoshenko梁的横向振动．北京机械工业学院学报，2000．15(3)：56～59
[56] 潘昌实，Pande G．N．黄土隧道列车动荷载响应有限元初步数定分析研究．上木工程学报，1984，17(4)
[57] 马筠．我国铁路环境振动现状及传播规律．中国环境科学，1987，7(5)：4～7
[58] 谢伟平，徐劲，左鹏飞，移动荷载作用下轨道系的反应谱分析．工程力学增刊，2001
[59] 彭波，谢伟平，蒋沧如．移动荷载作用下地基-轨道系统的土动力分析．华中科技大学学报(城市科学版)，2003，20(2)
[60] 李德建，曾庆元，黄玉盈．准高速列车-轨道时变系统空间振动随机分析．华中理工大学学报，1998，26(4)
[61] 李成辉，万复光．轨道结构随机振动．铁道学报，1998，20(3)
[62] 谢伟平，左鹏飞，徐劲．基于分层法的土动力分析．爆破，2002，19(1)
[63] 谢伟平，胡建武，徐劲．高速移动荷载作用下的轨道—地基系统的动力响应．岩石力学与工程学报，2002，21(7)
[64] 谢伟平，于艳丽，姚春桥．高速移动荷载作用下轨道系统的振动研究．地震[程与工程振动，2002，22(2)：85～90
[65] 邱舍朝，冯爱君．浅谈轨道交通高架桥的变形控制．铁道标准没计，1998，10
[66] 张安静．轻轨高架桥整体道床无缝线路轨道设计的探讨，铁道标准设计，1995，10
[67] 张弥，夏禾，冯爰君．轻轨列车和高架桥梁系统的动力响应分析．北方交通大学学报，1994，18(1)
[68] 谢伟平，徐劲．移动荷载作用下轻轨系统的动力响应分析．武汉理工大学学报，2002
[69] 王洪生，高秀华．Timoshenko梁的对偶积分变换解法．山东建筑工程学院学报，1996．1(4)：5～12
[70] 辜小安，田春芝．地铁振动对建筑物内二次结构噪声影响预测．铁道劳动安全卫生与环保，2000，27(1)：62～64
[71] 李保德，谢伟平，李荣．交通荷载所引起的地基振动的研究．武汉理工大学学报，2001．23(3)：77～79
[72] Schwedler J. W. Discussion on iron permanent way. In: Wood, Charles: Iron permanent way Minutes of Proc. of the Instn. of Civ. Engnrs, London, 1882, 67: 95-118
[73] Winkler E. Die Lehre yon der Elastizi(?)t und Festigkeit. Prag: Verlag H. Dominikus, 1867
[74] Timoshenko S. Strengths of rail. Transactions of the Institute of Ways of Communication. St. Petersburg, Russia, 1915
[75] Timoshenko S. Method of analysis of statical and dynamical stresses in rail. Proc. Second
Int. Congress for Appl. Mech. Zurich, 1926． 407-418
[76] Timoshenko S. and Langer F. B. Stresses in railroad track. J. Appl. Mech. 1932, 54: 277-302
[77] Prud' homme. M. A. and Janin G. The stability of track laid with long welded rails. Part Ⅰ and Ⅱ Bulletin of the International Railway Congress Association, June and July/August, 1969, 88 : 460-480
[78] Prud' homme. M. A. and La Voie. Revue Generale des Chemins de Fer. 1970, 91: 56-72
[79] Kerr A. D. The stress and stability analysis of railroad tracks. J. Appl. Mech. 1974, 41: 841-848
[80] Kerr A. D. On the stress analysis of rails and ties. American Railway Engineering Association, 1976, Bulletin 659: 19-43
[81] Dorr J. Der unedliche. Federnd gebettete Balken unter dem Einflu β einer gleichiormig bewegten Last. Ing. Arch. 1943,14: 167-192
[82] Dorr J. Das Schwingungsverhalten eines federnd gebetteten, unendlich langen Balkens. Ing. Arch. 1948, 16:287-298
[83] Alexander V. P., Lawrence A. B. Response of Elastic Continum Carrying Linear Oscillator. Journal of Engineering Mechanics, 1997, 8: 878-884
[84] Takemiya H., Yuasa S. Line Side Ground Vibration Induced By High-Speed Train And Mitigation Measure. W1B. Eurodyn' 99, 1999． 7
[85] Grassie S. L. ect. The dynamic response of railway track to high frequency vertical excitation. Journal of Engineering Mechanics, Science, 1982, 24(2)
[86] Johnson E. A., Ramallo J. C., Spencer B. F. etc. Intelligent base isolation systems. Proc. of 2nd World Conf. On Struct. Control, Vol. 1, Tokyo, 1998
[87] Lefeuve G, Mesgouez D and Le Houedec. Ground vibration due to a high speed moving harmonic load. Eurodyn'99, Prague, 1999． 7
[88] Lang J. Result of rneasurements on the control of structure-borne noise from subways. Seventh International Congress on Acoustics. Budapest, 1971, 421-424
[89] Urgar E. Vibrations produced in buildings by passage of subway trains. Parameter estimation for preliminary design. Inter-noise. 1975,491-498
[90] Kurzweil G. Prediction of noise and vibration in buildings near the New York City Subway. Inter-noise. 1982,213-216．
[91] 杨桂通，张善元．弹性动力学．中国铁道出版社，1988
[92] 佐藤泰夫．弹性波动论．岩波书屋，1977
[93] Nelson J. Prediction and control of ground-borne noise and vibration from rail transittrains. UMTAMA-06-0049-83-4 Report
[94] Melke J. Noise and Vibration from underground railway lines: proposals for a prediction procedure. J.S.& Vib. 1988, 120(2): 391～406
[95] Voberg K.G. Propagation of ground Vibrations near railway tracks. J.S & vib. 1983, 87(2):371～376
[96] Wei-Ping Xie, Yan-Li Yu and Hong-Gang Sun. The vibration response of Euler beam by moving load. The Seventh International Symposium on Structural Engineering for Young Experts (ISSEYE-7). Tianjin: Science Press, 2002. 177～181
[97] Wei-Ping Xie, Hong-Gang Sun and Yan-Li Yu. The Dynamic Response of Kailway System for the Moving Load. The 5th International Conference on Vibration Engineering (ICVE' 2002). Nanjing, 2002
[98] Jenkins H. H., Stephenson J. E., Clayton G. A. etc. The effect of Track and vehicle parameters on wheel/rail vertical dynamic forces. The Railway Engineering Journal, 1974, 3,2～16
[99] Krylov V. Vibrational impact of high-speed trains. Ⅰ. Effect of track dynamics. Acoustical Society of America, 1996, 100(5):3121～3129
[100] 谢伟平，于艳丽，李红兵．高速移动荷载下轨道系统振动模拟的数值算法．武汉理工大学学报，2001，23(12)：57～60
[101] 谢伟干，于艳丽，姚春桥．轨道系统动力模型及环境振动评价．岩土力学，2002增刊
[102] 谢伟平，孙洪刚，于艳丽．轻轨系统引起的地基振动响应分析．华中科技大学学报，2002，19(4)：23～26
[103] 谢伟平，徐劲，左鹏飞．移动荷载作用下轨道系的反应谱分析．第十届全国结构工程学术会议论文集，2001．8
[104] 谢伟平，左鹏飞，孙洪刚．基于Timoshenko梁的轨道系统动力响应模拟．武汉理工大学学报，2002，24(4)
[105] 彭波，谢伟平，蒋沧如．移动荷载作作下轨道-高架桥系统的动力分析，武汉理工大学学报，2003，25(5)
[106] 谢伟平，孙洪刚，姚春桥．基于有限元法的高速列车引起土的动力分析．岩土力学，2002增刊
[107] 潘昌实，李德武，谢正光．北京地铁列车振动对环境影响的探讨．振动与冲击，1995，14(4)：29～34
[108] 赵荣欣，谢永利，章勇等．泡沫塑料—水泥土充填沟隔振性状研究．西安公路交通大
学学报，1999，18(1)：38-42
[109] 王其昌．高速铁路土木工程．成都：西南交通大学出版社，1999年
[110] 王朝逢，夏禾，吴萱．列车振动对环境及建筑物的影响分析．北方交通大学学报，1999，23(4)
[111] 夏禾，吴萱，于大明．城市轨道交通系统引起的环境振动问题．北方交通大学学报，1999，23(4)
[112] 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
[113] 雷晓燕，陈水生．高速铁路轨道结构空间动力分析．铁道学报，2000，22(5)：76～80
[114] 胡用生，陆正刚，张辉．高速列车与轨道垂向动力耦合仿真模型的开发．铁道学报，1997，19卷增刊：15～21
[115] 张玉娥，白宝鸿．高速铁路隧道列车振动响应数值分析方法．振动与冲击，2001，20(3)：91～102
[116] 翟婉明，韩卫军，蔡成标等．高速铁路板式轨道动力特性研究．铁道学报，1999，21(6)：65～69
[117] 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
[118] 李文会，卢文良，许克宾．列车移动荷载作用下曲线上桥梁的振动响应分析．石家庄铁道学院学报，2001，14(2)：43～46
[119] 蔡成标，翟婉明．机车—轨道—桥梁垂向耦合动力学分析．西南交通大学学报，1997，32(6)：628～63
[120] 刘学毅，王平．高速轨道频域响应特性分析．西南交通大学学报，2000．35(4)：35～39
[121] 合田和哉．移动加振移动载荷次元成层地盘内波动传播关研究応用．岡山大学博士论文，1997．3．
[122] 竹宫宏和，里中修平，谢伟平．高速移动加振源轨道—底盘系动的応答周边地盘振动传播[J]．土木学会论文集，2001，682(7)：299～309
[123] 竹宫宏和，合田和哉，小森大资．高速列车运行时对沿线地基振动的计算机模拟和预测土木学会论文集，1998，NO．488／I-23，11～13
[124] 古田胜．时间域积分方程式法轨道系振动解析关基础的研究．岡山大学博士论文，1998．9
[125] Kazuhisa ABE,Masaru FURUTA. Time domain integral representation for track vibration analysis. [日本]土木学会构造工学论文集，1997.43A (3)
[126] 阿部和久，古田勝．时间域积分表现式轨道振动解析法．[日本]土木学会构造
工学论文集，1997．43A：9～16
[127] 吉冈修，芦谷公稔．新干线轨道振动的产生和传播模型．[日本]物理探查，1995，48(5)：299～315
[128] 塩津吉彦．高速列车运行引起的地基振动特性研究．1998
[129] 白旗弘实，三木千寿，馆石和雄．高速移动荷载作用下桥梁振动响应的解析算法．土木学会论文集，1996，NO．549／I-37，107～114
[130] 行武宗轨．人工振动源对象传播线路振动轻减工法关研究．1998
[131] 川谷充郎，山田靖则，金哲佑，川木秀昭．道路桥交通振动三次元解析床版応答评价。桥梁振动’97论文集
[132] 冈林隆敏．桥梁振动制振·制御，桥梁振动’97论文集
[133] 川谷充郎，小林羲和，今枝拓也。道路桥交通振动使用性确率论的评价．桥梁振动’97论文集