Train–bridge interaction – a review and discussion of key model parameters
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[1] Raid Karoumi,et al. Applicability of probabilistic methods for assessing a network of bridges for future high-speed traffic , 2012 .
[2] Kai Liu,et al. The effect of dynamic train–bridge interaction on the bridge response during a train passage , 2009 .
[3] G. De Roeck,et al. Dynamic analysis of a coupled high-speed train and bridge system subjected to collision load , 2012 .
[4] Dingqing Li,et al. Transition of Railroad Bridge Approaches , 2005 .
[5] Yeong-Bin Yang,et al. An element for analysing vehicle–bridge systems considering vehicle's pitching effect , 1999 .
[6] J. W. Lee,et al. Vibration reduction for a high-speed railway bridge in South Korea , 2012 .
[7] Jerome P. Lynch,et al. Experimental analysis of vehicle–bridge interaction using a wireless monitoring system and a two-stage system identification technique , 2012 .
[8] Yeong-Bin Yang,et al. Vehicle-Bridge Interaction Element for Dynamic Analysis , 1997 .
[9] Benno Hoffmeister,et al. On the prediction of the interaction effect caused by continuous ballast on filler beam railway bridges by experimentally supported numerical studies , 2010 .
[10] J. M. Biggs,et al. The Vibration of Simple Span Highway Bridges , 1957 .
[11] Yeong-Bin Yang,et al. Vehicle-bridge interaction dynamics: with applications to high-speed railways , 2004 .
[12] Mario Plos,et al. Development of a Guideline for Load and Resistance Assessment of Existing European Railway Bridges , 2006 .
[13] Kuang-Han Chu,et al. Impact in Truss Bridge Due to Freight Trains , 1985 .
[14] L Fryba,et al. VIBRATION OF SOLIDS AND STRUCTURES UNDER MOVING LOADS (3RD EDITION) , 1999 .
[15] Takahiro Suzuki,et al. Evaluation of Countermeasures against Differential Settlement at Track Transitions , 2007 .
[16] William Powrie,et al. An Assessment of Transition Zone Performance , 2011 .
[17] Enrique Alarcón Álvarez,et al. Influence of the Second Bending Mode on the Response of High-Speed Bridges at Resonance , 2005 .
[18] A. N. Lowan. LIV. On transverse oscillations of beams under the action of moving variable loads , 1935 .
[19] Takashi Matsumoto,et al. Numerical analysis on seismic response of Shinkansen bridge-train interaction system under moderate earthquakes , 2011 .
[20] João M. Rocha,et al. Train-bridge interaction effects on the dynamic response of a small span high-speed railway bridge , 2012 .
[21] Francis Franklin,et al. A structural articulation method for assessing railway bridges subject to dynamic impact loading from track irregularities , 2010 .
[22] Chul-YoungKim,et al. Effect of vehicle weight on natural frequencies of bridges measured from traffic-induced vibration , 2003 .
[23] Franklin Moon,et al. Structural identification of constructed systems , 2013 .
[24] Zhang Nan,et al. Analysis of Resonance Mechanism and Conditions of Train-Bridge System , 2006 .
[25] Wanming Zhai,et al. TWO SIMPLE FAST INTEGRATION METHODS FOR LARGE‐SCALE DYNAMIC PROBLEMS IN ENGINEERING , 1996 .
[26] Yeong-Bin Yang,et al. Impact response of high speed rail bridges and riding comfort of rail cars , 1999 .
[27] Nathan M. Newmark,et al. A Method of Computation for Structural Dynamics , 1959 .
[28] E. Moliner,et al. Free vibrations of simply-supported beam bridges under moving loads: Maximum resonance, cancellation and resonant vertical acceleration , 2013 .
[29] H. H. Jeffcott. VI.On the vibration of beams under the action of moving loads , 1929 .
[30] Ladislav Frýba,et al. Dynamics of Railway Bridges , 1996 .
[31] Ian Bucknall,et al. Permissible deck accelerations for rail bridge dynamic assessments , 2003 .
[32] Johan Oscarsson. Dynamic Train-Track Interaction: Linear and Non-Linear Track Models with Property Scatter , 2001 .
[33] Mubiao Su,et al. THE RESONANT VIBRATION FOR A SIMPLY SUPPORTED GIRDER BRIDGE UNDER HIGH-SPEED TRAINS , 1999 .
[34] Yong Lu,et al. Critical Speed and Resonance Criteria of Railway Bridge Response to Moving Trains , 2013 .
[35] Lawrence A. Bergman,et al. Revisiting the moving force problem , 2003 .
[36] José María Goicolea Ruigómez,et al. Research related to vibrations from high speed railway traffic , 2008 .
[37] M. Olsson. Finite element, modal co-ordinate analysis of structures subjected to moving loads , 1985 .
[38] Bing-Houng Lin,et al. Closure of "Vehicle-Bridge Interaction Analysis by Dynamic Condensation Method" , 1997 .
[39] G. De Roeck,et al. Integral model for train-track-bridge interaction on the Sesia viaduct: Dynamic simulation and critical assessment , 2012 .
[40] J. F. Fleming,et al. Dynamic Response of Highway Bridges , 1961 .
[41] Franklin Farell. Roadmap to a Single European Transport Area: Towards a competitive and resource efficient transport system , 2014 .
[42] Frederic Ward Williams,et al. Non-stationary random vibration analysis of three-dimensional train–bridge systems , 2010 .
[43] Oldrich Polach,et al. Modelling of suspension components in a rail vehicle dynamics context , 2011 .
[44] Yeong-Bin Yang,et al. EXTRACTING BRIDGE FREQUENCIES FROM THE DYNAMIC RESPONSE OF A PASSING VEHICLE , 2002 .
[45] Wanming Zhai,et al. Fundamentals of vehicle–track coupled dynamics , 2009 .
[46] Y. K. Cheung,et al. Impact study of cable-stayed railway bridges with random rail irregularities , 2002 .
[47] K. C. Chang,et al. Using two connected vehicles to measure the frequencies of bridges with rough surface: a theoretical study , 2012 .
[48] Jens C. O. Nielsen,et al. Dynamic train-turnout interaction in an extended frequency range using a detailed model of track dynamics , 2009 .
[49] João M. Rocha,et al. Safety assessment of a short span railway bridge for high-speed traffic using simulation techniques , 2012 .
[50] Y. K. Cheung,et al. IMPACT STUDY OF CABLE-STAYED BRIDGE UNDER RAILWAY TRAFFIC USING VARIOUS MODELS , 2001 .
[51] Shen-Haw Ju,et al. Resonance characteristics of high-speed trains passing simply supported bridges , 2003 .
[52] Michael Hartnett,et al. Effects of speed, load and damping on the dynamic response of railway bridges and vehicles , 2008 .
[53] Nevin Lianwen Zhang,et al. Dynamic analysis of a train-bridge system under wind action , 2008 .
[54] Eugene J. O'Brien,et al. Identification of damping in a bridge using a moving instrumented vehicle , 2012 .
[55] Akio Matsuura. A STUDY OF DYNAMIC BEHAVIOR OF BRIDGE GIRDER FOR HIGH SPEED RAILWAY , 1976 .
[56] Thomas J. R. Hughes,et al. Improved numerical dissipation for time integration algorithms in structural dynamics , 1977 .
[57] Zhang Zhe,et al. Non-stationary random vibration analysis for train–bridge systems subjected to horizontal earthquakes , 2010 .
[58] Shen-Haw Ju. Improvement of bridge structures to increase the safety of moving trains during earthquakes , 2013 .
[59] Yozo Fujino,et al. Vibration of reinforced concrete viaducts under high-speed train passage: measurement and prediction including train–viaduct interaction , 2010 .
[60] Z. Q. Chen,et al. EMD-based random decrement technique for modal parameter identification of an existing railway bridge , 2011 .
[61] R. Moreno Delgado,et al. Modelling of railway bridge-vehicle interaction on high speed tracks , 1997 .
[62] G. De Roeck,et al. Dynamic analysis of train–bridge system and its application in steel girder reinforcement , 2001 .
[63] R. H. Fries,et al. A State-Space Approach to the Synthesis of Random Vertical and Crosslevel Rail Irregularities , 1990 .
[64] Pedro Museros Romero,et al. Interacción vehículo-estructura y efectos de resonancia en puentes isostáticos de ferrocarril para líneas de alta velocidad , 2011 .
[65] John M. Biggs,et al. Introduction to Structural Dynamics , 1964 .
[66] Qi Li,et al. Stress and acceleration analysis of coupled vehicle and long-span bridge systems using the mode superposition method , 2010 .
[67] Yeong-Bin Yang,et al. Steady-state response and riding comfort of trains moving over a series of simply supported bridges , 2003 .
[68] Hoon Sohn,et al. Vibration reduction of high-speed railway bridges by adding size-adjusted vehicles , 2010 .
[69] M. D. Martínez-Rodrigo,et al. Dynamic performance of existing high-speed railway bridges under resonant conditions retrofitted with fluid viscous dampers , 2010 .
[70] Mahir Ülker-Kaustell,et al. Effect of Axle Load Spreading and Support Stiffness on the Dynamic Response of Short Span Railway Bridges , 2014 .
[71] Nan Zhang,et al. Vehicle bridge interaction analysis under high-speed trains , 2008 .
[72] Andreas Andersson,et al. A methodology for the preliminary assessment of existing railway bridges for high-speed traffic , 2014 .
[73] Andrzej S. Nowak,et al. SIMULATION OF DYNAMIC LOAD FOR BRIDGES , 1991 .
[74] Shahbaz Rashid. Parametric study of bridge response to high speed trains, ballasted track on concrete bridges , 2011 .
[75] Yao Shan,et al. Influence of different transition zones on the dynamic response of track–subgrade systems , 2013 .
[76] Marian Klasztorny,et al. Dynamic response of single‐span beam bridges to a series of moving loads , 1990 .
[77] P. Museros,et al. An investigation on the importance of train-bridge interaction at resonance , 2002 .
[78] Huajiang Ouyang,et al. Moving-load dynamic problems: A tutorial (with a brief overview) , 2011 .
[79] Carlos Rebelo,et al. Dynamic behaviour of twin single-span ballasted railway viaducts — Field measurements and modal identification , 2008 .
[80] Chang-Koon Choi,et al. A new three-dimensional finite element analysis model of high-speed train–bridge interactions , 2003 .
[81] Joseph G. Pigeon,et al. Statistics for Experimenters: Design, Innovation and Discovery , 2006, Technometrics.
[82] Mahir Ülker-Kaustell,et al. Essential modelling details in dynamic FE-analyses of railway bridges , 2013 .
[83] N. K. Cooperrider,et al. Guideway-Suspension Tradeoffs in Rail Vehicle Systems , 1981 .
[84] M. Kurihara,et al. STABILITY OF A SIMPLY-SUPPORTED BEAM SUBJECTED TO RANDOMLY SPACED MOVING LOADS , 1978 .
[85] Raid Karoumi,et al. Closed-form solution for the mode superposition analysis of the vibration in multi-span beam bridges caused by concentrated moving loads , 2013 .
[86] D. Galton,et al. Report of the commissioners appointed to inquire into the application of iron to railway structures , 1850 .
[87] David Cebon,et al. Dynamic Response of Highway Bridges to Heavy Vehicle Loads: Theory and Experimental Validation , 1994 .
[88] Ebrahim Esmailzadeh,et al. Importance of flexural mode shapes in dynamic analysis of high-speed trains traveling on bridges , 2014 .
[89] R. Calçada,et al. Dynamic Effects Induced by High Speed Traffic on Rail Bridges , 2012 .
[90] K. Weiss. Vibration Problems in Engineering , 1965, Nature.
[91] É. Savin. DYNAMIC AMPLIFICATION FACTOR AND RESPONSE SPECTRUM FOR THE EVALUATION OF VIBRATIONS OF BEAMS UNDER SUCCESSIVE MOVING LOADS , 2001 .
[92] Renda Zhao,et al. Reliability Evaluation of Vehicle-Bridge Dynamic Interaction , 2007 .
[93] Mahir Ülker-Kaustell,et al. Influence of rate-independent hysteresis on the dynamic response of a railway bridge , 2013 .
[94] Yeong-Bin Yang,et al. Vibration of simple beams due to trains moving at high speeds , 1997 .
[95] Nan Zhang,et al. Dynamic analysis of railway bridge under high-speed trains , 2005 .
[96] Guido De Roeck,et al. Dynamic analysis of high speed railway bridge under articulated trains , 2003 .
[97] Yeong-Bin Yang,et al. DYNAMIC STABILITY OF TRAINS MOVING OVER BRIDGES SHAKEN BY EARTHQUAKES , 2002 .
[98] Raid Karoumi,et al. Response of cable-stayed and suspension bridges to moving vehicles : Analysis methods and practical modeling techniques , 1998 .
[99] Shen-Haw Ju. Vibration Analysis of 3D Timoshenko Beams Subjected to Moving Vehicles , 2011 .
[100] M. Luu,et al. An optimization method of multi-resonant response of high-speed train bridges using TMDs , 2012 .
[101] Mahir Ülker-Kaustell,et al. A simple finite element to consider the non-linear influence of the ballast on vibrations of railway bridges , 2011 .
[102] X Lei,et al. Influence of Track Stiffness Distribution on Vehicle and Track Interactions in Track Transition , 2010 .
[103] Ping Lou,et al. Finite element analysis for train–track–bridge interaction system , 2007 .
[104] Wanming Zhai,et al. High-speed train–track–bridge dynamic interactions – Part II: experimental validation and engineering application , 2013 .
[105] Pedro Galvín,et al. Soil-structure interaction in resonant railway bridges , 2013 .
[106] Khadri Youcef,et al. Dynamic analysis of train-bridge system and riding comfort of trains with rail irregularities , 2013 .
[107] Jaap Wardenier,et al. Numerical simulation of train–bridge interactive dynamics , 2001 .
[108] M. Kurihara,et al. Vibration of an Elastic Beam Subjected to Discrete Moving Loads , 1978 .
[109] Rui Calçada,et al. Design and construction of backfills for railway track transition zones , 2015 .
[110] V. Markine,et al. Combatting RCF on switch points by tuning elastic track properties , 2011 .
[111] J. N. Varandas,et al. Dynamic behaviour of railway tracks on transitions zones , 2011 .
[112] T. Tsao,et al. On asymptotics of the solution of the moving oscillator problem , 2003 .
[113] Nan Zhang,et al. Dynamic analysis of coupled vehicle-bridge system based on inter-system iteration method , 2013 .
[114] Atef F. Saleeb,et al. Automated Finite Element Analysis of Complex Dynamics of Primary System Traversed by Oscillatory Subsystem , 2011 .
[115] J. Hardin,et al. On the response of beams to an arbitrary number of concentrated moving masses , 1969 .
[116] Yeong-Bin Yang,et al. A versatile element for analyzing vehicle–bridge interaction response , 2001 .
[117] Raid Karoumi,et al. Strengthening of a steel railway bridge and its impact on the dynamic response to passing trains , 2011 .
[118] M. Zacher,et al. Dynamic behaviour of ballast on railway bridges , 2009 .
[119] Pennung Warnitchai,et al. Dynamic analysis of three-dimensional bridge–high-speed train interactions using a wheel–rail contact model , 2009 .
[120] Rui Calçada,et al. A direct method for analyzing the nonlinear vehicle–structure interaction , 2012 .
[121] Massood Mofid,et al. Closure of "Numerical Solution for Response of Beams With Moving Mass" , 1991 .
[122] S. Timoshenko. CV. On the forced vibrations of bridges , 1922 .
[123] Julio Blanco-Lorenzo,et al. Dynamic comparison of different types of slab track and ballasted track using a flexible track model , 2011 .
[124] E. C. Ting,et al. A general algorithm for moving mass problems , 1974 .
[125] Q. Li,et al. Computer-aided Nonlinear Vehicle-bridge Interaction Analysis , 2010 .
[126] Sang Hyo Kim,et al. Structural analysis of 3D high-speed train–bridge interactions for simple train load models , 2010 .
[127] F. Au,et al. Vibration of multi-span non-uniform bridges under moving vehicles and trains by using modified beam vibration functions , 1999 .
[128] Mahir Ülker-Kaustell,et al. Simplified analysis of the dynamic soil–structure interaction of a portal frame railway bridge , 2010 .
[129] Christian Cremona,et al. Guideline for Load and Resistance Assessment of Existing European Railway Bridges: Advices on the use of advanced methods , 2007 .
[130] Chi-Chang Lin,et al. Train-Induced Vibration Control of High-Speed Railway Bridges Equipped with Multiple Tuned Mass Dampers , 2005 .
[131] Fabrizio Vestroni,et al. Closed-form solutions for the structural response to train loads , 2007 .
[132] Mahir Ülker-Kaustell,et al. Influence of non-linear stiffness and damping on the train-bridge resonance of a simply supported railway bridge , 2012 .
[133] Jungyoul Choi,et al. Influence of Track Support Stiffness of Railway Tracks on Track Impact Factor , 2014 .
[134] Mahir Ülker-Kaustell,et al. Seasonal effects on the stiffness properties of a ballasted railway bridge , 2013 .
[135] Jian Dai,et al. Response analysis of high-speed rail system accounting for abrupt change of foundation stiffness , 2013 .
[136] Raid Karoumi,et al. Statistical screening of individual and joint effect of several modelling factors on the dynamic finite element response of a railway bridge , 2012 .
[137] Ping Lou,et al. A vehicle-track-bridge interaction element considering vehicle's pitching effect , 2005 .
[138] J. M. Goicolea,et al. The Dynamics of High-Speed Railway Bridges: A Review of Design Issues and New Research for Lateral Dynamics , 2012 .
[139] Yeong-Bin Yang,et al. Mechanism of resonance and cancellation for train-induced vibrations on bridges with elastic bearings , 2004 .
[140] Peter Keith Woodward,et al. Frequency characteristics of railway bridge response to moving trains with consideration of train mass , 2012 .
[141] M. Olsson,et al. ON THE FUNDAMENTAL MOVING LOAD PROBLEM , 1991 .
[142] A. V. Pestereva,et al. Revisiting the moving force problem , 2003 .
[143] Kai Liu,et al. Experimental and numerical analysis of a composite bridge for high-speed trains , 2009 .
[144] M. D. Martínez-Rodrigo,et al. Transverse vibrations in existing railway bridges under resonant conditions: Single-track versus double-track configurations , 2010 .
[145] Luís Simões da Silva,et al. Influence of ballast models in the dynamic response of railway viaducts , 2010 .
[146] Mark A. Bradford,et al. Lateral dynamic interaction analysis of a train–girder–pier system , 2008 .
[147] Daniel Cantero,et al. TRACING THE EVOLUTION OF BRIDGE NATURAL FREQUENCIES AS A VEHICLE TRAVERSES THE BRIDGE , 2013 .
[148] C. Williams,et al. Review of full-scale dynamic testing of bridge structures , 1995 .
[149] V K Garg,et al. RAILWAY-BRIDGE IMPACT: SIMPLIFIED TRAIN AND BRIDGE MODEL , 1979 .
[150] R. Calçada,et al. University of Huddersfield Repository A direct method for analyzing the vertical vehicle-structure interaction , 2011 .
[151] T. E. Blejwas,et al. Dynamic interaction of moving vehicles and structures , 1979 .
[152] Yeong-Bin Yang,et al. Vehicle–bridge interaction dynamics and potential applications , 2005 .
[153] Karl Popp,et al. Vehicle-Track Dynamics in the Mid-Frequency Range , 1999 .
[154] Ping Lou,et al. Formulation of equations of motion for a simply supported bridge under a moving railway freight vehicle , 2007 .
[155] Khaled Galal,et al. A modified numerical VBI element for vehicles with constant velocity including road irregularities , 2011 .
[156] Y. K. Cheung,et al. Vibration analysis of bridges under moving vehicles and trains: an overview , 2001 .
[157] H. G. Natke. Updating computational models in the frequency domain based on measured data: a survey , 1988 .
[158] G. A. Fonder,et al. AN ITERATIVE SOLUTION METHOD FOR DYNAMIC RESPONSE OF BRIDGE–VEHICLES SYSTEMS , 1996 .
[159] Tseng Huang,et al. Analysis of Dynamic Response of Highway Bridges , 1970 .
[160] Davide Martino,et al. Höghastighetsprojekt - Bro : Inventering av järnvägsbroar för ökad hastighet på befintliga banor , 2011 .
[161] Francis Franklin,et al. Application of the structural articulation method to dynamic impact loading of railway bridges – a case study , 2010 .
[162] Giuseppe Muscolino,et al. A substructure approach for the dynamic analysis of train-track-bridge system , 2005 .
[163] M. Steenbergen. Physics of railroad degradation: The role of a varying dynamic stiffness and transition radiation processes , 2013 .
[164] Weiwei Guo,et al. Vehicle-bridge interaction analysis of heavy load railway , 2010 .
[165] Mahir Ülker-Kaustell,et al. Application of the continuous wavelet transform on the free vibrations of a steel–concrete composite railway bridge , 2011 .
[166] A. Emin Aktan,et al. Structural identification of constructed systems : approaches, methods, and technologies for effective practice of St-Id , 2013 .
[167] L Frýba,et al. A rough assessment of railway bridges for high speed trains , 2001 .
[168] Andreas Andersson,et al. Field testing and simulation of dynamic properties of a tied arch railway bridge , 2006 .
[169] Evert Andersson,et al. Green Train: concept and technology overview , 2014 .
[170] Khaled Galal,et al. A numerical element for vehicle–bridge interaction analysis of vehicles experiencing sudden deceleration , 2013 .
[171] G. De Roeck,et al. Fatigue assessment of a composite railway bridge for high speed trains. Part II: Conditions for which a dynamic analysis is needed , 2013 .
[172] Ping Lou,et al. Rail–bridge coupling element of unequal lengths for analysing train–track–bridge interaction systems , 2012 .
[173] Ping Lou,et al. Vertical dynamic responses of a simply supported bridge subjected to a moving train with two‐wheelset vehicles using modal analysis method , 2005 .
[174] Dingqing Li,et al. Railway Bridge Approaches under Heavy Axle Load Traffic: Problems, Causes, and Remedies , 2010 .
[175] Enrique Alarcón,et al. Advances in the analysis of short span railway bridges for high-speed lines , 2002 .
[176] Chi-Chang Lin,et al. Vibration suppression for high-speed railway bridges using tuned mass dampers , 2003 .
[177] Raid Karoumi,et al. Statistical screening of modelling alternatives in train–bridge interaction systems , 2014 .
[178] Ton-Lo Wang,et al. Ramp/Bridge Interface in Railway Prestressed Concrete Bridge , 1990 .
[179] Francis T.K. Au,et al. Vibration of railway bridges under a moving train by using bridge-track-vehicle element , 2001 .
[180] José M. Goicolea,et al. Analysis of lateral dynamics of railway vehicles on viaducts with coupled models , 2012 .
[181] Yeong-Bin Yang,et al. Three-Dimensional Analysis of Train-Rail-Bridge Interaction Problems , 2001 .
[182] George Gabriel Stokes,et al. Mathematical and Physical Papers vol.2: Discussion of a Differential Equation relating to the Breaking of Railway Bridges , 2009 .
[183] Xiaozhen Li,et al. High-speed train–track–bridge dynamic interactions – Part I: theoretical model and numerical simulation , 2013 .
[184] Tommy H.T. Chan,et al. Dynamic interaction of long suspension bridges with running trains , 2000 .
[185] Joel P. Conte,et al. Random Vibration Analysis of Dynamic Vehicle-Bridge Interaction Due to Road Unevenness , 2012 .
[186] Dan M. Frangopol,et al. Bridge Maintenance, Safety, Management, Resilience and Sustainability : Proceedings of the Sixth International IABMAS Conference, Stresa, Lake Maggiore, Italy, 8-12 July 2012 , 2012 .
[187] Tore Dahlberg. VEHICLE-BRIDGE INTERACTION , 1984 .
[188] Nan Zhang,et al. Consideration of nonlinear wheel–rail contact forces for dynamic vehicle–bridge interaction in high-speed railways , 2013 .
[189] Michael Hartnett,et al. Dynamic response of bridges to moving trains: A study on effects of random track irregularities and bridge skewness , 2009 .
[190] Andreas Lundqvist,et al. Railway track stiffness variation - consequences and countermeasures , 2010 .
[191] David Kennedy,et al. An algorithm to study non-stationary random vibrations of vehicle-bridge systems , 2009 .
[192] Raimundo Delgado. Dynamics of High-Speed Railway Bridges , 2009 .
[193] Andreas Andersson,et al. Semi-active damping systems for railway bridges , 2012 .
[194] Toshio Yoshimura,et al. A finite element method prediction of the vibration of a bridge subjected to a moving vehicle load , 1984 .
[195] Ton-Lo Wang,et al. Impact in Railway Prestressed Concrete Bridges , 1986 .
[196] Jianhui Lin,et al. Modelling and experiment of railway ballast vibrations , 2004 .