A time domain analysis of train induced vibrations

  • Romero, A. ;
  • Galvin, P. ;
  • Dominguez, J.
  • Received : 2011.12.07
  • Accepted : 2012.04.10
  • Published : 2012.06.25


This paper is intended to show the robustness and capabilities of a coupled boundary element-finite element technique for the analysis of vibrations generated by high-speed trains under different geometrical, mechanical and operation conditions. The approach has been developed by the authors and some results have already been presented. Nevertheless, a more comprehensive study is presented in this paper to show the relevance and robustness of the method which is able to predict vibrations due to train passage at the vehicle, the track, the free-field and any structure close to the track. Local soil discontinuities, underground constructions such as underpasses, and coupling with nearby structures that break the uniformity of the geometry along the track line can be represented by the model. Non-linear behaviour of the structures can be also considered. Results concerning the excitation mechanisms, track behaviour and sub-Rayleigh and super-Rayleigh train speed are summarized in this work.


FE/BE model;time domain;HST vibration


  1. Metrikine, A. and Popp, K. (1999), "Instability of vibrations of an oscillator moving along a beam on an elastic half-space", Eur. J. Mech. A-Solid., 18(2), 331-349.
  2. Metrikine, A. and Popp, K. (1999), "Vibration of a periodically supported beam on an elastic half-space", Eur. J. Mech. A-Solid., 18(4), 679-701.
  3. Metrikine, A., Verichev, S. and Blauwendraad, J. (2005), "Stability of a two-mass oscillator moving on a beam supported by a viscoelastic half-space", Int. J. Solids Struct., 42(3-4), 1187-1207.
  4. Pesterev, A., Bergman, L., Tan, C., Tsao, T.C. and Yang, B. (2003), "On asymptotics of the solution of the moving oscillator problem", J. Sound Vib., 260(3), 519-536.
  5. Esveld, C. (2001), Modern railway track, MRT Productions, Zaltbommel.
  6. Romero, A., Domínguez, J. and Galvín, P. (2012), Comportamiento dinámico de viaductos cortos considerando la interaccion vehículo-via-estructura-suelo, Revista Internacional de Metodos Numericos para Calculo y Diseno en Ingenieria, 28(1), 55-63.
  7. Olmos, B.A. and Roesset, J.M. (2010), "Effects of the nonlinear behavior of lead-rubber bearings on the seismic response of bridges", Earthq. Struct., 1(2), 215-230.
  8. Banister, D. and Hall, P. (1993), "The second railway age", Built Environ., 19(3-4), 157-162.
  9. Karabalis, D. and Beskos, D. (1985), "Dynamic response of 3-D flexible foundations by time domain BEM and FEM", Soil Dyn. Earthq. Eng., 4(2), 91-101.
  10. European Committee for Standardisation (CEN) (2002), Eurocode 1: Actions on structures. Part 2: traffic loads on bridges, Final Draft prEN 1991-2 (pre-European Standard).
  11. Lombaert, G. and Degrande, G. (2009), "Ground-borne vibration due to static and dynamic axle loads of intercity and highspeed trains", J. Sound Vib., 319(3-5), 1036-1066.
  12. Lombaert, G., Degrande, G., Kogut, J. and Francois, S. (2006), "The experimental validation of a numerical model for the prediction of railway induced vibrations", J. Sound Vib., 297(3-5), 512-535.
  13. Dieterman, H. and Metrikine, A. (1996), "The equivalent stiffness of a halfspace interacting with a beam. Critical velocities of a moving load along the beam", Eur. J. Mech. A-Solid., 15(1), 67-90.
  14. Xia, H. Zhang, N. and Guo, W. (2006), "Analysis of resonance mechanism and conditions of train-bridge system", J. Sound Vib., 297(3-5), 810-822.
  15. Xia, H., Cao, Y. and De Roeck, G. (2010), "Theoretical modeling and characteristic analysis of moving-train induced ground vibrations", J. Sound Vib., 329(7), 819-832.
  16. Takemiya, H. and Bian, X. (2005), "Substructure simulation of inhomogeneous track and layered ground dynamic interaction under train passage", J. Eng. Mech., 131(7), 699-711.
  17. International Organization for Standardization, ISO 8608 (1995), 1995 Mechanical vibration road surface profilesreporting of measured data.
  18. Dominguez, J. (1993), Boundary elements in dynamics, Computational Mechanics Publications and Elsevier Applied Science, Southampton.
  19. Knothe, K. and Grassie, S. (1993), "Modelling of railway track and vehicle/track interaction at high frequencies", Vehicle Syst. Dyn., 22(3-4), 209-262.
  20. Auersch, L. (2005), "The excitation of ground vibration by rail traffic: Theory of vehicle-track-soil interaction and measurements on high-speed lines", J. Sound Vib., 284(1-2), 103-132.
  21. Auersch, L. (2008), "The effect of critically moving loads on the vibrations of soft soils and isolated railway tracks", J. Sound Vib., 310(3), 587-607.
  22. Fryba, L. (2001), "A rough assessment of railway bridges for high-speed trains", Eng. Struct., 23(5), 548-556.
  23. Adam, M., Pflanz, G. and Schmid, G. (2000), "Two- and three-dimensional modelling of half-space and traintrack embankment under dynamic loading", Soil Dyn. Earthq. Eng., 19(8), 559-573.
  24. Hauck, M., Wettschureck, G. and Heckl, R. (1996), "Structure-borne sound and vibration from rail traffic", J. Sound Vib., 193(1), 175-184.
  25. Marrero, M. and Dominguez, J. (2003), "Numerical behavior of time domain BEM for three-dimensional transient elastodynamic problems", Eng. Anal. Bound. Elem., 27(1), 39-48.
  26. Newmark, N. (1959), "A method of computation for structural dynamics", J. Eng. Mech.-ASCE, 85(1) 67-94.
  27. von Estorff, O. and Pabrucki, M. (1990), "Dynamic response in the time domain by coupled boundary and finite elements", Comput. Mech., 6(1), 35-46.
  28. Zienkiewicz, O. (1986), The finite element method, 3rd Edition, McGraw-Hill.
  29. Galvín, P. and Dominguez, J. (2007a), "High-speed train-induced ground motion and interaction with structures", J. Sound Vib., 307(3-5), 755-777.
  30. Galvin, P. and Dominguez, J. (2007b), "Analysis of ground motion due to moving surface loads induced by high-speed trains", Eng. Anal. Bound. Elem., 31(11), 931-941.
  31. Galvin, P. and Dominguez, J. (2009), "Experimental and numerical analyses of vibrations induced by high-speed trains on the Córdoba-Málaga line", Soil Dyn. Earthq. Eng., 29(4), 641-657.
  32. Galvin, P., Romero, A. and Dominguez, J. (2010a), "Fully three-dimensional analysis of high-speed train-tracksoil- structure dynamic interaction", J. Sound Vib., 329(24), 5147-5163.
  33. Galvin, P., Romero, A. and Dominguez, J. (2010b), "Vibrations induced by HST passage on ballast and nonballast tracks", Soil Dyn. Earthq. Eng., 30(9), 862-873.
  34. Galvin, P., Fracois, S., Schevenels, M., Bongini, E., Degrande G. and Lombaert, G. (2010), "A 2.5D coupled FE-BE model for the prediction of railway induced vibrations", Soil Dyn. Earthq. Eng., 30(12), 1500-1512.
  35. Krylov, V. (1994), "On the theory of railway-induced ground vibrations", J. Phys., 4(5), 769-772.
  36. Krylov, V. (1995), "Generation of ground vibrations by superfast trains", Appl. Acoust., 44(2), 149-164.
  37. Sheng, X., Jones, C. and Thompson, D. (2003), "A comparison of a theoretical model for quasi-statically and dynamically induced environmental vibration from trains with measurements", J. Sound Vib., 267(3), 621-635.
  38. Sheng, X., Jones, C. and Thompson, D. (2004), "A theoretical model for ground vibration from trains generated by vertical track irregularities", J. Sound Vib., 272(3-5), 937-965.
  39. Sheng, X., Jones, C. and Thompson, D. (2006), "Prediction of ground vibration from trains using the wavenumber finite and boundary element methods", J. Sound Vib., 293(3-5), 575-586.

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Supported by : Ministerio de Ciencia e Innovacion of Spain