Dynamic Response of the Coupled Vehicle-Floating Slab Track System using Finite Element Method

Document Type : Research Paper


1 Associate Professor, School of Railway Engineering, Iran University of Science and Technology, Tehran, Iran

2 Assistant Professor, School of Railway Engineering, Iran University of Science and Technology, Tehran, Iran

3 PhD. Candidate, School of Railway Engineering, Iran University of Science and Technology, Tehran, Iran


In present study, a mathematical model of the vehicle–floating slab track (FST) interaction is established to investigate the coupled behaviour of vehicle–track system. The FST is modelled as the double Euler -Bernoulli beam including the rail and slab. The railway vehicle is simplified as a multi-rigid-body model. The wheel–rail interface is treated using a nonlinear Hertzian contact model, coupling the mathematical equations of the vehicle–FST systems. The dynamic interaction of the entire system is numerically studied in time domain, employing Newmark’s integration method. The numerical model of the present research is validated using benchmark model reported in the literature. Finally using the developed numerical tool many sensitivity analyses were performed on various important parameters affecting on dynamic behaviour of slab track, such as slab thickness, axle load and the track bed stiffness and consequently the deflection and bending moment of rail and slab were assessed. Slab thickness has more effect on slab than rail dynamic behaviour.


-Abu-Hilal, M. (2006) “Dynamic response of a double Euler–Bernoulli beam due to a moving constant load”, Journal of Sound and Vibration, Vol. 297, pp.477–491.
-Ames, W. F., Ames, W. (1972) “Nonlinear partial differential equations in engineering”, vol. 2. Academic Press, New York (1972).
-Chen, Y. H. and Shiu Z. M. (2004) “Resonant curves of an elevated railway to harmonic moving loads”, International Journal of Structural Stability and Dynamics, Vol. 4, No.2, pp. 237–257.
-Cox, S. J, Wang, A., Morison, C., Carels, P., Kelly, R. and Bewes, O. G. (2006) “A test rig to investigate slab track structures for controlling ground vibration”, Journal of Sound and Vibration, Vol. 293, pp. 901–909.
-Ding, D-y, Liu, W-n, Li, K-f, Sun, X-J. and Liu, W-f. (2011) “Low frequency vibration tests on a floating slab track in an underground laboratory”, Journal of Zhejiang University-Science A (Applied Physics & Engineering), Vol.12, No.5, pp.345-359.
-Gupta, S. and Degrande, G. (2009) “Modelling of continuous and discontinuous floating slab tracks in a tunnel using a periodic approach”, Journal of Sound and Vibration, Vol. 329, pp. 1101–1125.
-Hussein, M. F. M. and Hunt, H. E. M. (2006) “Modelling of floating-slab tracks with continuous slabs under oscillating moving loads”, Journal of Sound and Vibration, Vol. 297, pp. 37–54.
-Hussein, M. F .M. and  Hunt, H.E.M. (2009) “A numerical model for calculating vibration due to a harmonic moving load on a floating-slab track with discontinuous slabs in an underground railway tunnel”, Journal of Sound and Vibration, Vol. 297, pp. 901–909.
-Jun, X. , Dan, H. and Qing-yuan, Z. (2008) “Analysis theory of spatial vibration of high-speed train and slab track system”, Journal of Central South University of Technology, Vol.15, pp.121-126.
-Kalker, J. J. (1991) “Wheel rail rolling contact theory”. Wear, 144, pp.243–261.
-Kuo, Chen-Ming, Huang, Cheng-Hao and  Chen, Yi-Yi (2008) “Vibration characteristics of floating slab track”, Journal of Sound and Vibration, Vol.317, pp. 1017–1034.
-Li, Z. G. and Wu T. X. (2008) “Modelling and analysis of force transmission in floating-slab track for railways”, Journal of Rail and Rapid Transit, Part F, Vol. 222, pp.45-57.
-Lombaert, G., Degrande,G., Vanhauwere, B., Vandeborght, S. and Francois, S. (2006) “The control of ground-borne vibrations from railway traffic by means of continuous floating slabs”, Journal of Sound and Vibration, Vol. 297, pp.363–374.
-Mehrali, M., Mohammadzadeh, S., Esmaeili, M. and Nouri, M. (2014) “Investigating vehicle-slab track interaction considering random track bed stiffness”, Scientia Iranica, Transactions A: Civil Engineering, Vol. 21, pp. 82-90.
-Mohammadzadeh, S., Esmaeili, M. and Mehrali, M. (2013) “Dynamic response of double beam rested on stochastic foundation under harmonic moving load”, International Journal for Numerical and Analytical Methods in Geomechanics, doi: 10.1002/nag.2227.
-Mohammadzadeh, S., Ahadi, S. and Keshavarzian, H. (2014) “Assessment of fracture reliability analysis of crack growth in spring clip type Vossloh SKL14. Proc. Inst. Mech. Eng. O: J. Risk Reliab.
-Saurenman, H., Phillips, J.(2006) “In-service tests of the effectiveness of vibration control measures on the BART rail transit system”, Journal of Sound and Vibration, Vol. 293, pp.888–900.
-Steenbergen, M.J.M.M., Metrikine, A.V., Esveld, C. (2007) “Assessment of design parameters of a slab track railway system from a dynamic viewpoint”, Journal of Sound and Vibration, Vol. 306, pp. 361-371.
-Xiaobin, L., Shuangxi, X., Weiguo, Wu., Jun, L. (2014) “An exact dynamic stiffness matrix for axially loaded double-beam systems”, Sadhana, Vol. 39 No.3, pp. 607-623.
-Yen, S. T. and Lee, Y.H. (2007) “Parameter identification and analysis of a slab track system using 3d ABAQUS program”, Journal of Transportation Engineering © ASCE, pp. 288-297.
-Yuan, J., Zhu, Y. and Wu, M. (2009) “Vibration characteristics and effectiveness of floating slab track system”, Journal of Computers, Vol.4, No.12, pp. 1249-1254.
-Zakeri J. A. and Xia, H. (2008) “Sensitivity analysis of track parameters on train- track dynamic interaction”, Journal of Mechanical Science and Technology, Vol.22, No.7, pp. 1299-1304.
-Zhai,W., Wang, K. and Cai, C. (2009) “Fundamental of vehicle-track coupled dynamic”, Journal of vehicle system dynamics, Vol.47, No. 11, pp. 1349-1376
-Zhao X, Li Z. (2011) “The solution of frictional wheel–rail rolling contact with a 3D transient finite element model: validation and error analysis”. Wear, Vol. 271, pp.444–452.
-Zhao X, Li,  Z.  and Liu J. (2012) “Wheel–rail impact and the dynamic forces at discrete supports of rails in the presence of singular rail surface defects”, Proceeding of the Institution of Mechanical Engineering, Part F Journal of Rail and Rapid Transit, Vol.226, pp.124–139.