Abstract
In this study, a modal superposition approach was adopted to derive the dynamic response of coupled vehicle and bridge systems. The train comprises a number of railway cars, each of which is modelled with ten degrees of freedom. The railway bridge was represented by a simply supported beam modelled as Euler-Bernoulli beam. In the numerical simulations, dynamic responses at the mid-span of the bridge and dynamic responses of the train under different train speeds are computed with random and non random rail irregularities. Effect of parameters like the depth and the position of the imperfection on the rail are taken into account. The coupled system of equations is integrated numerically by the newmark’s β method. The results obtained show that the rail irregularities affect the vertical acceleration of the train, which serves as a measure of the riding comfort of the trains moving over a bridge.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
L. Frýba, Vibration of solids and structures under moving loads, Thomas Telford Ltd., London (1999).
J. M. Biggs, Introduction to structural dynamics, New York (NY, USA): McGraw-Hill (1964).
A. E. Martinez-Castro, P. Museros and A. Castillo-Linares, Semi-analytic solution in the time domain for non-uniform multi-span Bernoulli-Euler beams traversed by moving loads, Journal of Sound and Vibration, 294(1–2) (2006) 278–297.
M. Simsek, Vibration analysis of a functionally graded beam under a moving mass by using different beam theories, Composite Structures, 92(4) (2010) 904–917.
R. T. Wang, Vibration of multi-span Timoshenko beams to a moving force, Journal of Sound and Vibration, 207(5) (1997) 731–742.
J. S. Wu and L. K. Chiangn, Out-of-plane responses of a circular curved Timoshenko beam due to a moving load, International Journal of Solids and Structures, 40 (2003) 7425–7448.
P. Lou, Vertical dynamic responses of a simply supported bridge subjected to a moving train with two wheel-set vehicles using modal analysis method, International Journal for Numerical Methods in Engineering, 64(9) (2005) 1207–1235.
P. Lou, G. L. Dai and Q. Y. Zeng, Modal coordinate formulations for a simply supported bridge subjected to a moving train modelled as two-stage suspension vehicles, Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science, 219(10) (2005) 1027–1040.
Y. L. Xu., Q. Li, D. J. Wu and Z. W. Chen, Stress and acceleration analysis of coupled vehicle and long-span bridge systems using the mode superposition method, Engineering Structures, 32 (2010) 1356–1368.
K. C. Chang, F. B. Wu and Y. B. Yang, Disk model for wheels moving over highway bridges with rough surfaces, Journal of Sound and Vibration, 330 (2011) 4930–4944.
H. Azimi, K. Galal and O. A. Pekau, A modified numerical VBI element for vehicles with constant velocity including road irregularities, Engineering Structures, 33 (2011) 2212–2220.
J. D. Yau, Y. B. Yang and S. R. Kuo, Impact response of high speed rail bridges and riding comfort of rail cars, Engineering Structures, 21 (1999) 836–844.
X. W. Liu, J. Xie, C. Wu and X. C. Huang, Semi-analytical solution of vehicle-bridge interaction on transient jump of wheel, Engineering Structures, 30(9) (2008) 2401–2412.
Y. B. Yang and J. D. Yau, Vehicle-bridge interaction element for dynamic analysis, J Struct Eng ASCE, 123 (1997) 1512–8.
M. K. Song, H. C. Noh and C. K. Choi, A new three-dimensional finite element analysis model of high-speed train-bridge interactions, Engineering Structures, 25(13) (2003) 1611–1626.
Y. Cao, H. Xia and Z. Li, A semi-analytical/FEM model for predicting ground vibrations induced by high-speed train through continuous girder bridge, Journal of Mechanical Science and Technology, 26(8) (2012) 2485–2496.
H. Xia, G. D. Roeck, N. Zhang and J. Maeck, Experimental analysis of a high-speed railway bridge under Thalys trains, Journal of Sound and Vibration, 268 (2003) 103–113.
N. Zhang, H. Xia and G. D. Roeck, Dynamic analysis of a train-bridge system under multi-support seismic excitations, Journal of Mechanical Science and Technology, 24(11) (2010) 2181–2188.
K. Liu, E. Reynders, G. D. Roeck and G. Lombaert, Experimental and numerical analysis of a composite bridge for high-speed trains, Journal of Sound and Vibration, 320(1–2) (2009) 201–220.
X. Lei and N. A. Noda, Analyses of dynamic response of vehicle and track coupling system with random irregularity of track vertical profile, Journal of Sound and Vibration, 258(1) (2002) 147–65.
H. Honda, Y. Kajikawa and T. Kobori, Spectra of road surface roughness on bridges, Journal of Structural Division, ASCE, 108(ST9) (1982) 1956–1966.
W. Cai, Z. Wen, X. Jin and W. Zhai, Dynamic stress analysis of rail joint with height difference defect using finite element method, Engineering Failure Analysis, 14 (2007) 1488–1499.
E. Kabo, J. C. O. Nielsen and A. Ekberg, Prediction of dynamic train-track interaction and subsequent material deterioration in the presence of insulated rail joints, Vehicle System Dynamics, 44 (2006) 718–729.
T. X. Wu and D. J. Thompson, An investigation into rail corrugation due to micro-slip under multiple wheel-rail interactions, Wear, 258 (2005) 1115–1125.
Y. G. Kim, H. B. Kwon, S. W. Kim, C. K. Park and T. W. Park, Correlation of ride comfort evaluation methods for railway vehicles, Proc. IMech F, J. Rail and Rapid Transit, 217(2) (2003) 73–88.
Y. S. Wu and Y. B. Yang, Steady-state response and riding comfort of trains moving over a series of simply supported bridges, Engineering Structures, 25 (2003) 251–265.
C. H. Lee, C. W. Kim, M. Kawatani, N. Nishimura and T. Kamizono, Dynamic response analysis of monorail bridges under moving trains and riding comfort of trains, Engineering Structures, 27 (2005) 1999–2013.
ISO 2631/2. Evaluation of human exposure to whole-body vibration-Part 2: Continuous and shock-induced vibration in buildings (1 to 80 Hz) (1989).
N. M. Newmark, A Method of computation for structural dynamics, ASCE, Journal of Engineering Mechanics Division, 85(EM3) (1970) 67–94.
L. Frýba, A rough assessment of railway bridges for high speed trains, Engineering Structures, 23(5) (2001) 548–556.
Y. B. Yang and J. D. Yau, Vehicle-bridge interaction element for dynamic analysis, Journal of Structural Engineering, ASCE, 123(11) (1997) 1512–1518.
W. H. Press and S. H. Teukolsky, Portable random number generators, Computers in Physics, 6 (1992) 522–524.
Y. B. Yang, J. D. Yau and Y. S. Wu, Vehicle-Bridge interaction dynamics with applications to high-speed railways, World scientific publishing Co Pte Ltd., Singapore (2004).
J. Grandi and P. Ramondenc, The dynamic behavior of railways on high speed lines, SNCF, France (1990).
European Committee for Standardization, EUROCODE 1: basis of design and actions on structures, part 3: traffic loads on bridges, ENV 1991-3, (1995).
Author information
Authors and Affiliations
Corresponding author
Additional information
Recommended by Editor Yeon June Kang
Youcef Khadri received his Magister and Ph.D from University of Badji Mokhtar, Annaba. He is currently a Assistant Professor in the Department of Mechanical Engineering, University Badji Mokhtar, B.P. 12 Annaba, Algeria. His research interests include vibration and dynamic systems, composite materials and vibratoire diagnosis of the machine failures.
Rights and permissions
About this article
Cite this article
Youcef, K., Sabiha, T., El Mostafa, D. et al. Dynamic analysis of train-bridge system and riding comfort of trains with rail irregularities. J Mech Sci Technol 27, 951–962 (2013). https://doi.org/10.1007/s12206-013-0206-8
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12206-013-0206-8