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Civil-Comp Proceedings ISSN 1759-3433
CCP: 77 PROCEEDINGS OF THE NINTH INTERNATIONAL CONFERENCE ON CIVIL AND STRUCTURAL ENGINEERING COMPUTING
Edited by: B.H.V. Topping
Paper 89 Analysis of Bridge-Vehicle Interaction by Component-Mode Synthesis Method
B. Biondi+, G. Muscolino* and A. Sofi* +Department of Civil and Environmental Engineering, University of Catania, Italy
*Department of Advanced Constructions and Technologies, University of Messina, Italy
Full Bibliographic Reference for this paper
B. Biondi, G. Muscolino, A. Sofi, "Analysis of Bridge-Vehicle Interaction by Component-Mode Synthesis Method", in B.H.V. Topping, (Editor), "Proceedings of the Ninth International Conference on Civil and Structural Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 89, 2003. doi:10.4203/ccp.77.89
Keywords: railway bridge, running train, railway track, dynamic interaction, substructures, component-mode synthesis.
Summary
Owing to the construction of an increasing number of high-speed railways
worldwide, the problem of train-bridge interaction has received much attention in
the last two decades. A comprehensive review of the history and literature on this
topic can be found in Reference [ 1]. In early studies, the bridge has been modelled
as a beam-like structure and the train as a series of moving forces or moving masses.
Such simplified models in some cases allow to recover closed-form solutions for the
dynamic response of the bridge (see e.g. Reference [ 2]). However, when the riding
comfort or response of rail cars are of concern, more sophisticated vehicle models
comprising also the suspension units are needed. In References [ 3, 4] an interaction
element consisting of a beam element and the masses and suspension units of the
car-body directly acting on it has been developed. Such element, however, accounts
only partially for the track structure modelling the ballast stiffness by continuously
distributed springs, while neglecting the flexural stiffness of the rail. This limitation
has been partially overcome in References [ 5, 6] by introducing a new element
called bridge-track-vehicle element, which allows to investigate the interactions
between a moving train and its supporting railway track and bridge structure.
This paper presents an alternative procedure based on substructure technique,
which takes into account the effects of both vehicle suspension units and railway
track structure. Following an approach recently proposed for analysing the vibration
of railway suspension bridges [7], the train, rails and bridge deck are here regarded
as three substructures. The train is idealized as a sequence of identical vehicles
moving at constant speed, each of which comprises a car-body, two bogies and
axles. Both the rails and bridge deck are modelled as linear elastic Bernoulli-Euler
beams, while the rail bed is characterized as a Winkler elastic foundation. According
to substructure technique, the equations ruling the dynamic response of the
compound train-rails-bridge system are obtained by assembling the equations of
motion of the three subsystems separately taken and imposing the compatibility and
equilibrium conditions at the contact points between wheels and rails. In particular,
by applying a variant of the component-mode synthesis method [8,9], the axle
degrees-of-freedom are condensed into those of the rails in contact, and a set of
reduced ordinary differential equations with time-dependent coefficients in the
generalized coordinates of the bridge and rails, and physical displacements of the
railway vehicles is obtained. So operating, the dynamic responses of the three
subsystems can be simultaneously handled, taking into account the interaction
effects. Numerical results concerning a single-span simply supported prestressed
concrete bridge of length 20 m [5] are presented in the paper. The dynamic
magnification factors for displacement and bending moment at bridge deck midspan
are computed and compared with those reported in Reference [5], finding good
agreements. By analysing an analogous bridge of length 40 m, the influence of span
length on the dynamic amplification factors is also examined. Furthermore, through
appropriate comparisons with the results obtained modelling the bridge as a beam-like
structure and applying the "improved series" expansion proposed in Reference [10],
it is shown that to obtain a realistic prediction of bending moment and shear
force distributions along bridge deck, the railway track has to be accounted for.
References
- 1
- Frýba, L., "Dynamics of Railway Bridges", Thomas Telford, London, 1996.
- 2
- Yang, Y.B., Yau, J.D., Hsu, L.C., "Vibration of Simple Beams due to Trains Moving at High Speeds", Engineering Structures, 19(11), 936-944, 1997. doi:10.1016/S0141-0296(97)00001-1
- 3
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- 4
- Yau, J.D., Yang, Y.B., Kuo, S.R., "Impact Response of High Speed Rail Bridges and Riding Comfort of Rail Cars", Engineering Structures, 21, 836-844, 1999. doi:10.1016/S0141-0296(98)00037-6
- 5
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- 6
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- 7
- Biondi, B., Muscolino, G., Sofi, A., "Analysis of Dynamic Interaction between Suspension Bridges and Running Trains", Structural Dynamics, EURODYN2002, Grundmann & Schuëller (eds.), 1041-1046, 2002.
- 8
- Biondi, B., Muscolino, G., "Component-Mode Synthesis Method Variants in the Dynamics of Coupled Structures", Meccanica, 35(1), 17-38, 2000. doi:10.1023/A:1004730011796
- 9
- Muscolino, G., "Dynamic Analysis of Structural Systems Using Component Mode Synthesis", in "Computational Structures Technology", (Edited by B.H.V. Topping and Z. Bittnar), Saxe-Coburg Publications, Stirling, Scotland, Chapter 11, 255-282, 2002. doi:10.4203/csets.7.11
- 10
- Pesterev, A.V., Bergman, L.A., "An Improved Series Expansion of the Solution to the Moving Oscillator Problem", Journal of Vibration and Acoustics (ASME), 122, 54-61, 2000. doi:10.1115/1.568436
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