Keywords: high-speed railway bridges, local vibrations, global vibrations, resonance, generalized beam theory.

High-speed railways have rapidly expanded worldwide. However, the state-of-the-art technology involved is associated with many specific complex engineering problems, such as the need to estimate/mitigate the vibrations induced by the high-speed trains on the track, ground, bridge decks or tunnels. Concerning the bridge decks, previous studies showed that a train (a set of "equally spaced" moving loads) travelling at high speed may be in resonance with the deck natural vibration frequencies or modes. Then, the ensuing vibrations have a strong impact on the bridge (i) structural safety, (ii) track stability and wheel-rail contact, and also (iii) passenger comfort. To avoid these problems, the design of such bridges must include a dynamic analysis, already specified in the new Eurocode 2, the deck response is assumed to involve only global deformations, e.g. flexural and, or torsional displacements. However, this assumption is not adequate for slender thin-walled decks; indeed, local deformation may play an important role in the response of such decks.

Numerical local or global dynamic analyses of thin-walled prismatic members are mainly performed resorting to (i) shell finite element or (ii) finite strip analyses. However, an alternative approach was recently developed, although it has not yet been applied in this specific context: the use of generalised beam theory (GBT) [1], valid for the analysis of such members. The GBT trademark is expressing the member deformed configurations (e.g. a vibration mode) as linear combinations of structurally meaningful deformation modes; this makes it possible (i) to acquire a better understanding about the mechanics of the member dynamics and also (ii) to perform efficient analyses; here quite small degree of freedom numbers are involved. Note that a rather original "doubly modal" representation of the thin-walled member response is obtained by combining a GBT-based dynamic analysis with the vibration mode superposition method [2].

The aforementioned GBT formulation is presented and applied to study the dynamic behaviour of a simply supported pre-stressed concrete box girder (part of the Spanish El Genil high-speed railway viaduct). Using a GBT-based code, variation of the maximum deck vertical displacements and accelerations are assessed with the train crossing speed, for ten representative HSLM-A trains. Particular attention is paid to the influence of the local deformation on the deck vibration and dynamic behaviour.

1

D. Camotim, N. Silvestre, R. Bebiano, "GBT local and global vibration analysis of thin-walled members", Analysis and Design of Plated Structures - Volume 2: Dynamics, N.E. Shanmugam, C.M. Wang, (eds.), Woodhead Publishing Ltd., Cambridge, 36-76, 2007.

2

R. Bebiano, N. Silvestre, D. Camotim, "GBT-based dynamic analysis of thin-walled members", Proceedings of Fifth International Conference on Thin-Walled Structures - Recent Innovations and Developments (ICTWS 2008, Brisbane, 18-20/6), M. Mahendran, (ed.), 1197-1210, 2008.

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