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

The high-speed railway is a very efficient and clean transport mode that has been rapidly expanding worldwide. The existing network is expected to triple over the next decade. However, this state-of-the art technology involves many specific engineering complexities, such as the need to estimate or mitigate the vibrations induced by the passage of the high-speed trains, which affect the track, ground, bridge decks, close buildings, tunnels, etc. Concerning bridges, earlier investigations have shown that the passage of a high-speed train on a given deck, which can be viewed as a set of "equally spaced" moving loads (the train axles) crossing a beam, is bound to cause (at high speeds) resonance with the deck natural vibration modes. The ensuing vibration behaviour may have a strong impact on the bridge (i) structural safety, (ii) track stability and wheel-rail contact or even (iii) passenger comfort. In order to avoid (or, at least, minimise) these problems, the design of such railway bridges requires the performance of dynamic analyses, which usually assume that the deck vibrates on (global) flexural and, or torsional modes. However, in the case of slender decks local vibration phenomena may also play an important role in the bridge response.

In order to perform local-global dynamic analyses of thin-walled prismatic members (such as slender bridge decks), two main numerical methods are traditionally employed: (i) the shell finite element method or (ii) the finite strip method. Recently, the authors have developed an alternative approach to be applied in this context: the dynamic analysis based on the generalised beam theory (GBT). The trademark of GBT consists of discretising the member deformed configuration (e.g. a vibration mode shape) as a linear combination of physically-structurally meaningful deformation modes. This feature makes it possible (i) to acquire a better understanding about the mechanics of the member dynamics and (ii) to perform structural analyses that are numerically very efficient, in the sense that they involve only a quite small number of degrees of freedom. Moreover, when combined with the vibration mode superposition principle, the GBT-based dynamic analyses provide a rather original "doubly modal" representation of the response.

The objective of this work is to employ the GBT-based formulation mentioned in the previous paragraph to investigate the dynamic response of a high-speed railway bridge deck, consisting of a simply supported concrete box-girder that carries two tracks. Using a computer code developed by the authors, it is possible to determine the maximum displacements and accelerations taking place in the bridge deck, expressed as functions of the train crossing speed. These characteristics are determined for the passage of (i) seven real high-speed trains and (ii) the ten representative trains comprising the HSLM-A load model. Particular attention is devoted to studying the influence of the local deformations on the bridge deck dynamic response. Moreover, it is considered that either one or both tracks are loaded (i.e. trains crossing in both directions). In the latter case it is very important to assess the influence of the synchronicity between the two crossing trains. For validation purposes, most of the GBT-based results obtained are compared with values yielded by shell finite element analyses performed using a commercial code.

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