Keywords: dynamic analysis, railway bridges, geometric irregularities, contact forces, iterative procedure, frequency-domain spectrum.

This paper addresses a simplified dynamic-analysis methodology for the study of vibrations in railway bridges produced by a passenger train. The analysis starts with a vehicle model composed of fifteen degrees-of-freedom, according to [1], related to vertical (bounce) and horizontal (sway) displacements and rotations about the longitudinal (roll), transverse (pitch) and vertical (yaw) axes. In this methodology, dynamic models of the train and the bridge were assumed to be initially uncoupled, yet being bound by the contact train-bridge forces. Thus, the loads were evaluated from the dynamic modelling of the train, initially adopting the hypothesis of rigid and fixed deck, in addition to considering geometric irregularities, in both the vertical and horizontal track planes, as well as in the wheels, as seen in [2]. A study was carried out to find the parameters of the irregularity functions in the rails (number of half-waves and phase angles), that could potentially lead to maximal amplification of the bending moment at mid span of the bridge. It was considered a thirty-six-metre long concrete bridge with box-girder section, as seen in [3], and a train running at a speed of twenty metres per second. The contact forces obtained from the vehicle model subjected to support excitation were statically condensed in its centre of gravity and applied on the low-hierarchy there-dimensional beam finite-element model. The main purpose of this paper is to evaluate the influence of the hypothesis of the rigid deck on the dynamic response. Thus, it is proposed that the correction of the displacements imposed on the wheel-rail interface, using an iterative procedure, so that the updated "equivalent rail irregularities" should be the sum of the deck displacements subjected to the first estimate of contact forces and the "actual" rail irregularities. Thereby, it is possible to obtain the new interaction forces, which will be re-applied to the bridge model to determine the new displacements, repeating the procedure until the results are very close to those of the previous iteration.

1

P.G. Cunha, "Análise Dinâmica de Pontes Ferroviárias: Uma Metodologia Simplificada", Dissertação de Mestrado, POLI/USP, São Paulo, Brasil, 2011.

2

W.L. Correa, "Controle das Vibrações Induzidas pela Interação Dinâmica entre Trens-Trilhos-Dormentes-Estrutura de Aço de Pontes Ferroviárias", Tese, COPPE/UFRJ, Rio de Janeiro, Brasil, 2008.

3

L.G. Clemente, L.A. Borges e F. Stucchi, "Projeto de viaduto unicelular para pista dupla na extensão da linha Norte/Sul do Metrô de São Paulo", Anais do Primeiro Simpósio EPUSP de Estrutura de Concreto, 1989.

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