Keywords: high-speed railway bridges, bridge dynamics, resonance in railway bridges, passive energy dissipation devices, fluid viscous dampers, moving loads.

The dynamic performance of railway bridges due to the passing of high-speed trains has become an issue and main concern for many scientists and engineers in the last decades. The main reason for this growing interest is the extensive construction of new high-speed lines and the reuse of old lines for higher operating train velocities. Fast trains can induce resonance situations in railway bridges, especially in those where the main structural elements are simply supported beams. As the train velocity approaches the resonant one a dynamic amplification of the structural response is to be expected, and in particular inadmissible vertical accelerations may occur on the bridge that may cause passenger discomfort, a reduction of the service life of the bridge, ballast deconsolidation, and the subsequent risk of derailment, as reported by some members of the D-214 Committee of the European Rail Research Institute [1,2]. Therefore, it becomes essential to control the resonant vibration of such structures under the circulation of trains.

Vibration control systems have been applied to reduce the dynamic response of structures since the 1960s but, even though, only a few authors have addressed the practical application of this technology to bridges excited by moving vehicles [3,4,5,6,7,8,9,10]. In the particular case presented herein the proposed strategy is based on the use of linear fluid viscous dampers connecting the bridge deck with an auxiliary structure. The aim of the investigation is to prove that the resonant response of the bridge may be drastically reduced by this type of device. The retrofitted bridge is firstly analysed under a sinusoidal excitation in order to capture the variables governing the resonant behaviour and the optimal parameters for the dampers which minimise the bridge dynamic response are obtained in closed form. Afterwards the adequacy of these optimal expressions to real bridges subjected to railway traffic is proven over a wide range of velocities. It may be concluded that (i) the resonant vibrations in simply supported bridges subjected to moving loads can be drastically reduced with the retrofit design proposed herein without neither exceeding the damper capacity nor the maximum yield stress of the auxiliary structure or the punching load capacity of the bridge slab; (ii) for a particular auxiliary structure, an optimum value of the FVD constants exists that minimises the bridge response; (iii) analytical expressions for the optimal damper constants are provided which lead to very accurate results as long as the maximum response of the bridge in the range of evaluated velocities that occur at resonance.

1

Frýba, L., "Dynamic behaviour of bridges due to high-speed trains", in "Workshop Bridges for High-Speed Railways", Porto, 137-158, 2004.

2

Mancel, F., "Cedypia: Analytical software for calculating dynamic effects on railway bridges", in "Proceedings of the Fourth European Conference on Structural Dynamics (Eurodyn '99)", Vol. 2, Prague, 675-680, 1999.

3

Kwon, H.C., Kim, M.C., Lee, I.W., "Vibration control of bridges under moving loads", Computers & Structures, 66, 473-480, 1988. doi:10.1016/S0045-7949(97)00087-4

4

Wang, J.F., Lin, C.C., Chen, B.L., "Vibration suppression for high-speed railway bridges using tuned mass dampers", International Journal of Solid and Structures, 40, 465-491, 2003. doi:10.1016/S0020-7683(02)00589-9

5

Yau, J.D., Yang, Y.B., "Vibration reduction for cable-stayed bridges travelled by high-speed trains", Finite Elements in Analysis and Design, 40, 341-359, 2004. doi:10.1016/S0168-874X(03)00051-9

6

Das, A.K., Dey, S.S., "Effects of tuned mass dampers on random response of bridges", Computers & Structures, 43, 745-750, 1992. doi:10.1016/0045-7949(92)90518-5

7

Minsili, L.S., Zhong, T., Xia, H., Manguelle, D.E., "Design and vibration control by friction dampers in truss bridges", in "Proceeding of the 2nd International Conference on Construction in Developing Countries: Challenges Facing the Construction Industry in Developing Countries", Botswana, 2002.

8

Choo, J.F., Koh, H.M., Kang, S.C., Kim, B.S., "Vibration control of long-span high-speed railway bridges under periodic moving loading using viscoelastic damper", in "Structures for high-speed railway transportation, International association for bridge and structural engineering", Antwerp, (Belgium), 2003.

9

Oliveto, G., Santini, A., Tripodi, E., "Complex modal analysis of a flexural vibrating beam with viscous end conditions", Journal of Sound and Vibration, 200, 327-345, 1997. doi:10.1006/jsvi.1996.0717

10

Greco, A., Santini, A., "Dynamic response of a flexural non-classically damped continuous beam under moving loadings", Computers & Structures, 80, 1945-1953, 2002. doi:10.1016/S0045-7949(02)00218-3

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