Keywords: elastically-supported beams, moving loads, railway bridges, resonance, cancellation, high-speed trains.

In this paper the transverse vibration response of elastically supported beams traversed by moving loads in the free vibration phase is investigated in detail. Unlike in previous works published by other authors [1,2] the spatial response of the beam is expressed as a linear combination of the analytical normal modes of vibration [3], being now the analysis applicable to modes higher than the fundamental one. First, the amplitude of the free vibrations induced on the beam by a single load is derived in terms of the relative flexural rigidity of the beam with respect to the vertical stiffness of the elastic supports. Situations of maximum response and cancellation are detected for particular nondimensional speeds of the load, and the conditions leading to these situations are derived. Then, the dynamic response of the elastically supported beam under trains of equidistant loads is addressed, focusing in the appearance of resonance phenomena associated with the characteristic distance of the trains. Equating the conditions for resonance of a particular beam with that of maximum free response and cancellation under a single load, ratios of the bridge length and train characteristic distances leading to resonances of remarkable amplitudes or, contrarily, cancelled resonances are obtained. Finally the analytical conditions for resonance and cancellation of resonance extracted from the elastically supported beam case are verified in a finite element analysis of a real railway bridge accounting for the three-dimensional deformation of the deck, structural damping, a non-uniform distribution of masses over the platform area and a skewed plan geometry of the deck. Despite all these factors that separate the real case from the simplified beam model, the analytical conditions for resonance and cancellation of resonance predict accurately the occurrence of these phenomena in the real case.

A practical application of this study is the set up of dynamic tests in experimental campaigns performed on railway bridges. Selecting velocities of the trains used in the campaign may lead to abnormally low structural responses resulting in erroneous conclusions regarding the bridge dynamic performance, and inaccurate evaluations of the structural damping to be expected under normal operation conditions.

1

Y.B. Yang, C.L. Lin, J.D. Yau, D.W. Chang, "Mechanism of resonance and cancellation for train-induced vibrations on bridges with elastic bearings", Journal of Sound and Vibration 269, 345-360, 2004. doi:10.1016/S0022-460X(03)00123-8

2

Y.B. Yang, J.D. Yau, Y.S. Wu, "Vehicle-bridge interaction dynamics with applications to highspeed railways", World Scientific Publishing, 2004.

3

I.A. Karnovsky, O.I. Lebed, "Formulas for structural dynamics. Tables, graphs and solutions", McGraw Hill, 2000.

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