Vibration suppression of elastically supported beams subjected to moving loads is investigated in this work. For a Timoshenko beam with an arbitrary number of elastic supports, subjected to a constant axial compressive force, and having a tuned mass damper (TMD) installed at the mid-span, the equations of motion are derived and using the Galerkin approach the solution is sought. The optimum values of the frequency and damping ratio are determined both analytically and numerically and presented as some design curves directly applicable in the TMD design for bridge structures. To show the efficiency of the designed TMD, computer simulation for two real bridges, subjected to a S.K.S Japanese high-speed train, is carried out and the results obtained are compared for before and after the installation of the TMD system.

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