A mathematical evaluation of rail flexural vibrations is proposed. The rail is modelled as a Timoshenko beam. The differential equation of bending motion, including the action of an external force is given. The Green's function for a beam on regularly spaced identical supports is evaluated. The final expressions obtained with the Timoshenko model come out to be of the same order of complexity than the corresponding expressions obtained using the Euler model. Although the Euler model, valid in the low frequency domain, is well adapted for getting a physical insight of the phenomena, the Timoshenko model has a broader frequency domain of validity and is better suited for quantitative evaluations. [References: 8]
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