Railway noise: Use of the Timoshenko model in rail vibration studies

A mathematical evaluation of rail flexural vibrations is proposed. The rail is modelled as a Timoshenko beam. The differential equation of bending mot ion, including the action of an external force is given. The Green's functi on for a beam on regularly spaced identical supports is evaluated. The fina l 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, i s well adapted for getting a physical insight of the phenomena, the Timoshe nko model has a broader frequency domain of validity and is better suited f or quantitative evaluations.