On the critical velocity of a mass moving along an infinite beam supported by three viscoelastic layers

Numerical assessment of the dynamic behaviour of structures subject to moving loads are under huge development, as are other approaches, to mention e.g. (semi)analytical methods and methods based on frequency-domain moving Green's function. This contribution is focused on an infinite beam supported by three viscoelastic layers, which, due to its computational efficiency and relatively good approximation of reality, is a quite common model of a railway line. New developments that are presented concern the instability of a moving mass. The critical velocity in this context will be used for the lowest velocity that separates stable and unstable behaviour. The two above-mentioned methods are compared in terms of computational efficiency and accuracy of the obtained results. All results are presented in dimensionless form to cover a wide range of possible scenarios. When the frequency-domain moving Green's function is used to calculate the critical velocity via D-decomposition method, then a little damping should be considered for numerical stability. The semianalytical approach, on the other hand, can deal with both undamped and damped structures without any problems. Nevertheless, the final results obtained by the two methods (in the Green's function approach under the assumption of very low damping) are identical.