Abstract Summary
Moving load problems have attracted the scientific community for many years since the first railway lines were build. Numerical assessment of the dynamic behaviour of structures subject to moving loads are under huge development, as are other approaches, to mention e.g. semianalytical methods and dynamic 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. There is no emphasis on adapting the data to any real part of the railway track. First, the model is presented along with its basic assumptions and simplifications. A set of dimensionless parameters necessary to describe the model is identified, along with a range of possible numerical values. The governing equations are stated, and solutions are presented by these two methods. Several cases are selected to demonstrate the results. It turns out that there are several situations with quite unpredictable behaviour, especially at low damping. In the semianalytical approach, the so-called lines of instability are tracked as a function of the ratio of velocity and moving mass. It is shown that there are several such lines. They can have quite a strange evolution, since they can form a closed curve, but they usually end up with asymptotes tending to infinite mass ratio at a fixed velocity ratio, and always one of them is tending to zero mass ratio at infinite velocity. It is also shown that the expected relation to the critical velocity of the moving force is not confirmed. First, three values of this critical velocity do not always exist. Sometimes there is only one, then the others are compensated by pseudocritical velocities, which may or may not be dominant, affecting their influence on instability lines. Second, especially for low damping levels, there are more than three asymptotes at fixed velocity ratios, so they cannot correspond to three possible values.
