Shamalta M., Metrikine A.V.


Analytical modelling of the dynamic response of an embedded railway track to a moving load


Archive of Applied Mechanics 73(1-2), 131-146, 2003

Doi: 10.1007/s00419-002-0248-3


Summary. In this paper, the steady-state dynamic response of an embedded railway track to a moving train is investigated theoretically. The model for the track consists of a flexible plate performing vertical vibrations, two beams that are connected to the plate by continuous visco-elastic elements, and an elastic foundation that supports the plate. Two harmonic loads that move uniformly on the beams describe the train loading. The plate, beams and elastic foundation are employed to model the concrete slab of an embedded track, the rails and the ground reaction, respectively. The problem is studied by employing the Fourier integral transforms in the following way. Firstly, the dispersion analysis of waves that may propagate along the system is accomplished in the frequency-wavenumber domain. On the basic of this analysis, critical velocities of the loads are found both for the in-phase and anti-phase vibrations of the loads. Secondly, the vertical displacement of the rails and the slab, along with the stresses in the slab are investigated as functions of the velocity and frequency of the loads. Finally, the response of the two-dimensional model is compared to that of a simplified one-dimensional model.