Keywords: transversal vibration, moving load, moving mass, dynamic stiffness matrix, semi-infinite elements, critical velocity, finite element model.

Railway transportation is facing the challenge of tailoring the railway system for the 21st century in order to improve its competiveness with air transport. This increases demands on creating new lines, on the modernization of existing lines and on increasing the capacity of the whole railway network. As a consequence new issues related to their dynamic response still arise. It is necessary to have an efficient computational tool providing a quick response with sufficient accuracy to the questions that arise. Thus it is necessary to evaluate the applicability of the traditionally used simplified models which have a closed form solution.

Regarding simplified models used in this contribution, transverse vibrations induced by the time variable load moving at a constant velocity on a beam on visco-elastic foundation are solved by the normal-mode analysis. Shear distortion, rotary inertia and the effect of axial force are accounted for. The natural frequencies are obtained numerically exploiting the concept of the global dynamic stiffness matrix. Reflected waves at the extremities of the full beam are avoided by the introduction of semi-infinite zones, which is the new contribution.

It is verified that the finite element method can yield errors in places where they are not predictable. Therefore: (i) it is important to continue with analytical solutions and use them as benchmark problems; (ii) it is necessary to establish the range of the validity of the simplified models, because their results are obtained faster and in a more accurate way, than the ones obtained by standard finite element codes. This contribution gives a first step to such a systematic comparison.

There are several ways of possible comparison. One of then is a critical velocity comparison in systems with a non-homogeneous foundation. Then in the validation process of simplified models the following issues have to be solved: (i) what terms from the general formulation are really necessary; (ii) can the real discrete foundation be substituted by the continuous one; (iii) how are reflecting waves removed; (iv) is the mass of the load important, and if yes, how is the mass associated to the foundation; (v) are the results meaningless because in fact the foundation should be tensionless?

After solving issues (i)-(iv) in an analytical way, the critical velocity of the most adequate simplified model can be compared with the full finite element analysis to validate issue (v). A finite element model using the ABAQUS code will be presented. Infinite elements will be used to model infinite soil layers.

The new contributions of this paper consist of: (i) implementation of semi-infinite zones; (ii) the first part of extensive comparison of several models. Such a systematic work was not presented before, although its importance is obvious.

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