[EN] In this paper three formulations based on an Eulerian approach are presented to obtain the dynamic response of an elastic solid of revolution, which rotates around its main axis at constant angular velocity. The formulations are especially suitable for the study of the interaction of a solid with a non-rotating structure, such as occurs in the coupled dynamics of a railway wheelset with the track. With respect to previous publications that may adopt similar hypotheses, this paper proposes morecompact formulations and eliminates certain numerical problems associated with the presence of second-order derivatives with respect to the spatial coordinates. Three different models are developed depending the basis function that represents the displacements associated with the deformation; these basis functions are: (1) the shape functions that are used in the three dimensional finite element (FE) method; (2) the undamped mode shapes of the solid; (3) the shape functions that are adopted in the axisymmetric FE approach. Comparisons are shown of calculations carried out using these models. These show the existence of modal veering when analysing the Campbell diagram for a railway wheel.

The authors gratefully acknowledge the financial support of the European Commission through the project "RUN2Rail - Innovative RUNning gear soluTiOns for new dependable, sustainable, intelligent and comfortable RAIL vehicles" (Horizon 2020 Shift2Rail JU call 2017, grant number 777564), as well as Ministerio de Ciencia, Innovacion y Universidades and the European Regional Development Fund (projects TRA2017-84701-R and MTM2015-64013-P).