An Eulerian coordinate-based method for analysing the structural vibrations of a solid of revolution rotating about its main axis

This article presents a technique for modelling the dynamic response of spinning solids of revolution. The method is especially adequate for considering those cases where the interesting displacements and the external forces are associated with points at which the Eulerian coordinates are constant. The method is based on the modal properties of solids of revolution: any deformed shape of the solid after rotation can be calculated as a linear combination of the non-rotating modes. The obtained formulation takes account of the flexibility of the solid and the inertial and gyroscopic effects due to the rotation. In this paper, the method is applied to a cylinder (considering an analytical and a numerical approach), and to a railway wheelset.