A harmonic finite element for the analysis of flexural, torsional and axial rotordynamic behaviour of discs

Abstract The aim of this paper is to develop the formulation of a finite element for the study of the axial, torsional and flexural dynamic behavior of a rotating array of blades taking into account the gyroscopic effect and the centrifugal loadings. The displacements within the element are described in terms of superposition of the rigid body motion and the deflections relative to the rigid body configuration. A truncated Fourier's series has been adopted to approximate the dependence on tangential direction of the displacement field while polynomial shape functions are employed in the radial direction. Just the zero and one nodal diameter deflections have been considered in the Fourier series as they are the only ones coupled to the axial, torsional and flexural behavior of the disc–shaft system. The element equations of the motion are obtained using a complex co-ordinate formulation. Analytical solutions and experimental results have been compared to the results of the FEM model to test its accuracy.