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

Rotors are usually modeled as deformable beams for the shafts and as rigid bodies, whose mass and moments of inertia are concentrated in chosen locations for all other components. If the rotor is provided with thin discs, however, the rigid body assumption can be too crude to yield satisfactory results. This can happen in many fields of technology such as wood-working machines or turbomachinery. The aim of this paper is to develop the formulation of a finite element for the study of the axial, torsional and flexural dynamic behaviour of thin rotating discs with account taken of the gyroscopic effect and the influence of the centrifugal and the thermoelastic loadings. The displacements within the element are assumed to be due to the superposition of its rigid body motion and the deflections relative to the rigid body configuration. The latter have been approximated by using a truncated Fourier series as shape functions in the tangential direction and polynomial shape functions in the radial direction. The element is developed in a complex co-ordinate formulation in order to implement it in an existing FEM code. (C) 1996 Academic Press Limited