On the Interaction of Torsion and Bending in Rotating Shafts

Abstract

The problem of torsional and transverse deformations of a shaft rotating at a constant speed is considered. The displacements are expressed in a perturbation series in terms of a small parameter. Energy expressions are derived to each order and Hamilton’s principle is applied to obtain the equations of motion and the boundary conditions governing the displacement functions of different orders. It is clearly shown that the interaction of torsion and transverse vibration occurs at second order. Previous work reporting results of torsional vibration caused at a frequency equal to twice the rotational speed due to this interaction is confirmed.