Vibration analysis of a rotating flexible shaft-disk system

Free vibrations of a spinning disk-shaft system are analysed using the finite-element method. The spinning disk is described by the Kirchhoff plate theory. The shaft is modelled by a rotating beam. Using Lagrange's principle and including the rigid-body translation and tilting motion, equations of motion of the spinning flexible disk and shaft are derived consistently to satisfying the geometric compatibility conditions on the internal boundaries among the substructures. The finite-element method is then used to discretize the derived governing equations. The method is applied to the shaft-disk spinning system. The sensitivity to the running speed as well as the effect of both disk flexibility and boundary condition on the natural frequencies of the spinning system are numerically investigated.