Dynamics of a Flexible-hub Geometrically Nonlinear Beam with a Tip Mass

The dynamics of a flexible-hub geometrically nonlinear beam carrying a tip mass is presented. The hub-beam system is assumed to move in plane and the hub is restrained by a translational and a rotational spring. Hamilton's principle is used to derive the equations of motion and their boundary conditions. A flexural model that takes into account the geometrical coupling between the axial and lateral deformations and ignores the axial deformation and its time derivatives is obtained. An exact solution for the natural frequencies and mode shapes of the free vibration problem is obtained. Using these mode shapes, a reduced-order model of the system is obtained using the Galerkin's method. The dynamic response of the system using the present low-order model shows excellent agreement with the recent finite-element solutions available in the literature.