Free vibrations of a rotating inclined beam

By utilizing the Hamilton principle and the consistent linearization of the fully nonlinear beam theory. two coupled governing differential equations for a rotating inclined beam are derived. Both the extensional deformation and the Coriolis force effect are considered. It is shown that the vibration system can be considered as the superposition of a static subsystem and a dynamic subsystem. The method of Frobenius is used to establish the exact series solutions of the system. Several frequency relations that provide general qualitative relations between the natural frequencies and the physical parameters are revealed without numerical analysis. Finally, numerical results are given to illustrate the general qualitative relations and the influence of the physical parameters on the natural frequencies of the dynamic system.