Free vibration characteristics of rotating Timoshenko beams

The in-plane and out-of-plane free vibrations of a rotating Timoshenko beam are analyzed by means of a finite element technique. The beam is discretized into a number of simple elements with four degrees of freedom each. The governing equations for the free vibrations of the rotating beam are derived from Hamilton's principle. The effects of hub radius, setting angle, shear deformation and rotary inertia are incorporated into a finite element model for determining the bending frequencies of the rotating beam. Numerical results for uniform cantilever beams with and without the hub radius are given for various values of the rotational speed, and are compared with the available results. It is shown that the present technique offers an accurate and effective method for solving the free vibration problems of rotating beams.