Energy expressions and free vibration analysis of a rotating Timoshenko beam featuring bending-bending-torsion coupling

In this study, free vibration analysis of a uniform, rotating, cantilever Timoshenko beam featuring bending-bending-torsion coupling is performed. To the best of the authors' knowledge, there is no explicit formulation in open literature for rotating Timoshenko beams featuring bending-bending-torsion coupling. Therefore, in this study, derivation of the kinetic and the potential energy expressions for the mentioned beam model is carried out in a detailed way by using several explanatory tables and figures. The parameters for the hub radius, rotational speed, rotary inertia, shear deformation and bending-bending-torsion coupling are incorporated into the energy expressions. The governing differential equations of motion are obtained by applying the Hamilton's principle to the derived energy expressions and solved using an efficient mathematical technique, called the differential transform method. The natural frequencies are calculated, and comparisons are made with the results in open literature. Consequently, it is observed that there is a good agreement between the results, which validates the accuracy of the derived formulation and the built beam model.