Vibration analysis of a rotating tapered Timoshenko beam using DTM

In this study, free vibration analysis of a rotating, tapered Timoshenko beam that undergoes flapwise bending vibration is performed. Derivation of the equations of motion of a rotating, uniform Timoshenko beam was made step by step in a previous work of the authors. Therefore, differential equations of motion are given directly without making any derivations in this paper. The parameters for the hub radius, rotational speed, taper ratio, rotary inertia, shear deformation and slenderness ratio are incorporated into the equations of motion. In the solution part, an efficient mathematical technique called the Differential Transform Method, DTM, is used. Finally, using the computer package Mathematica, the natural frequencies are calculated and the effects of the incorporated parameters are examined. Moreover, numerical examples are solved to make comparisons with the existing results in open literature and it is observed that the agreement between the results is very good.