Bending frequency of rotating tapered Timoshenko beams

In the present modelling, the shear and the rotary inertia effect on the modal characteristics are correctly included based on the Timoshenko beam theory. The kinetic and potential energy expression of this model are derived from the Rayleigh- Ritz method; (R-R). The problem with many discrete degrees of freedom is studied through the adoption of orthogonal polynomial functions satisfying the essential conditions only. The parameters for the hub radius, rotational speed, tapered ratio, rotary inertia and slenderness ratio are incorporated into the equation of motion. The effects of dimensionless parameters are successfully examined through numerical studies. Finally the resonance frequency of rotating bema is evaluated. The nondimensional frequency coefficients are given in tabular form. Some numerical examples are presented and the influence of different non-dimensional parameters on frequency values is discussed.