Free Vibration Analysis of Spinning Beams Using Higher-Order Shear Deformation Beam Theory

In this paper, equations of motion of spinning beams using higher-order shear deformation beam theory with different boundary conditions are derived. Both exact and approximate solutions are investigated. In previous studies, Timoshenko beam theory or first-order shear deformation beam theory was mostly applied to find modal properties of spinning beams. Despite the Timoshenko beam theory, in the proposed method, the use of shear correction factor is not necessary and the results are more accurate. The present analysis is especially useful for slender spinning beam in higher modes. The effects of slenderness ratio, spinning speed, and centripetal forces on forward and backward whirling modes are investigated using exact and approximate methods. Considering centripetal forces, it is shown that forward whirling frequencies are always higher than the corresponding backward ones in every spinning speed. It is shown that the difference between results of two beam theories for clamped–clamped boundary condition is maximum and for hinged–hinged and hinged–free boundary conditions is minimum.