A finite beam element for vibration analysis of rotating tapered timoshenko beams

A finite beam element for vibration analysis of a rotating tapered beam including shear deformations and rotary inertia is derived in this paper. The finite element has four degrees of freedom, and accounts for linear tapering in two planes. This formulation permits any combination of taper ratios as well as unequal element lengths. Explicit expressions for the finite element mass and stiffness matrices are derived using the consistent mass approach, while accounting for the centrifugal stiffness effects. The generalized eigenvalue problem is defined and numerical solutions are generated for a wide range of rotational speed and taper ratios. Results obtained include the first ten free vibrational modes for both fixed and hinged end conditions. Comparisons are made whenever possible with exact solutions and with numerical results available in the literature. The results display high accuracy when compared with other numerical results.