Vibration frequencies of rotating tapered beam including rotary inertia and transverse shear deformation

Abstract

The out-of-plane free vibration of a rotating tapered beam based on both Euler and Timoshenko theories are presented by means of the finite element technique. The beam which is assumed to be linearly tapered in two planes is discretized into a number of simple elements with four degrees of freedom each. The governing equations for the free vibrations of the rotating tapered beam are derived from Hamilton's principle. Explicit expressions for the finite element mass and stiffness matrices are derived by using a consistent mass formulation. 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 frequencies 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.