Vibration frequencies of a rotating tapered beam with end mass

Abstract The natural frequencies of vibration of a rotating tapered beam with tip mass are investigated. Explicit expressions for the finite element mass and stiffness matrices are derived by using a consistent mass formulation. The beam is assumed to be linearly tapered in two planes. The generalized eigenvalue problem is defined and numerical solutions are generated for a wide range of rotational speed and tip mass variations. Both fixed and hinged end conditions are considered. Comparisons are made, whenever possible, with exact solutions and numerical results available in the literature. The results display high accuracy when compared with the exact solutions.

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