In general, eigenvalue analysis for beams considering rotatory inertia and shear deformation is not trivial, even in the case of uniform beams. In this paper, a practical method is proposed for calculating natural bending frequencies of uniform elastic beams considering rotatory inertia and shear deformation. The proposed method is based on the modified Timoshenko beam theory, which is more rigorous and realistic than the traditional Timoshenko beam theory. It is shown that the proposed method calculates the natural frequencies of an arbitrary order-vibration mode for beams of arbitrary cross-sections with a high level of accuracy, similar to numerical analysis.
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