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The finite-element method for solution of problems in structural mechanics is extended to vibration of beams, including shear and rotary inertia effects. Use is made of a consistent mass matrix in conjunction with the corresponding stiffness matrix. The method is applicable to uniform and nonuniform beams with any boundary conditions. Excellent agreement with exact results has been obtained, even for a very coarse subdivision of the beam.
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Kanwar K. Kapur (1966) studied this question.
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