Eigenfrequencies of Continuous Plates With Arbitrary Number of Equal Spans

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Abstract
An approximate analytical technique is developed for determination of the eigenfrequencies of rectangular isotropic plates continuous over rigid supports at regular intervals with arbitrary number of spans. All possible combinations of simple support and clamping at the edges are considered. The solution is given by the modified Bolotin method, which involves solution of two problems of the Voigt-Le´vy type in conjunction with a postulated eigenfrequency/wave-number relationship. These auxiliary problems yield a pair of transcendental equations in the unknown wave numbers. The number of spans figures explicitly in one of the transcendental equations, so that numerical complexity does not increase with the number of spans. It is shown that the number of eigenfrequencies associated with a given pair of mode numbers equals that of spans. The essential advantage of the proposed method is the possibility of finding the eigenfrequencies for any prescribed pair of mode numbers. Moreover, for plates simply supported at two opposite edges and continuous over rigid supports perpendicular to those edges, the result is identical with the exact solution.

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