An analytical-type solution is developed for the free vibration analysis of rectangular plates with uniform elastic edge support symmetrically distributed about the plate central axes. Both linear elastic rotational and translational support are considered to act simultaneously. Rapid convergence is encountered. Because of the symmetry of the problem, the free vibration modes fall into three distinct families. Eigenvalues are tabulated for the first four modes of vibration of a square plate with identical stiffnesses on each edge and with various ratios of translational to rotational stiffnesses. This represents, to the author’s knowledge, the first comprehensive treatment of this problem.
A Comprehensive Study of the Free Vibration of Rectangular Plates Resting on Symmetrically-Distributed Uniform Elastic Edge Supports
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Gorman, D. J. (December 1, 1989). "A Comprehensive Study of the Free Vibration of Rectangular Plates Resting on Symmetrically-Distributed Uniform Elastic Edge Supports." ASME. J. Appl. Mech. December 1989; 56(4): 893–899. https://doi.org/10.1115/1.3176188
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