Summary
A membrane analogy is presented for eigenvalue problems of simply supported Mindlin plates of arbitrary polygonal planform. Influence of hydrostatic inplane forces and Pasternak-type foundation of the plate domain is taken into account. Analytical results are derived in a non-dimensional form, which — using the analogous membrane eigenvalues as parameters — is independent of the special shape of the plate.
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Irschik, H. Membrane-type eigenmotions of Mindlin plates. Acta Mechanica 55, 1–20 (1985). https://doi.org/10.1007/BF01267975
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DOI: https://doi.org/10.1007/BF01267975