Abstract
This work attempts to present comprehensive and accurate analytical results for the free vibration of rectangular plates. Twenty-one cases exist which involve the possible combinations of clamped, simply-supported, and free edge conditions. Exact characteristic equations are given for the six cases having two opposite sides simply-supported. The existence of solutions to the various characteristic equations is carefully delineated. The Ritz method is employed with 36 terms containing the products of beam functions to analyze the remaining 15 cases. Accurate frequency parameters are presented for a range of aspect ratios (a/b = 0·4, 2/3, 1·0, 1·5, and 2·5) for each case. For the last 15 cases, comparisons are made with Warburton's useful, approximate formulas. The effects of changing Poisson's ratio are studied.
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