Abstract
Based on Mindlin's plate theory, it is presented a free vibration analysis of plates with a lumped mass. By using the method of superimposition, it is shown that solutions which satisfy both the differential equation and the boundary condition are obtained. The rectangular plates under consideration are as follows : a) all edges simply supported and b) all edges built-in. Eigenvalues of four digit accuracy are provided for a wide range of plate aspect ratio. Numerical results are compared with those by Rayleigh-Ritz method and interpolative values using Dunkerley's equation, to verify the accuracy of the proposed method.
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