Abstract
Natural frequencies and buckling loads of a simply supported thick plate subjected to in-plane initial tensile and/or compressive forces are analysed. By using the method of power series expansion of displacement components, a set of fundamental dynamic equations of a two-dimensional higher-order plate theory is derived through Hamilton's principle. Several sets of truncated approximate theories are applied to solve the eigenvalue problems of a thick plate. In order to assure the accuracy of the present theory, convergence properties of the minimum natural frequency and the buckling load for the out-of-plane problem of a simply supported square plate are examined in detail. It is noticed that the present approximate theories can predict the frequencies and buckling loads of an extremely thick plate more accurately compared to other refined theories and classical plate theory.
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