Natural vibration of rectangular plates considered as tridimensional solids

A variational method developed by the authors (named WEM) for one- and two-dimensional boundary value problems is extended to three dimensions. The availability of a classical solution obtained through the inverse method, which is briefly included in an appendix, allows the confirmation of the exactness of the alternative solution herein presented. A prismatic solid supported by shear diaphragms at four consecutive faces is analysed in particular. The numerical values of natural transversal frequencies enable the evaluation of the degree of approximation involved in using Mindlin's theory for thick plates. Also, comparison is made with results from a three-dimensional Ritz formulation. (C) 1998 Academic Press Limited.