Abstract
It is known that exploitation of the traditional superposition method for analyzing plate free vibration problems becomes a very demanding and difficult task when one moves from thin isotropic plate theory to be the thick plate Mindlin theory, and to the analysis of laminated plates. Difficulties arise because of the vast families of roots encountered, real and complex, when solving associated differential equations. The presence of hyperbolic functions tends to produce computer over-flow and under-flow and computational difficulties. In this paper, the modified Superposition-Galerkin method is introduced. All of the above problems are eliminated and excellent agreement is encountered when results obtained by both methods are compared.
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