الفهرس 
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Abstract
Hamilton’s principle is applied to analyze the free lateral oscillations of two dimensional elastic models which are thin plates of regular polygonal boundary shapes. Based on the calculus of finite elements, the Lagrangian function is constructed . Firstly, it is assumed that the elastic deformations of the models are due to bending only . A high precision eighteen degrees of freedom triangular plate bending element - T18 is used. The constrained equations of motion are derived in a matrix form which represents a non-symmetric generalized eigenvalue problem. The convergence of the solutions is demonstrated by obtaining results for several different mesh divisions which comprise minimizing sequences. The present results are found to be in good agreement with those previously published in the literature. The found solutions in the literature are only available for special cases of isotropic and specially orthotropic plates that have uniform boundary conditions. In the present thesis, full mode solutions are obtained for isotropic as well as generally orthotropic and laminated plates that have some complex combinations of rigidly clamped, simply supported and free edge conditions. The effects of variation of both the composite filament angle and the orthotropic modulus ratio on the frequency coefficients have been investigated. The fundamental frequency coefficients are found to be monotonically increasing with the increase of the orthotropicity parameter while the results indicate a generally strong lack of monotonic dependence of the fiber angle.