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In this paper, three dimensional frequency analysis of moderately thick plate with considering the effect of a circular hole is presented by using of Three Dimensional theory of Elasticity and a numerical mesh-less method with radial point interpolation functions. Using this numerical method, the field variable (such as displacement) is interpolated just using nodes scattered in the plate domain. Because there is no relation between nodes, they can be scattered arbitrarily in the problem domain. The plate is made of a functionally graded material that is consists of two different phases of metal and ceramic. Mechanical properties of the plate change independently in the length, width and thickness directions of it using (according to) Mori-Tanaka model. The effects of radius of holes, different volume fraction exponents of functionally graded plate in three directions and different boundary conditions on natural frequencies of the plate is investigated by using of the code written in MATLAB and simulation in ABAQUS. The results have been compared with results in available papers and it shows the high accuracy of the method used in this present work.

Keywords: Frequency Analysis, Meshless method, Three- dimensional Elasticity Theory, Three- dimensional Functionally Graded Material

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