Free Vibration Analysis of Functionally Graded Elliptical Plates

This paper deals with a free vibration analysis of functionally graded elliptical plates with different classical boundary conditions on the basis of polynomial-Ritz method and classical plate theory. The proposed admissible function is capable to obtain accurate natural frequencies of various classical boundary conditions namely, clamped, free and simply supported edges. The mechanical properties of the FG plate are assumed to vary continuously through the thickness of the plate and obey a power law distribution of the volume fraction of the constituents. The convergency of applied polynomial-Ritz method is investigated. In order to verify the accuracy of the present solution, a comprehensive comparison study is performed with the available results in the literature for homogeneous elliptical plate and FG circular plate. Also, the numerical results of the present solution for FG elliptical plate are compared with those of the finite element method (FEM). Finally, the effects of the plate geometry and inhomogeneity on the natural frequencies are investigated and some vibrational mode shapes related to symmetric-symmetric, symmetric-antisymmetric, antisymmetric- symmetric and antisymmetric- antisymmetric states are presented.