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.

This article investigates the static behavior of Functionally graded plate under mechanical loads by using a new quasi 3D model. The theory is designated as fifth-order shear and normal deformation theory (FOSNDT). Properties of Functionally graded material are graded across the transverse direction by using the rule of mixture i. e. power-law. The effect of thickness stretching is considered to develop the present theory. In this theory, axial and transverse displacement components respectively involve fifth-order and fourth-order shape functions to evaluate shear and normal strains. The theory involves nine unknowns. Zero transverse shear stress conditions are satisfied by employing constitutive relations. Analytical solutions are obtained by implementing the double Fourier series technique. The results predicted by the FOSNDT are compared with existing results. It is pointed out that the present theory is helpful for accurate structural analysis of isotropic and Functionally graded plates compared to other plate models.

Buckling analysis of rectangular Functionally graded plates with geometrical imperfections is studied in this paper the equilibrium, stability, and compatibility equations of an imperfect Functionally graded plate are derived using the first order shear deformation theory. It is assumed that the non-homogeneous mechanical properties of the plate, graded through the thickness, are described by a power function of the thickness variable. The plate is assumed to be under in-plane compressive load. Resulting equations are employed to obtain the closed-form solutions for the critical buckling load of an imperfect Functionally graded plate. The influence of transverse shear on buckling behavior of the plate is discussed. The results are validated with the known data in the literature.

Nonlinear forced vibrations of thin Functionally graded circular plates under classical clamped boundary conditions are investigated based on the classical plate theory. The von Karman strain-displacement relations are employed to include the geometrical nonlinearity caused by large transverse displacements of the order of the plate thickness. Modal expansion in polar coordinate system along with the perturbation method of multiple scales is used to solve the governing equations. The material properties are graded through the plate thickness according to a power-law distribution of the volume fraction of the constituents. Transverse forcing is supposed to be harmonic with the angular frequency near to the natural frequency of one particular asymmetric mode. Nonlinear vibration phenomena such as jump phenomenon and internal resonance are studied and the effects of boundary conditions, power-law distribution, amplitude and frequency of external load on dynamical behavior of circular plate are examined. The validity of results is established by comparison with the existing results in the literature as well as FEM results.

A theoretical formulation, of Navier solutions of rectangular plates based on a new higher order shear deformation model is presented for the static response of Functionally graded plates (FGPs). This theory enforces traction free boundary conditions at plate surfaces. Shear correction factors are not required because a correct representation of transverse shearing strain is given. Unlike any other theory, the number of unknown functions involved is only four, as against five in cases of other shear deformation theories. The mechanical properties of the plate are assumed to vary continuously in the thickness direction by a simple power-law distribution in terms of the volume fractions of the constituents. Numerical illustrations concern the flexural behavior of FG plates with metal-ceramic composition. Parametric studies are performed for varying ceramic volume fractions, volume fraction profiles, aspect ratios and length to thickness ratios. Results are verified with available results in the literature. It can be concluded that the proposed theory is accurate and simple in solving the static bending behavior of Functionally graded plates.