Based on the first-order shear deformation theory, this paper focuses on the free vibration behavior of two-dimensional functionally graded material truncated conical shells resting on Winkler–Pasternak foundations. The materials are assumed to be isotropic and inhomogeneous in the length and thickness directions of truncated conical shell. The material properties of the truncated conical shell are varied in these directions according to power law functions. The derived governing equations are solved using differential quadrature method. Convergence of this method is checked and the fast rate of convergence is observed. The primary results of this study are obtained for ( SS− SL), ( CS− CL), and ( CS− SL) boundary conditions and compared with those available in the literatures. Furthermore, effects of geometrical parameters, material power indexes, mechanical boundary conditions, Winkler and Pasternak foundation moduli on the nondimensional frequency parameters of the two-dimensional functionally graded material truncated conical shell are studied.

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Based on the First order Shear Deformation Theory (FSDT), the free vibration of the functionally graded (FG) truncated conical shells is analyzed. The truncated conical shell materials are assumed to be isotropic and inhomogeneous in the longitudinal direction. The twoconstituent (FG) shell consists of ceramic and metal. These constituents are graded through the length, from one end of the shell to the other end. Using Hamilton's principle the derived governing equations are solved using Differential Quadrature Method (DQM). Fast rate of convergence of this method is tested and its advantages over other existing solver methods are observed. The primary results of this study were obtained for four different ends boundary conditions and for some special cases acquire results were compared with those available in the * Graduate Student † Corresponding author, (Ali.Asanjarani@Gmail.com) Downloaded by [University of Connecticut] at 20:02 11 April 2015 ACCEPTED MANUSCRIPT ACCEPTED MANUSCRIPT 2 literature. Furthermore, effects of geometrical parameters, material graded power index, and boundary conditions on the natural frequencies of the FG truncated conical shell are carried out.

In this paper, free vibration of two-dimensional functionally graded (2D-FG) sectorial plate with variable thickness resting on Winkler–Pasternak elastic foundation has been studied. It is assumed that the plate properties vary continuously through its both circumference and thickness according to power law distribution of the volume fraction. Primarily, the motion equations have been derived based on first order shear deformation theory (FSDT). The numerical two-dimensional differential quadrature method (2D-DQM) has been employed to solve the motion equations. Four different kinds of boundary condition are considered. The effects of geometrical and elastic foundation parameters along with 2D-FG power indices effects on the natural frequencies have been studied. Also the frequency parameters of the sectorial plate with uniform, linear and nonlinear variation of thickness for various boundary conditions have been computed and the effects of variable thickness parameters on natural frequency have been investigated.