Elasticity solution for the free vibration analysis of two-dimensional functionally graded (2D-FGM) curved panels

As a first endeavor, the three-dimensional free vibration of two-dimensional functionally graded (2D-FGM) curved panels under various boundary conditions is presented. In the present formulation, the panels have a smooth variation of volume fraction in the radial and axial directions with power law functions. The study is carried out based on the three-dimensional, linear and small strain elasticity theory. In this work, panel is assumed to be simply supported at one pair of opposite edges and arbitrary boundary conditions at the other edges such that trigonometric functions expansion can be used to satisfy the boundary conditions precisely at simply supported edges. The generalized differential quadrature method (GDQM) as an efficient and accurate numerical tool is used to discretize the governing equations and to implement the boundary conditions. The convergence of the method is demonstrated and to validate the results, comparisons are made with the available solutions for conventional FGM curved panels. Results indicate the advantages of using functionally graded curved panels with graded volume fractions in two directions to a more flexible design. The effects of different boundary conditions, various geometrical parameters and volume fraction indices in radial and axial directions on the vibration characteristics of 2D-FGM curved panels are investigated.