Nonlinear free vibration of functionally graded doubly curved shear deformable panels using finite element method

Abstract

Nonlinear free vibration responses of functionally graded single/doubly curved shell panels are computed based on higher order shear deformation theory and Green-Lagrange type nonlinearity. The material properties of functionally graded materials are obtained based on the Voigt model in conjunction with power-law distribution for a smooth variation of material along with the thickness coordinate. The governing equation of the vibrated curved panel has been obtained using Hamilton’s principle. The model has been discretized using a nine node quadrilateral Lagrangian shell element and solved numerically using a direct iterative method. The convergence and comparison behavior of the nonlinear model has been checked by comparing the responses with the published literature. The influence of the power-law index, curvature ratio, thickness ratio, aspect ratio, amplitude ratio and support conditions on the nonlinear responses of cylindrical, elliptical and hyperbolic shell panels are discussed.