Three-dimensional natural frequency analysis of anisotropic functionally graded annular sector plates resting on elastic foundations

Natural frequency analysis of anisotropic functionally graded material (FGM) annular sector plates on Winkler elastic foundations based on three-dimensional theory of elasticity was investigated. The three-dimensional graded finite element formulation was derived based on the principle of minimum potential energy and the Rayleigh-Ritz method. For an orthotropic FGM, the material properties were assumed to have in-plane polar orthotropy and transverse heterogeneity according to an exponential law, whereas the mass density was assumed to be constant. For an isotropic FGM, material properties varied continuously through the thickness direction according to a power-law distribution, whereas Poisson's ratio was set to be constant. The effects of material gradient exponents, different sector angles, different thickness ratio, Winkler parameter and two different boundary conditions on the natural frequencies and mode shapes of FGM annular sector plates have been investigated. Numerical solution was compared with the result of an FGM annular circular plate, which showed good agreement.