Free vibration analysis of laminated composite and functionally graded sector plates with general boundary conditions

A modified Fourier series method is applied to study the free vibration of laminated composite and four-parameter functionally graded sector plates with general boundary conditions. The first-order shear deformation plate theory is employed to include the effects of rotary inertias and shear deformation. Regardless of the boundary conditions, each of the displacement and rotation components of the sector plates is described as a linear superposition of a double Fourier cosine series and several supplementary functions introduced to accelerate the convergence of series representations. The Rayleigh–Ritz procedure based on the energy functions of the sector plates is adopted to solve the exact solutions. In order to verify the accuracy and reliability of the present method, comparisons of the present results with those published are presented. New numerical results for laminated composite and functionally graded sector plates with elastic restraints are given. The effects of the boundary conditions and material and geometrical properties on the frequencies of the sector plates are investigated.