NATURAL FREQUENCIES OF FUNCTIONALLY GRADED PLATES BASED ON REFINED HIGHER-ORDER SHEAR DEFORMATION THEORY

Abstract This study introduces an efficient shear strain theory for analyzing the vibration of functionally graded plates. The theory incorporates the parabolic distribution of transverse shear strains using a new hyperbolic warping function and meets zero-tension boundary conditions on the plate surfaces without employing shear correction factors. The mechanical properties of functionally graded plates are assumed to vary following a power-law distribution of the constituent volume fractions. The equations of motion are derived using the principle of variational energy and virtual work. Analytical solutions for the natural frequency are obtained for simply supported plates. The accuracy of these solutions is validated by comparing the results with those predicted by classical theory, first-order shear deformation theory, and higher-order shear deformation theory. It can be concluded that the proposed theory is both accurate and straightforward for predicting the natural frequencies of functionally graded plates.