Free vibration of FGM plates with in-plane material inhomogeneity

An analysis is presented for the free vibration of a functionally graded isotropic elastic rectangular plate with in-plane material inhomogeneity. A Levy-type solution is obtained for plates with a pair of simply supported edges that are parallel with the material gradient direction. A particular integration method is adopted to solve the fourth-order ordinary differential equation with non-constant coefficients. The efficiency and accuracy of the analysis are demonstrated through numerical examples.