A new fourth-order shear deformation theory for the free vibration analysis of functionally graded rectangular plates

A new fourth-order shear deformation theory is introduced for the free vibration analysis of simply supported functionally graded rectangular plates. Using the Hamilton principle, the governing equation of motion has been achieved. Navier solutions have been considered to satisfy the boundary conditions using a double Fourier series expansion. This theory is valid for thick and thin plates, and for arbitrary variation of material properties in the thickness direction. The numerical results have been presented and compared with the referenced articles.