Exact vibration analysis of variable thickness thick annular isotropic and FGM plates

Annular plates are used in many engineering structures. In many cases variable thickness is used in order to save weight and improve structural characteristics. In recent years functionally graded materials (FGM) are used in many engineering applications. A FGM plate is an inhomogeneous composite made of two constituents (usually ceramic and metal), with both the composition and the material properties varying smoothly through the thickness of the plate. An optimal distribution of material properties may be obtained. The plate vibrations will have a strong bending-stretching coupling effect. The equations of motion including the effect of shear deformations using the first-order shear deformation theory are derived and solved exactly for various combinations of boundary conditions. The solution is obtained by using the exact element method. Exact vibration frequencies and modes are given for several examples for the first time.