Vibration frequencies of functionally graded cylindrical and conical shells

In recent years functionally graded materials (FGM) are used in many engineering applications. A FGM shell 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 shell. An optimal distribution of material properties may be obtained. The shell 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 using the exact element method. Exact vibration frequencies and modes are given for several examples.