Free vibration of three-layer circular cylindrical shells with functionally graded middle layer

We study free vibrations of a simply supported three-layer circular cylindrical shell with the inner and the outer layers made of the same homogeneous material and the middle layer composed of a functionally graded material. We use Flügge's shell theory to derive governing equations, express mid-plane displacements in terms of trigonometric functions that identically satisfy the boundary conditions, and compute natural frequencies in terms of the geometrical and the material parameters. Computed results show that the fundamental natural frequency decreases with an increase in the radius-to-thickness ratio, and increases with an increase in the ratio of Young's modulus at the mid-surface to that of the outer (or the inner) layer.