Abstract
The present functionally graded cylindrical shell problem is shaped by taking into consideration the strain and kinetic energies of a vibrating cylindrical shell and is in the integral form. Calculus of variations is employed to change the integral expressions into the PDEs. This generates three differential equations in three unknown deformation displacement functions. The radial deflection is restrained by ring supports. This factor is expressed by the polynomial functions which carry the degree equal to the number of ring supports. The axial modal dependence is measured by characteristic beam functions which guarantee to fulfill edge conditions fixed both ends of a cylindrical shell. Energy variational approaches are widely exploited to research vibration cylindrical shells of cylindrical shells. The Galerkin technique is chosen to solve the present shell and the vibration shell frequency is attained in the eigenvalue form. The thickness is controlled with trigonometric fraction law. The behavior of various exponent of trigonometric function are observed with ring supports. The programming is performed in MATLAB software to study shell vibration characteristics. Results are shown in tabular forms. Their authenticity is verified by comparing them with other ones found in the literature.