Free Vibration Analysis of Thin and Relatively Thick Two Dimensional Functionally Graded Cylindrical Shell Based on First Order Shear Deformation Theory

In this paper, the free vibration of a two dimensional functionally graded (2D-FG) cylindrical shell is studied. The mechanical properties of the material alter continuously through its both length and thickness of cylindrical shell based on the power law distribution of volume fraction. The governing equations of motion are achieved by using Hamilton’s principal based on the first order shear deformation theory. Since there is no closed form solution, the generalized differential quadrature (GDQ) method is applied for solving equations with assuming simply supported for both end of cylindrical shell. To verify the results, they are compared with the finite element analysis and the results of other literatures. It is shown there is a good agreement between the results. Finally, the effects of shell geometry parameters and the volume fraction exponent on the natural frequencies and the mode shapes of 2D-FG cylindrical shell are investigated. The results show that the natural frequencies of the 2D-FG cylindrical shells are higher than the conventional FG cylindrical shells at the same geometric conditions. In fact, the natural frequency of 2D-FG cylindrical shell can be controlled using more parameters and proper selection of basic material.