Analysis of Free Vibrations of Moderately Thick Cylindrical Shells Made of Functionally Graded Materials Using Differential Quadrature Method

In this paper vibration frequency characteristics of functionally graded cylindrical (FGM) shells are investigated using the differential quadrature method (DQM). The essence of the differential quadrature method is that the partial derivative of a smooth function with respect to a variable is approximated by a weighted sum of function values at all discrete points in that direction. Its weighting coefficients are not related to any special problem and only depend on the grid points and the derivative order. The material properties are graded in the thickness direction of the shell according to the volume fraction power law distribution. The fast convergence behavior of the method is demonstrated and its accuracy is verified by comparing the results with those of other shell theories obtained using conventional methods and also with those of ABAQUS software. Effects of the exponential volume fraction law on the natural frequencies of FGM cylindrical shells for classical boundary conditions (all possible combinations of clamped (C) and simply supported (S) boundary conditions) are studied against circumferential wave number, length to radius ratio and thickness to radius ratio for different values of power law exponents