Analysis of free vibration of functionally graded material (FGM) cylinders by a meshless method

In the present work, a new axisymmetric weak form meshless method is presented for analysis of free vibration of functionally graded material (FGM) cylinders. This method is based on weak form of equilibrium equation and moving least squares (MLS) approximation. Essential boundary conditions are imposed by transformation method. In this method, shape functions that do not satisfy the Kronecker delta condition are corrected, then essential boundary conditions are imposed easily as in the finite element method (FEM). In the present work, the material is assumed to be functionally graded in the radial direction. Variations in the material properties such as Young's modulus and Poisson's ratio may be arbitrary functions of the radial coordinate. The FGM cylinder material varies continuously from silicon carbide (SiC) on the inner surface to stainless steel (SUS304) on the outer surface. Free vibration analysis of FGM cylinders with any arbitrary combination of boundary conditions is possible by the proposed model. Natural frequencies obtained from the presented model are in good agreement with results of finite element simulation. Effects of various types of boundary conditions, geometrical parameters, and mechanical properties on the natural frequencies are studied.