Analysis of free vibration of functionally graded material cylinders by Hermitian collocation meshless method. Issue 2 (3rd May 2016) - Foroutan, M.; Shirzadi, N.
Abstract: In the present work, a new axisymmetric Hermitian collocation meshless method is presented for analysis of free vibration of functionally graded material (FGM) cylinders. This method is based on strong form of equilibrium equation and Hermitian moving least squares approximation. Collocation method is purely meshless and numerical integration is not needed in this method. But this method has difficulty of instability in analysis of P.D.E.s with natural boundary conditions. In the present work, Hermitian shape functions were used to overcome this difficulty. 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 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 a good agreement with analytical solutions. Effect of various types of boundary conditions, geometrical parameters and mechanical properties on the natural frequencies are studied.