Free Vibration Analysis of Orthotropic FGM Cylinders by a Mesh-Free Method

In this paper, free vibration analysis of orthotropic functionally graded material (FGM) cylinders was carried out by a Mesh-Free method. In this analysis, moving least squares shape functions are used for approximation of displacement field in the weak form of equilibrium equation. Essential boundary conditions are imposed by transformation method. In this simulation, an axisymmetric model is used. The orthotropic FGM cylinders are assumed to be a mixture of two isotropic materials as fiber and matrix. The volume fraction of the fiber is changed in the radial direction. Consequently, mechanical properties of these cylinders are changed in the radial direction. Free vibration analysis of orthotropic 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 and other results from literature. Effects of various types of boundary conditions, geometrical parameters, and mechanical properties on the natural frequencies are studied.