Analysis of free vibration of functionally graded material cylinders by Hermitian collocation meshless method

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.

Keywords:

• Free vibration
• FGM cylinder
• Mesh-free method
• Hermitian collocation

Notes on contributors

Foroutan has received his PhD in the field of mechanical engineering from Isfahan University of Technology in 2000. He has been working as a member of mechanical engineering department of Razi University since 2000. He is interested in static and dynamic analysis of FGM and composite structures by numerical methods, especially mesh-free methods. He has supervised several numbers of graduate students in this field at Razi University and published several numbers of papers in this field.

Navid Shirzadi has received his MS degree in Mechanical engineering from Razi University in 2011. He carried out his thesis in the field of free vibration analysis of FGM cylinders by mesh-free method under supervision of Foroutan. His research fields of interest are numerical methods, dynamic analysis and impact mechanics.

Disclosure statement

No potential conflict of interest was reported by the authors.