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

Abstract

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.

Keywords

Free vibration FGM cylinder meshfree method MLS shape functions axisymmetric

Get full access to this article

View all access options for this article.

References

Koizumi

. The concept of FGM. Ceram Trans Func Grad Mater 1993; 34: 3–10.

Kashtalyan

. Three-dimensional elasticity solution for bending of functionally graded rectangular plates. Eur J Mech A – Solid 2004; 23: 853–864.

Loy

Lam

Reddy

. Vibration of functionally graded cylindrical shells. Int J Mech Sci 1999; 41: 309–324.

Pradhan

Loy

Reddy

. Vibration characteristics of functionally graded cylindrical shells under various boundary conditions. Appl Acoust 2000; 61: 111–129.

Kadoli

Ganesan

. Buckling and free vibration analysis of functionally graded cylindrical shells subjected to a temperature-specified boundary condition. J Sound Vib 2006; 289: 450–480.

Haddadpour

Mahmoudkhani

Navazi

. Free vibration analysis of functionally graded cylindrical shells including thermal effects. Thin-Walled Structures 2007; 45: 591–599.

Ansari

Darvizeh

. Prediction of dynamic behaviour of FGM shells under arbitrary boundary conditions. Compos Struct 2008; 85: 284–292.

Zhi-yuan

Hua-ning

. Free vibration of FGM cylindrical shells with holes under various boundary conditions. J Sound Vib 2007; 306: 227–237.

Allahverdizadeh

Naei

Bahrami

. Nonlinear free and forced vibration analysis of thin circular functionally graded plates. J Sound Vib 2008; 310: 966–984.

10.

Santos

Mota Soares

Reddy

. A semi-analytical finite element model for the analysis of cylindrical shells made of functionally graded materials. Compos Struct 2009; 91: 427–432.

11.

Hutchinson

. Axisymmetric vibrations of a free finite length rod. J Acoust Soc Am 1972; 51: 233–240.

12.

Leissa

. Accurate vibration frequencies of circular cylinders from three dimensional analysis. JAcoust Soc Am 1995; 98: 2136–2141.

13.

Zhou

Cheung

FTK

. 3D vibration analysis of solid and hollow circular cylinders via Chebyshev–Ritz method. Comput Methods Appl Mech Engrg 2003; 192: 1575–1589.

14.

Belytschko

. Element-free Galerkin methods. Int J Numer Methods Engrg 1994; 37: 229–256.

15.

Liu

Jun

Zhang

. Reproducing kernel particle methods. Int J Numer Methods Fluids 1995; 20: 1081–1106.

16.

Fernández-Méndez

Huerta

. Imposing essential boundary conditions in mesh-free methods. Comput Methods Appl Mech Engrg 2004; 193: 1257–1275.

17.

Chen

Wang

. Boundary condition treatment in mesh-free computation of contact problem. Comput Methods Appl Mech Engrg 2000; 187: 441–468.

18.

Lancaster

Salkauskas

. Surface generated by moving least squares methods. Math Comput 1981; 37: 141–158.

19.

Hutchinson

. Comments on “Accurate vibration frequencies of circular cylinders from three-dimensional analysis.”. J Acoust Soc Am 1995; 98: 2136–2141. JAcoust Soc Am 1996; 100: 1894–1895.

20.

Leissa

. Comparisons of vibration frequencies for rods and beams from 1D and 3D analysis. JAcoust Soc Am 1995; 98: 2122–2135.