Free vibration analysis of functionally graded thin annular sector plates using the differential quadrature method

In this article, the differential quadrature method (DQM) is used to study the free vibration of functionally graded (FG) thin annular sector plates. The material properties of the FG-plate are assumed to vary continuously through the thickness, according to the power-law distribution. The governing differential equations of motion are derived based on the classical plate theory and solved numerically using DQM. The natural frequencies of thin FG annular sector plates under various combinations of clamped, free, and simply supported boundary conditions are presented for the first time. To ensure the accuracy of the method, the natural frequencies of a pure metallic plate are calculated and compared with those existing in the literature for the homogeneous plate. In this case, the result shows very good agreement. For the FG-plates, the effects of boundary conditions, volume fraction exponent, and variation of Poisson's ratio on the free vibrational behaviour of the plate are studied.

[1]  Serge Abrate,et al.  FUNCTIONALLY GRADED PLATES BEHAVE LIKE HOMOGENEOUS PLATES , 2008 .

[2]  Hui-Shen Shen,et al.  VIBRATION CHARACTERISTICS AND TRANSIENT RESPONSE OF SHEAR-DEFORMABLE FUNCTIONALLY GRADED PLATES IN THERMAL ENVIRONMENTS , 2002 .

[3]  R. Bellman,et al.  DIFFERENTIAL QUADRATURE AND LONG-TERM INTEGRATION , 1971 .

[4]  G. Geiger.  CERAMICS COATINGS : ENHANCE MATERIAL PERFORMANCE , 1992 .

[5]  C. Bert,et al.  Two new approximate methods for analyzing free vibration of structural components , 1988 .

[6]  J. N. Reddy,et al.  Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates , 1998 .

[7]  S. Sahraee.  Bending analysis of functionally graded sectorial plates using Levinson plate theory , 2009 .

[8]  Charles W. Bert,et al.  Differential quadrature: a powerful new technique for analysis of composite structures , 1997 .

[9]  S. Vel,et al.  Three-dimensional exact solution for the vibration of functionally graded rectangular plates , 2004 .

[10]  Chun-Sheng Chen.  Nonlinear vibration of a shear deformable functionally graded plate , 2005 .

[11]  M. R. Eslami,et al.  BUCKLING ANALYSIS OF CIRCULAR PLATES OF FUNCTIONALLY GRADED MATERIALS UNDER UNIFORM RADIAL COMPRESSION , 2002 .

[12]  Hui-Shen Shen,et al.  Dynamic response of initially stressed functionally graded rectangular thin plates , 2001 .

[13]  C. Bert,et al.  Differential Quadrature Method in Computational Mechanics: A Review , 1996 .

[14]  A. Evans,et al.  On the Role of Imperfections in The Failure of a Thermal Barrier Coating Made by Electron Beam Deposition , 2000 .

[16]  S. R. Atashipour,et al.  An analytical approach for stress analysis of functionally graded annular sector plates , 2009 .

[17]  R. Ramakrishnan,et al.  Free vibration of annular sector plates , 1973 .

[18]  Yang Xiang,et al.  TRANSVERSE VIBRATION OF THICK ANNULAR SECTOR PLATES , 1993 .

[19]  J. Tinsley Oden,et al.  Functionally graded material: A parametric study on thermal-stress characteristics using the Crank-Nicolson-Galerkin scheme , 2000 .

[20]  Serge Abrate,et al.  Free vibration, buckling, and static deflections of functionally graded plates , 2006 .

[21]  Akbar Alibeigloo,et al.  DIFFERENTIAL QUADRATURE ANALYSIS OF FUNCTIONALLY GRADED CIRCULAR AND ANNULAR SECTOR PLATES ON ELASTIC FOUNDATION , 2010 .

[22]  K. Liew,et al.  Active control of FGM plates with integrated piezoelectric sensors and actuators , 2001 .

[23]  K. M. Liew,et al.  Free vibration analysis of functionally graded plates using the element-free kp-Ritz method , 2009 .

[24]  Anthony G. Evans,et al.  Mechanisms controlling the durability of thermal barrier coatings , 2001 .

[25]  J. Hutchinson,et al.  Buckling of Bars, Plates and Shells , 1975 .

[26]  E. Jomehzadeh,et al.  On the analytical approach for the bending/stretching of linearly elastic functionally graded rectangular plates with two opposite edges simply supported , 2009 .

[27]  Xinwei Wang,et al.  FREE VIBRATION ANALYSES OF THIN SECTOR PLATES BY THE NEW VERSION OF DIFFERENTIAL QUADRATURE METHOD , 2004 .

[28]  Tapabrata Ray,et al.  On the use of computational intelligence in the optimal shape control of functionally graded smart plates , 2004 .

[29]  G. Karami,et al.  Application of a new differential quadrature methodology for free vibration analysis of plates , 2003 .

[30]  Zheng Zhong,et al.  Vibration analysis of functionally graded annular sectorial plates with simply supported radial edges , 2008 .

[31]  M. Koizumi.  FGM activities in Japan , 1997 .

[32]  S. Timoshenko,et al.  Theory of elasticity , 1975 .

[33]  S. M. Dickinson,et al.  On the free, transverse vibration of annular and circular, thin, sectorial plates subject to certain complicating effects , 1989 .