SHAPE EFFECT ON FREE VIBRATION OF FUNCTIONALLY GRADED PLATES

In this article, shape effect on free vibration behavior of functionally graded plates is investigated. Square, rectangular, skew, circular, elliptical, annular and equilateral triangular plates with the same surface area and thickness are considered. Frequency values of these plates are compared for simply supported and clamped boundary conditions. Finite element method (FEM) is used in calculating frequency values and mode shapes. Since commercial codes do not allow inputting functionally graded material properties directly, MATLAB code was developed for FEM solution. Findings of this study can be useful for designers that have freedom to choose the plate shape in engineering applications

[1]  Hiroyuki Matsunaga,et al.  Free vibration and stability of functionally graded circular cylindrical shells according to a 2D higher-order deformation theory , 2009 .

[2]  Mahmoud Kadkhodaei,et al.  Buckling analysis of rectangular functionally graded plates under various edge conditions using Fourier series expansion , 2013 .

[3]  K. K. Shukla,et al.  Geometrically nonlinear static and dynamic analysis of functionally graded skew plates , 2013, Commun. Nonlinear Sci. Numer. Simul..

[4]  A. Saidi,et al.  An explicit exact analytical approach for free vibration of circular/annular functionally graded plates bonded to piezoelectric actuator/sensor layers based on Reddy’s plate theory , 2013 .

[5]  Abdolreza Ohadi,et al.  Three-dimensional free vibration of variable thickness thick circular and annular isotropic and functionally graded plates on Pasternak foundation , 2011 .

[6]  S. Hosseini-Hashemi,et al.  A NOVEL APPROACH FOR IN-PLANE/OUT-OF-PLANE FREQUENCY ANALYSIS OF FUNCTIONALLY GRADED CIRCULAR/ANNULAR PLATES , 2010 .

[7]  Zheng Zhong,et al.  Dynamic analysis of multi-directional functionally graded annular plates , 2010 .

[8]  Da-Guang Zhang,et al.  Non-linear bending analysis of super elliptical thin plates , 2013 .

[9]  G. J. Nie,et al.  SEMI-ANALYTICAL SOLUTION FOR THREE-DIMENSIONAL VIBRATION OF FUNCTIONALLY GRADED CIRCULAR PLATES , 2007 .

[10]  M. Ganapathi,et al.  Thermal buckling of simply supported functionally graded skew plates , 2006 .

[11]  S. Hosseini-Hashemi,et al.  Study on the free vibration of thick functionally graded rectangular plates according to a new exact closed-form procedure , 2011 .

[12]  A. Allahverdizadeh,et al.  Nonlinear free and forced vibration analysis of thin circular functionally graded plates , 2008 .

[13]  S. Hosseini-Hashemi,et al.  A new exact analytical approach for free vibration of Reissner–Mindlin functionally graded rectangular plates , 2011 .

[14]  Young-Wann Kim,et al.  TEMPERATURE DEPENDENT VIBRATION ANALYSIS OF FUNCTIONALLY GRADED RECTANGULAR PLATES , 2005 .

[15]  A. Saidi,et al.  Vibration analysis of functionally graded rectangular plates resting on elastic foundation using higher-order shear and normal deformable plate theory , 2013 .

[16]  M. H. Yas,et al.  Free vibration analysis of functionally graded annular plates by state-space based differential quadrature method and comparative modeling by ANN , 2012 .

[17]  A. Allahverdizadeh,et al.  Vibration amplitude and thermal effects on the nonlinear behavior of thin circular functionally graded plates , 2008 .

[18]  Masoud Derakhshani,et al.  An accurate mathematical study on the free vibration of stepped thickness circular/annular Mindlin functionally graded plates , 2013 .

[19]  B. P. Patel,et al.  Free vibration analysis of functionally graded elliptical cylindrical shells using higher-order theory , 2005 .

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

[21]  M. Ganapathi,et al.  Nonlinear free flexural vibrations of functionally graded rectangular and skew plates under thermal environments , 2005 .

[22]  A. Houmat,et al.  Nonlinear free vibration of functionally graded shear deformable sector plates by a curved triangular p-element , 2012 .

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

[24]  Lin-Tsang Lee,et al.  An inverse problem for a functionally graded elliptical plate with large deflection and slightly disturbed boundary , 2006 .

[25]  J. Reddy.  Mechanics of laminated composite plates and shells : theory and analysis , 1996 .

[26]  M. K. Singha,et al.  Nonlinear vibration of symmetrically laminated composite skew plates by finite element method , 2007 .

[27]  Seyit Çeribaşı,et al.  Static analysis of superelliptical clamped plates by Galerkin's method , 2008 .

[28]  K. M. Liew,et al.  A local Kriging meshless method for free vibration analysis of functionally graded circular plates in thermal environments , 2012 .

[29]  O. G. McGee,et al.  Three-dimensional vibrations of cracked rectangular parallelepipeds of functionally graded material , 2013 .

[30]  Ali Asghar Atai,et al.  A THEORETICAL ANALYSIS OF SMART MODERATELY THICK SHEAR DEFORMABLE ANNULAR FUNCTIONALLY GRADED PLATE , 2009 .