Comptes Rendus
no. 9
Free vibration analysis of FG plates resting on an elastic foundation and based on the neutral surface concept using higher-order shear deformation theory
Rabia Benferhat1 ; Tahar Hassaine Daouadji2  ; Mohamed Said Mansour1
1 Laboratoire de géomatériaux, Département de génie civil, Université de Chlef, Algérie
2 Département de génie civil, Université Ibn-Khaldoun, BP 78 Zaaroura, 14000 Tiaret, Algérie
Comptes Rendus. Mécanique, Volume 344 (2016) no. 9, pp. 631-641.

An analytical solution based on the neutral surface concept is developed to study the free vibration behavior of a simply supported functionally graded plate reposing on the elastic foundation by taking into account the effect of transverse shear deformations. No transversal shear correction factors are needed because a correct representation of the transversal shearing strain obtained by using a new refined shear deformation theory. The foundation is described by the Winkler–Pasternak model. The Young's modulus of the plate is assumed to vary continuously through the thickness according to a power law formulation, and the Poisson ratio is held constant. The equation of motion for FG rectangular plates resting on an elastic foundation is obtained through Hamilton's principle. Numerical examples are provided to show the effect of foundation stiffness parameters presented for thick to thin plates and for various values of the gradient index, aspect, and the side-to-thickness ratio. It was found that the proposed theory predicts the fundamental frequencies very well, consistently with those available in the literature.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2016.03.002
Mots clés : Functionally graded material, Analytical solution, Free vibration analysis, Neutral surface concept, Elastic foundation
Rabia Benferhat 1 ; Tahar Hassaine Daouadji 2 ; Mohamed Said Mansour 1

1 Laboratoire de géomatériaux, Département de génie civil, Université de Chlef, Algérie
2 Département de génie civil, Université Ibn-Khaldoun, BP 78 Zaaroura, 14000 Tiaret, Algérie 
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Rabia Benferhat; Tahar Hassaine Daouadji; Mohamed Said Mansour. Free vibration analysis of FG plates resting on an elastic foundation and based on the neutral surface concept using higher-order shear deformation theory. Comptes Rendus. Mécanique, Volume 344 (2016) no. 9, pp. 631-641. doi : 10.1016/j.crme.2016.03.002. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2016.03.002/

[1] M. Koizumi FGM activities in Japan, Composites, Part B, Eng., Volume 28B (1997), pp. 1-4

[2] A.D. Kerr Elastic and viscoelastic foundation models, ASME J. Appl. Mech., Volume 31 (1964) no. 3, pp. 491-498

[3] P.L. Pasternak, Gosudarstvennoe Izdatelstvo Literaturi po Stroitelstvu i Arkhitekture, Moscow, USSR (1954), pp. 1-56

[4] Y. Xiang; C.M. Wang; S. Kitipornchai Exact vibration solution for initially stressed Mindlin plates on Pasternak foundation, Int. J. Mech. Sci., Volume 36 (1994), pp. 311-316

[5] D. Zhou; Y.K. Cheung; S.H. Lo; F.T.K. Au Three-dimensional vibration analysis of rectangular thick plates on Pasternak foundations, Int. J. Numer. Methods Eng., Volume 59 (2004) no. 10, pp. 1313-1334

[6] J.N. Reddy Analysis of functionally graded plates, Int. J. Numer. Methods Eng., Volume 47 (2000), pp. 663-684

[7] Senthil S. Vel; R.C. Batra Exact solution for thermoelastic deformations of functionally graded thick rectangular plates, AIAA J., Volume 40 (2002) no. 7

[8] Mohammad Talha; B.N. Singh Static response and free vibration analysis of FGM plates using higher order shear deformation theory, Appl. Math. Model., Volume 34 (2010), pp. 3991-4011

[9] A.J.M. Ferreira; R.C. Batra; C.M.C. Roque; L.F. Qian; P.A.L.S. Martins Static analysis of functionally graded plates using third-order shear deformation theory and a meshless method, Compos. Struct., Volume 69 (2005), pp. 449-457

[10] F. Ramirez; P.R. Heyliger; E. Pan Static analysis of functionally graded elastic anisotropic plates using a discrete layer approach, Composites, Part B, Eng., Volume 37 (2006), pp. 10-20

[11] Jae-Sang Park; Ji-Hwan Kim Thermal postbuckling and vibration analyses of functionally graded plates, J. Sound Vib., Volume 289 (2006), pp. 77-93

[12] G.N. Praveen; J.N. Reddy Nonlinear transient thermoelastic analysis of functionally graded ceramic–metal plates, Int. J. Solids Struct., Volume 35 (1998), pp. 4457-4476

[13] D.G. Zhang; Y.H. Zhou A theoretical analysis of FGM thin plates based on physical neutral surface, Comput. Mater. Sci., Volume 44 (2008), pp. 716-720

[14] S. Hosseini-Hashemi; M. Fadaee; H. Rokni Damavandi Taher Exact solutions for free flexural vibration of Lévy-type rectangular thick plates via third-order shear deformation plate theory, Appl. Math. Model., Volume 35 (2011), pp. 708-727

[15] D. Zhou; Y.K. Cheung; F.T.K. Au; S.H. Lo Three-dimensional vibration analysis of thick rectangular plates using Chebyshev polynomial and Ritz method, Int. J. Solids Struct., Volume 39 (2002), pp. 6339-6353

[16] H. Matsunaga Free vibration and stability of functionally graded plates according to a 2-D higher-order deformation theory, Compos. Struct., Volume 82 (2008), pp. 499-512

[17] A.W. Leissa The free vibration of rectangular plates, J. Sound Vib., Volume 31 (1973) no. 3, pp. 257-293

[18] F.L. Liu; K.M. Liew Analysis of vibrating thick rectangular plates with mixed boundary constraints using differential quadrature element method, J. Sound Vib., Volume 225 (1999) no. 5, pp. 915-934

[19] X. Zhao; Y.Y. Lee; K.M. Liew Free vibration analysis of functionally graded plates using the element-free kp-Ritz method, J. Sound Vib., Volume 319 (2009), pp. 918-939

[20] S.S. Akavci An efficient shear deformation theory for free vibration of functionally graded thick rectangular plates on elastic foundation, Compos. Struct., Volume 108 (2014), pp. 667-676

[21] H. Akhavan; Sh. Hosseini Hashemi; H. Rokni Damavandi Taher; A. Alibeigloo; Sh. Vahabi Exact solutions for rectangular Mindlin plates under in-plane loads resting on Pasternak elastic foundation. Part II: frequency analysis, Comput. Mater. Sci., Volume 44 (2009), pp. 951-961

[22] A. Hassen; T. Abdelouahed; M. Ismail; A.B. El Abbas Free vibration analysis of functionally graded plates resting on Winkler–Pasternak elastic foundations using a new shear deformation theory, Int. J. Mech. Mater. Des., Volume 6 (2010), pp. 113-121

[23] H.T. Thai; D.H. Choi A refined shear deformation theory for free vibration of functionally graded plates on elastic foundation, Composites, Part B, Eng., Volume 43 (2012), pp. 2335-2347

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