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 Benferhat; Tahar Hassaine Daouadji; Mohamed Said Mansour

doi:10.1016/j.crme.2016.03.002

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 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

Comptes Rendus. Mécanique, Volume 344 (2016) no. 9, pp. 631-641.

Abstract

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.

Received: 2015-10-25
Accepted: 2016-03-05
Published online: 2016-07-09

DOI: 10.1016/j.crme.2016.03.002

Keywords: Functionally graded material, Analytical solution, Free vibration analysis, Neutral surface concept, Elastic foundation

Author's affiliations:

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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     author = {Rabia Benferhat and Tahar Hassaine Daouadji and Mohamed Said Mansour},
     title = {Free vibration analysis of {FG} plates resting on an elastic foundation and based on the neutral surface concept using higher-order shear deformation theory},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {631--641},
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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/

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