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Free vibration analysis of functionally graded plates resting on Winkler–Pasternak elastic foundations using a new shear deformation theory

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Abstract

Free vibration analysis of simply supported functionally graded plates (FGP) resting on a Winkler–Pasternak elastic foundation are examined by a new higher shear deformation theory in this paper. Present theory exactly satisfies stress boundary conditions on the top and the bottom of the plate. The material properties change continuously through the thickness of the plate, which can vary according to power law, exponentially or any other formulations in this direction. The equation of motion for FG rectangular plates resting on elastic foundation is obtained through Hamilton’s principle. The closed form solutions are obtained by using Navier technique, and then fundamental frequencies are found by solving the results of eigenvalue problems. The numerical results obtained through the present analysis for free vibration of functionally graded plates on elastic foundation are presented, and compared with the ones available in the literature.

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Authors and Affiliations

  1. Département de Génie Civil, Faculté des Sciences de l’Ingénieur, Univesité Hassiba Benbouali de Chlef, Chlef, Algerie

    Hassen Ait Atmane

  2. Laboratoire des Matériaux et Hydrologie, Université de Sidi Bel Abbes, BP 89 Cité Ben M’hidi, 22000, Sidi Bel Abbes, Algérie

    Hassen Ait Atmane, Abdelouahed Tounsi, Ismail Mechab & El Abbas Adda Bedia

Authors
  1. Hassen Ait Atmane
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  2. Abdelouahed Tounsi
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  3. Ismail Mechab
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  4. El Abbas Adda Bedia
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Correspondence to Abdelouahed Tounsi.

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Ait Atmane, H., Tounsi, A., Mechab, I. et al. Free vibration analysis of functionally graded plates resting on Winkler–Pasternak elastic foundations using a new shear deformation theory. Int J Mech Mater Des 6, 113–121 (2010). https://doi.org/10.1007/s10999-010-9110-x

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  • DOI: https://doi.org/10.1007/s10999-010-9110-x

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