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Free vibration response of functionally graded Porous plates using a higher-order Shear and normal deformation theory

  • Bennai, Riadh (Department of Civil Engineering, Faculty of Civil Engineering and Architecture, University of Hassiba Benbouali of Chlef) ;
  • Atmane, Hassen Ait (Department of Civil Engineering, Faculty of Civil Engineering and Architecture, University of Hassiba Benbouali of Chlef) ;
  • Ayache, Belqassim (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Tounsi, Abdelouahed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Bedia, E.A. Adda (Centre of Excellence for Advanced Materials Research, King Abdulaziz University) ;
  • Al-Osta, Mohammed A. (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals)
  • Received : 2018.10.04
  • Accepted : 2019.03.28
  • Published : 2019.05.25
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Abstract

In this work, a new analytical approach using a theory of a high order hyperbolic shear deformation theory (HSDT) has been developed to study the free vibration of plates of functionally graduated material (FGM). This theory takes into account the effect of stretching the thickness. In contrast to other conventional shear deformation theories, the present work includes a new displacement field that introduces indeterminate integral variables. During the manufacturing process of these plates defects can appear as porosity. The latter can question and modify the global behavior of such plates. The materials constituting the plate are assumed to be gradually variable in the direction of height according to a simple power law distribution in terms of the volume fractions of the constituents. The motion equations are derived by the Hamilton principle. Analytical solutions for free vibration analysis are obtained for simply supported plates. The effects of stretching, the porosity parameter, the power law index and the length / thickness ratio on the fundamental frequencies of the FGM plates are studied in detail.

Keywords

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