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On wave dispersion properties of functionally graded plates resting on elastic foundations using quasi-3D and 2D HSDT

  • Bennai, Riadh (Department of Civil Engineering, Faculty of Civil Engineering and Architecture, University Hassiba Benbouali of Chlef) ;
  • Mellal, Fatma (Laboratory of Structures, Geotechnics and Risks, Department of Civil Engineering, Hassiba Benbouali University of Chlef) ;
  • Nebab, Mokhtar (Laboratory of Structures, Geotechnics and Risks, Department of Civil Engineering, Hassiba Benbouali University of Chlef) ;
  • Fourn, Hocine (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Benadouda, Mourad (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Atmane, Hassen Ait (Department of Civil Engineering, Faculty of Civil Engineering and Architecture, University Hassiba Benbouali of Chlef) ;
  • Tounsi, Abdelouahed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Hussain, Muzamal (Department of Mathematics, Govt. College University Faisalabad)
  • Received : 2020.12.29
  • Accepted : 2022.04.18
  • Published : 2022.05.25
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Abstract

In this article, wave propagation in functional gradation plates (FG) resting on an elastic foundation with two parameters is studied using a new quasi-three-dimensional (3D) higher shear deformation theory (HSDT). The new qausi-3D HSOT has only five variables in fields displacement, which means has few numbers of unknowns compared with others quasi-3D. This higher shear deformation theory (HSDT) includes shear deformation and effect stretching with satisfying the boundary conditions of zero traction on the surfaces of the FG plate without the need for shear correction factors. The FG plates are considered to rest on the Winkler layer, which is interconnected with a Pasternak shear layer. The properties of the material graded for the plates are supposed to vary smoothly, with the power and the exponential law, in the z-direction. By based on Hamilton's principle, we derive the governing equations of FG plates resting on an elastic foundation, which are then solved analytically to obtain the dispersion relations. Numerical results are presented in the form of graphs and tables to demonstrate the effectiveness of the current quasi-3D theory and to analyze the effect of the elastic foundation on wave propagation in FG plates.

Keywords

References

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