Structural Engineering and Mechanics

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A simple analytical model for free vibration and buckling analysis of orthotropic rectangular plates

  • Sellam, Souad (LMPM, Department of Mechanical Engineering, University of Sidi Bel Abbes) ;
  • Draiche, Kada (Department of Civil Engineering, Ibn Khaldoun University) ;
  • Tlidji, Youcef (Department of Civil Engineering, Ibn Khaldoun University) ;
  • Addou, Farouk Yahia (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Benachour, Abdelkader (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
  • Received : 2019.12.31
  • Accepted : 2020.02.12
  • Published : 2020.07.25
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Abstract

In the present paper, a simple analytical model is developed based on a new refined parabolic shear deformation theory (RPSDT) for free vibration and buckling analysis of orthotropic rectangular plates with simply supported boundary conditions. The displacement field is simpler than those of other higher-order theories since it is modeled with only two unknowns and accounts for a parabolic distribution of the transverse shear stress through the plate thickness. The governing differential equations related to the present theory are obtained from the principle of virtual work, while the solution of the eigenvalue problem is achieved by assuming a Navier technique in the form of a double trigonometric series that satisfy the edge boundary conditions of the plate. Numerical results are presented and compared with previously published results for orthotropic rectangular plates in order to verify the precision of the proposed analytical model and to assess the impacts of several parameters such as the modulus ratio, the side-to-thickness ratio and the geometric ratio on natural frequencies and critical buckling loads. From these results, it can be concluded that the present computations are in excellent agreement with the other higher-order theories.

Keywords

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