A Comparison of Closed-Form and Finite-Element Solutions for the Free Vibration of Hybrid Crossply Laminated Plates

  • M. A. Benhenni
  • B. Adim
  • T. Hassaine Daouadji
  • B. AbbèsEmail author
  • F. Abbès
  • Y. Li
  • A. Bouzidane

The natural frequencies of hybrid cross-ply laminated plates are predicted using a high-order shear deformation theory and the three-dimensional finite-element analysis. The equations of motion for simply supported laminated hybrid rectangular plates are derived using the Hamilton principle. Closed-form solutions for antisymmetric cross-ply and angle-ply laminates are found employing the Navier solution. In the finite-element method, eight-node linear interpolation brick elements are used to model the composite plates. First, the analytical and numerical results are validated for an antisymmetric cross-ply square laminate by results available in the literature. Then, the effects of side-to-thickness ratio, aspect ratio, lamination schemes, and material properties on the fundamental frequencies for simply supported carbon/glass hybrid composite plates are investigated. Since no data are available in the literature for hybrid composite plates, the finite-element solution is used for comparison purposes. A comparison of the analytical solution with the corresponding 3D finite-element simulations shows a good accuracy of the proposed analytical solution in predicting the fundamental frequencies of hybrid cross-ply laminated plates.


hybrid composite plate high-order shear deformation theory 3D finite-element method free vibration 



This research was supported by the French Ministry of Foreign Affairs and International Development (MAEDI), Ministry of National Education, Higher Education and Research (MENESR), and the Algerian Ministry of Higher Education and Scientific Research under Grant No. PHC Tassili 17MDU992. Their support is greatly appreciated.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • M. A. Benhenni
    • 1
    • 2
    • 3
  • B. Adim
    • 1
    • 2
  • T. Hassaine Daouadji
    • 1
    • 2
  • B. Abbès
    • 3
    Email author
  • F. Abbès
    • 3
  • Y. Li
    • 3
  • A. Bouzidane
    • 1
  1. 1.Département de génie civilUniversité Ibn Khaldoun TiaretTiaretAlgeria
  2. 2.Laboratoire de Géomatique et Développement DurableUniversité Ibn Khaldoun TiaretTiaretAlgeria
  3. 3.GRESPI – University of Reims Champagne-ArdenneReims cedex 2France

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