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

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Mechanics of Composite Materials Aims and scope

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.

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Acknowledgments

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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Authors and Affiliations

  1. Département de génie civil, Université Ibn Khaldoun Tiaret, 14000, Tiaret, Algeria

    M. A. Benhenni, B. Adim, T. Hassaine Daouadji & A. Bouzidane

  2. Laboratoire de Géomatique et Développement Durable, Université Ibn Khaldoun Tiaret, Tiaret, Algeria

    M. A. Benhenni, B. Adim & T. Hassaine Daouadji

  3. GRESPI – University of Reims Champagne-Ardenne, Campus du Moulin de la Housse, BP 1039, 51687, Reims cedex 2, France

    M. A. Benhenni, B. Abbès, F. Abbès & Y. Li

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  1. M. A. Benhenni
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  2. B. Adim
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  3. T. Hassaine Daouadji
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  4. B. Abbès
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  5. F. Abbès
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  6. Y. Li
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  7. A. Bouzidane
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Correspondence to B. Abbès.

Additional information

Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 55, No. 2, pp. 259-276, March-April, 2019.

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Benhenni, M.A., Adim, B., Daouadji, T.H. et al. A Comparison of Closed-Form and Finite-Element Solutions for the Free Vibration of Hybrid Cross-Ply Laminated Plates. Mech Compos Mater 55, 181–194 (2019). https://doi.org/10.1007/s11029-019-09803-2

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  • DOI: https://doi.org/10.1007/s11029-019-09803-2

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