A novel four variable refined plate theory for wave propagation in functionally graded material plates

Hocine Fourn , Hassen Ait Atmane , Mohamed Bourada , Abdelmoumen Anis Bousahla , Abdelouahed Tounsi , S.R. Mahmoud

Abstract

In This work an analysis of the propagation of waves of functionally graduated plates is presented by using a high order hyperbolic (HSDT) shear deformation theory. This theory has only four variables, which is less than the theory of first order shear deformation (FSDT). Therefore, a shear correction coefficient is not required. Unlike other conventional shear deformation theories, the present work includes a new field of displacement which introduces indeterminate integral variables. The properties of materials are supposed classified in the direction of the thickness according to two simple distributions of a power law in terms of volume fractions of constituents. The governing equations of the wave propagation in the functionally graded plate are derived by employing the Hamilton's principle. The analytical dispersion relation of the functionally graded plate is obtained by solving an eigenvalue problem. The convergence and the validation of the proposed theoretical numerical model are performed to demonstrate the efficacy of the model.

Key Words

wave propagation; phase velocity; vibration; functionally graded plate; plate theory; porosity

Address

(1) Hocine Fourn, Mohamed Bourada, Abdelouahed Tounsi — Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria
(2) Hassen Ait Atmane — Advanced Materials and Structures Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria
(3) Hassen Ait Atmane — Département de génie civil, Faculté de génie civil et d'architecture, Univesité Hassiba Benbouali de Chlef, Algérie
(4) Abdelmoumen Anis Bousahla — Laboratoire de Modélisation et Simulation Multi-échelle, Université de Sidi Bel Abbés, Algeria
(5) Abdelmoumen Anis Bousahla — Centre Universitaire de Relizane, Algérie
(6) Abdelouahed Tounsi — Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia
(7) S.R. Mahmoud — Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia.

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