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

Riadh Bennai , Fatma Mellal , Mokhtar Nebab , Hocine Fourn , Mourad Benadouda , Hassen Ait Atmane , Abdelouahed Tounsi , Muzamal Hussain

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 quasi3D. 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.

Key Words

dynamics responses advanced composite plates; quasi-3D theory; variables elastic foundations

Address

Riadh Bennai — 1)Department of Civil Engineering, Faculty of Civil Engineering and Architecture, University Hassiba Benbouali of Chlef, Algeria 2)Laboratory of Structures, Geotechnics and Risks, Department of Civil Engineering, Hassiba Benbouali University of Chlef, Algeria
Fatma Mellal — 1)Laboratory of Structures, Geotechnics and Risks, Department of Civil Engineering, Hassiba Benbouali University of Chlef, Algeria 2)Department of Technology, Faculty of Science and Technology, Djilali Bounaama University, Khemis Miliana, Algeria
Mokhtar Nebab — 1)Laboratory of Structures, Geotechnics and Risks, Department of Civil Engineering, Hassiba Benbouali University of Chlef, Algeria 2)Department of Civil Engineering, Faculty of Sciences, University of M'Hamed BOUGARA Boumerdes, Algeria
Hocine Fourn — Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria
Mourad Benadouda — Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria
Hassen Ait Atmane — 1)Department of Civil Engineering, Faculty of Civil Engineering and Architecture, University Hassiba Benbouali of Chlef, Algeria 2)Laboratory of Structures, Geotechnics and Risks, Department of Civil Engineering, Hassiba Benbouali University of Chlef, Algeria
Abdelouahed Tounsi — 1)Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria 2)YFL (Yonsei Frontier Lab), Yonsei University, Seoul, Korea 3)Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia
Muzamal Hussain — Department of Mathematics, Govt. College University Faisalabad, 38000, Faisalabad, Pakistan

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