On the wave dispersion and vibration characteristics of FG plates resting on elastic Kerr foundations via HSDT

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

Abstract

In this article, vibrational behavior and wave propagation characteristics in (FG) functionally graded plates resting on Kerr foundation with three parameters is studied using a 2D dimensional (HSDT) higher shear deformation theory. The new 2D higher shear deformation theory has only four variables in field's displacement, which means has few numbers of unknowns compared with others theories. The shape function used in this theory satisfies the nullity conditions of the shear stresses on the two surfaces of the FG plate without using shear correction factors. The FG plates are considered to rest on the Kerr layer, which is interconnected with a Pasternak-Kerr shear layer. The FG plate is materially inhomogeneous. The material properties are supposed to vary smoothly according to the thickness of the plate by a Voigt's power mixing law of the volume fraction. The equations of motion due to the dynamics of the plate resting on a three-parameter foundation are derived using the principle of minimization of energies; which are then solved analytically by the Navier technique to find the vibratory characteristics of a simply supported plate, and the wave propagation results are derived by using the dispersion relations. Perceivable numerical results are fulfilled to evaluate the vibratory and the wave propagation characteristics in functionally graded plates and some parameters such wave number, thickness ratio, power index and foundation parameters are discussed in detail.

Key Words

FGM plates; HSDT theory; Kerr foundations; natural frequency; phase velocity

Address

(1) Riadh Bennai, Hassen Ait Atmane: Department of Civil Engineering, Faculty of Civil Engineering and Architecture, University Hassiba Benbouali of Chlef, Algeria; (2) Riadh Bennai, Mokhtar Nebab, Fatma Mellal, Hassen Ait Atmane: Laboratory of Structures, Geotechnics and Risks, Department of Civil Engineering, Hassiba Benbouali University of Chlef, Algeria; (3) Fatma Mellal: Department of Technology, Faculty of Science and Technology, Djilali Bounaama University, Khemis Miliana, Algeria; (4) Mokhtar Nebab: Department of Civil Engineering, Faculty of Sciences, University of M'Hamed Bougara Boumerdes, Algeria; (5) Hocine Fourn, Redhwane Ait Atmane, Mourad Benadouda, Abdelouahed Tounsi: Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria; (6) Abdelouahed Tounsi: YFL (Yonsei Frontier Lab), Yonsei University, Seoul, Korea; (7) Abdelouahed Tounsi: Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia.

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