Dynamic and wave propagation investigation of FGM plates with porosities using a four variable plate theory

Riadh Bennai , Hocine Fourn , Hassen Ait Atmane , Abdelouahed Tounsi , Aicha Bessaim

Abstract

In this paper, an analytical analysis for the study of vibratory behavior and wave propagation of functionally graded plates (FGM) is presented based on a high order shear deformation theory. The manufacture of these plates\'s defects can appear in the form of porosity. This latter can question and modify the global behavior of such plates. A new shape of the distribution of porosity according to the thickness of the plate was used. The field of displacement of this theory is present of indeterminate integral variables. The modulus of elasticity and the mass density of these plates are assumed to vary according to the thickness of the plate. Equations of motion are derived by the principle of minimization of energies. Analytical solutions of free vibration and wave propagation are obtained for FGM plates simply supported by integrating the analytic dispersion relation. Illustrative examples are given also to show the effects of variation of various parameters such as (porosity parameter, material graduation, thickness-length ratio, porosity distribution) on vibration and wave propagation of FGM plates.

Key Words

functionally graded plate; higher-order plate theory; porosity; free vibration; wave propagation

Address

Riadh Bennai — Department of civil engineering, Faculty of civil engineering and architecture, University of Hassiba Benbouali of Chlef, Algeria
Hocine Fourn — Material and Hydrology Laboratory, Faculty of Technology, Department of Civil Engineering, University of Sidi Bel Abbes, Algeria
Hassen Ait Atmane — Department of civil engineering, Faculty of civil engineering and architecture, University of Hassiba Benbouali of Chlef, Algeria; Material and Hydrology Laboratory, Faculty of Technology, Department of Civil Engineering, University of Sidi Bel Abbes, Algeria
Abdelouahed Tounsi — Material and Hydrology Laboratory, Faculty of Technology, Department of Civil Engineering, University of Sidi Bel Abbes, Algeria; Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia
Aicha Bessaim — Material and Hydrology Laboratory, Faculty of Technology, Department of Civil Engineering, University of Sidi Bel Abbes, Algeria; Department of Civil Engineering, Université Mustapha Stambouli de Mascara, Mascara, Algeria

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