Free vibration of FGM plates with porosity by a shear deformation theory with four variables

Mahfoud Yousfi, Hassen Ait Atmane, Mustapha Meradjah, Abdelouahed Tounsi and Riadh Bennai

Abstract

In this work, a high order hyperbolic shear deformation theory with four variables is presented to study the vibratory behavior of functionally graduated plates. The field of displacement of the theory used in this work is introduced indeterminate integral variables. In addition, the effect of porosity is studied. It is assumed that the material characteristics of the porous FGM plate, varies continuously in the direction of thickness as a function of the power law model in terms of volume fractions of constituents taken into account the homogeneous distribution of porosity. The equations of motion are obtained using the principle of virtual work. An analytical solution of the Navier type for free vibration analysis is obtained for a FGM plate for simply supported boundary conditions. A comparison of the results obtained with those of the literature is made to verify the accuracy and efficiency of the present theory. It can be concluded from his results that the current theory is not only accurate but also simple for the presentation of the response of free vibration and the effect of porosity on the latter.

Key Words

high orders hyperbolic shear deformation theory; functionally graded plate; porosity; free vibration

Address

Mahfoud Yousfi: 1) Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria 2) Department of Civil Engineering, Faculty of Technology, University of Medea, Algeria Hassen Ait Atmane: 1) Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria 2) Department of Civil Engineering, Faculty of Civil Engineering and Architecture, University of Chlef, Algeria Mustapha Meradjah: Department of Civil Engineering, Faculty of Technology, University of Sidi Bel Abbes, Algeria Abdelouahed Tounsi: 1) Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria 2) Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia Riadh Bennai: Department of Civil Engineering, Faculty of Civil Engineering and Architecture, University of Chlef, Algeria

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