Free vibration analysis of FG plates with volume fraction-dependent porosity

Ahmed Amine Daikh, Amine Chergui, Abdessamed Amara, Azzedine Brik, Mohamed Ouejdi Belarbi, Mohamed Sid Ahmed Houari, Azza M. Abdraboh and Mohamed A. Eltaher

Abstract

This study presents a corrigendum regarding the inclusion of porosity in functionally graded structures. Typically, researchers incorporate the porosity function into the rule of mixture without accounting for specific fabrication steps, which relate to the proportions of the material constituents as represented by the volume fraction. This paper investigates the free vibration of functionally graded plates analytically and proposes a novel approach to porosity inclusion, where the porosity function is directly related to the volume fraction. Tow schemes of porosity are analysed, volume fraction porosity-dependent (VFD) and rule of mixture porosity dependent (RMD). Four types of porosity are proposed, Even, Uneven, linear (1) and linear (2). Based on the generalized field of displacement, a new higher-order shear deformation theory is proposed in this work. The equilibrium equations are performed on the basis of the virtual work principle, and solved by applying Galerkin method to cover various boundary conditions. The influence of the structure geometry, materials combination parameter, type of porosity, and different boundary conditions on the vibration frequency of the FG plate is investigated in detail.

Key Words

functionally graded plate; Galerkin method; higher-order shear deformation plate theory; rule of mixture porosity dependent (RMD); vibration behavior; volume fraction porosity-dependent (VFD)

Address

Ahmed Amine Daikh: Artificial Intelligence Laboratory for Mechanical and Civil Structures, and Soil, University Centre of Naama, P.O. Box 66, Naama 45000, Algeria/ Laboratoire d'Etude des Structures et de Mécanique des Matériaux, Département de Génie Civil, Faculté des Sciences et de la Technologie, Université Mustapha Stambouli B.P. 305, R.P.29000 Mascara, Algérie Amine Chergui, Abdessamed Amara and Azzedine Brik: Department of Mechanical Engineering, University Centre of Naama, 45000, Algeria Mohamed Ouejdi Belarbi: Laboratoire de Recherche en Génie Civil, LRGC, Université de Biskra, B.P. 145, R.P. 07000, Biskra, Algeria Mohamed Sid Ahmed Houari: Laboratoire d'Etude des Structures et de Mécanique des Matériaux, Département de Génie Civil, Faculté des Sciences et de la Technologie, Université Mustapha Stambouli B.P. 305, R.P.29000 Mascara, Algérie Azza M. Abdraboh: Physics Department, Faculty of science, Benha university, Benha, Egypt Mohamed A. Eltaher:6 Faculty of Engineering, Mechanical Engineering Department, King Abdulaziz University, P.O. Box 80204, Jeddah, Saudi Arabia/ Faculty of Engineering, Mechanical Design and Production Department, Zagazig University, P.O. Box 44519, Zagazig, Egypt

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