Sinusoidal shear deformation theory for dynamic analysis of FG plates under various boundary conditions: Influence of micromechanical models

Mohamed Saad, Latifa Ould Larbi, Lazreg Hadji, Nafissa Zouatnia, Hassen Ait Atmane and Royal Madan

Abstract

In the present study, free vibration analysis of an FG plate has been performed by employing trigonometric shear deformation plate theory. The selection of an appropriate homogenization model is important as it could significantly influence the material behavior. Therefore, well-known micromechanical models such as Voigt, Reuss, and representative volume element method have been studied and their results are compared. The effect of various boundary conditions was also seen by changing the boundary conditions as SSSS, CCCC, CSCS, and FCFC. The mechanical properties change uni-directionally across the thickness according to a simple power law. Hamilton's principle is applied to derive the governing equations of motion, and Navier-type analytical solutions are formulated for vibration analysis. The study examined the impact of the power-law index, length-to-thickness ratio, micromechanical models, and boundary conditions on the natural frequencies of the FG plate.

Key Words

boundary conditions; FG plate; free vibration; functionally graded material; micromechanical models

Address

Mohamed Saad: Department of Mechanical Engineering, University of Tiaret, BP 78 Zaaroura, 14000 Tiaret, Algeria Latifa Ould Larbi and Hassen Ait Atmane: Laboratory of Structures, Geotechnics and Risks, Department of Civil Engineering, Hassiba Benbouali University of Chlef, Chlef, Algeria Lazreg Hadji and Nafissa Zouatnia: Department of Civil Engineering, University of Tiaret, BP 78 Zaaroura, 14000 Tiaret, Algeria Royal Madan: Department of Mechanical Engineering, Graphic Era (Deemed to be University) Dehradun- 248002, Uttarakhand, India

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