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Steel and Composite Structures Volume 18, Number 4, April 2015 , pages 1063-1081 DOI: https://doi.org/10.12989/scs.2015.18.4.1063 |
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On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable model |
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Ismahene Belkorissat, Mohammed Sid Ahmed Houari, Abdelouahed Tounsi, E.A. Adda Bedia and S.R. Mahmoud
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| Abstract | ||
| In this paper, a new nonlocal hyperbolic refined plate model is presented for free vibration properties of functionally graded (FG) plates. This nonlocal nano-plate model incorporates the length scale parameter which can capture the small scale effect. The displacement field of the present theory is chosen based on a hyperbolic variation in the in-plane displacements through the thickness of the nano-plate. By dividing the transverse displacement into the bending and shear parts, the number of unknowns and equations of motion of the present theory is reduced, significantly facilitating structural analysis. The material properties are assumed to vary only in the thickness direction and the effective properties for the FG nano-plate are computed using Mori-Tanaka homogenization scheme. The governing equations of motion are derived based on the nonlocal differential constitutive relations of Eringen in conjunction with the refined four variable plate theory via Hamilton\'s principle. Analytical solution for the simply supported FG nano-plates is obtained to verify the theory by comparing its results with other available solutions in the open literature. The effects of nonlocal parameter, the plate thickness, the plate aspect ratio, and various material compositions on the dynamic response of the FG nano-plate are discussed. | ||
| Key Words | ||
| nonlocal elasticity theory; nano-plates; free vibration; refined plate theory; functionally graded materials | ||
| Address | ||
| (1) Ismahene Belkorissat, Abdelouahed Tounsi, E.A. Adda Bedia: Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria; (2) Mohammed Sid Ahmed Houari, Abdelouahed Tounsi: Laboratoire des Structures et Matériaux Avancés dans le Génie Civil et Travaux Publics, Université de Sidi Bel Abbes, Faculté de Technologie, Département de génie civil, Algérie; (3) S.R. Mahmoud: Department of Mathematics, Faculty of Science, King Abdulaziz University, Saudi Arabia; (4) S.R. Mahmoud: Mathematics Department, Faculty of Science, University of Sohag, Egypt. | ||