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Structural Engineering and Mechanics Volume 69, Number 5, March10 2019 , pages 511-525 DOI: https://doi.org/10.12989/sem.2019.69.5.511 |
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Vibration response and wave propagation in FG plates resting on elastic foundations using HSDT |
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Mokhtar Nebab, Hassen Ait Atmane, Riadh Bennai, Abdelouahed Tounsi and E.A. Adda Bedia
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| Abstract | ||
| This paper presents an analytical study of wave propagation in simply supported graduated functional plates resting on a two-parameter elastic foundation (Pasternak model) using a new theory of high order shear strain. Unlike other higher order theories, the number of unknowns and governing equations of the present theory is only four unknown displacement functions, which is even lower than the theory of first order shear deformation (FSDT). Unlike other elements, the present work includes a new field of motion, which introduces indeterminate integral variables. The properties of the materials are assumed to be ordered in the thickness direction according to the two power law distributions in terms of volume fractions of the constituents. The wave propagation equations in FG plates are derived using the principle of virtual displacements. The analytical dispersion relation of the FG plate is obtained by solving an eigenvalue problem. Numerical examples selected from the literature are illustrated. A good agreement is obtained between the numerical results of the current theory and those of reference. A parametric study is presented to examine the effect of material gradation, thickness ratio and elastic foundation on the free vibration and phase velocity of the FG plate. | ||
| Key Words | ||
| FG plate; shear deformation theory; free vibration; wave propagation; phase velocity; elastic foundations | ||
| Address | ||
| Mokhtar Nebab and Riadh Bennai: Department of Civil Engineering, Faculty of Civil Engineering and Architecture, University of Hassiba Benbouali of Chlef, Algeria Hassen Ait Atmane: 1) Department of Civil Engineering, Faculty of Civil Engineering and Architecture, University of Hassiba Benbouali of Chlef, Algeria 2) Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, 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 E.A. Adda Bedia: Centre of Excellence for Advanced Materials Research, King Abdulaziz University, Jeddah, 21589, Saudi Arabia | ||