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Structural Engineering and Mechanics Volume 75, Number 2, July 2020 , pages 193-209 DOI: https://doi.org/10.12989/sem.2020.75.2.193 |
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A novel hyperbolic plate theory including stretching effect for free vibration analysis of advanced composite plates in thermal environments |
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Setti Elmascri, Aicha Bessaim, Ouahiba Taleb, Mohammed Sid Ahmed Houari, Sekkal Mohamed, Fabrice Bernard and Abdelouahed Tounsi
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| Abstract | ||
| This paper presents a new hyperbolic shear deformation plate theory including the stretching effect for free vibration of the simply supported functionally graded plates in thermal environments. The theory accounts for parabolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factors. This theory has only five unknowns, which is even less than the other shear and normal deformation theories. The present one has a new displacement field which introduces undetermined integral variables. Material properties are assumed to be temperature-dependent, and graded in the thickness direction according to a simple power law distribution in terms of the volume power laws of the constituents. The equation of motion of the vibrated plate obtained via the classical Hamilton’s principle and solved using Navier’s steps. The accuracy of the proposed solution is checked by comparing the present results with those available in existing literature. The effects of the temperature field, volume fraction index of functionally graded material, side-to-thickness ratio on free vibration responses of the functionally graded plates are investigated. It can be concluded that the present theory is not only accurate but also simple in predicting the natural frequencies of functionally graded plates with stretching effect in thermal environments. | ||
| Key Words | ||
| Functionally Graded (FG) plates; vibration; new plate theory; shear and normal deformation, analytical modeling, thermal environment | ||
| Address | ||
| Setti Elmascri, Sekkal Mohamed: Department of Civil Engineering, University Abdelhamid Ibn Badis of Mostaganem, Algeria Aicha Bessaim, Ouahiba Taleb, Mohammed 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, Mascara, Algeria Sekkal Mohamed, and Abdelouahed Tounsi: Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria Fabrice Bernard: Université Européenne de Bretagne, INSA Rennes, LGCGM, 20 avenue des Buttes de coësmes 35708 Rennes Cedex 7, France Abdelouahed Tounsi: Department of Civil and Environmental Engineering, King Fahd University of Petroleum and Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia | ||