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Steel and Composite Structures Volume 20, Number 2, February10 2016 , pages 227-249 DOI: https://doi.org/10.12989/scs.2016.20.2.227 |
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A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation |
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Fatima Bounouara, Kouider Halim Benrahou, Ismahene Belkorissat and Abdelouahed Tounsi
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| Abstract | ||
| The objective of this work is to present a zeroth-order shear deformation theory for free vibration analysis of functionally graded (FG) nanoscale plates resting on elastic foundation. The model takes into consideration the influences of small scale and the parabolic variation of the transverse shear strains across the thickness of the nanoscale plate and thus, it avoids the employ use of shear correction factors. Also, in this present theory, the effect of transverse shear deformation is included in the axial displacements by using the shear forces instead of rotational displacements as in available high order plate theories. The material properties are supposed to be graded only in the thickness direction and the effective properties for the FG nanoscale plate are calculated by considering Mori-Tanaka homogenization scheme. The equations of motion are obtained using the nonlocal differential constitutive expressions of Eringen in conjunction with the zeroth-order shear deformation theory via Hamilton's principle. Numerical results for vibration of FG nanoscale plates resting on elastic foundations are presented and compared with the existing solutions. The influences of small scale, shear deformation, gradient index, Winkler modulus parameter and Pasternak shear modulus parameter on the vibration responses of the FG nanoscale plates are investigated. | ||
| Key Words | ||
| nonlocal elasticity theory; nanoscale-plates; free vibration; plate theory; functionally graded materials | ||
| Address | ||
| (1) Fatima Bounouara, Kouider Halim Benrahou, Ismahene Belkorissat, Abdelouahed Tounsi: Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria; (2) 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) Abdelouahed Tounsi: Laboratoire de Modélisation et Simulation Multi-échelle, Departement de Physique, Faculté des Sciences Exactes, Département de Physique, Université de Sidi Bel Abbés, Algeria; (4) Abdelouahed Tounsi: Algerian National Thematic Agency of Research in Science and Technology (ATRST), Algeria. | ||