A nonlocal quasi-3D trigonometric plate model for free vibration behaviour of micro/nanoscale plates

Aicha Bessaim , Mohammed Sid Ahmed Houari , Fabrice Bernard , Abdelouahed Tounsi

Abstract

In this work, a nonlocal quasi-3D trigonometric plate theory for micro/nanoscale plates is proposed. In order to introduce the size influences, the Eringen\'s nonlocal elasticity theory is utilized. In addition, the theory considers both shear deformation and thickness stretching effects by a trigonometric variation of all displacements within the thickness, and respects the stress-free boundary conditions on the top and bottom surfaces of the plate without considering the shear correction factor. The advantage of this theory is that, in addition to considering the small scale and thickness stretching effects (ez=x0), the displacement field is modelled with only 5 unknowns as the first order shear deformation theory (FSDT). Analytical solutions for vibration of simply supported micro/nanoscale plates are illustrated, and the computed results are compared with the available solutions in the literature and finite element model using ABAQUS software package. The influences of the nonlocal parameter, shear deformation and thickness stretching on the vibration behaviors of the micro/nanoscale plates are examined.

Key Words

trigonometric shear deformation theory; nanoplates; nonlocal elasticity theory; navier solution; stretching effect; vibration

Address

Aicha Bessaim and Mohammed Sid Ahmed Houari — Laboratoire des Structures et Materiaux Avances dans le Genie Civil et Travaux Publics, Universite de Sidi Bel Abbes, Faculte de Technologie, Departement de genie civil, Algeria; Departement de genie civil, Faculte des Sciences et Technologie, Universite de Mascara, Route de Mamounia 29000 Mascara, Algerie
Fabrice Bernard — Universite Europeenne de Bretagne, INSA Rennes, LGCGM, 20 avenue des Buttes de coesmes 35708 Rennes Cedex 7, France
Abdelouahed Tounsi — Laboratoire des Structures et Materiaux Avances dans le Genie Civil et Travaux Publics, Universite de Sidi Bel Abbes, Faculte de Technologie, Departement de genie civil, Algeria; Laboratoire des Materiaux et Hydrologie, Faculte de Technologie, Universite de Sidi Bel Abbes, Algeria; Laboratoire de Modelisation et Simulation Multi-echelle, Departement de Physique, Faculte des Sciences Exactes, Departement de Physique, Universite de Sidi Bel Abbes, Algeria

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