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

Aicha Bessaim (1) , Mohammed Sid Ahmed Houari (1) , Fabrice Bernard (2) , Abdelouahed Tounsi (1)

1 UDL - جامعة جيلالي اليابس [سيدي بلعباس، الجزائر] = Université Djillali Liabès [Sidi Bel Abbès, Algérie] = Djillali Liabes University [Sidi Bel Abbès, Algeria]
2 LGCGM - Laboratoire de Génie Civil et Génie Mécanique

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 (epsilon(z)not equal 0), 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

Mots clés: bending analysis; boundary-conditions; elasticity theory; graded sandwich plates; graphene sheets; higher-order shear; nanoplates; navier solution; neutral surface position; nonlocal elasticity theory; normal deformation-theory; stretching effect; trigonometric shear deformation theory; Vibration; walled carbon nanotubes; wave-propagation

Domaines: Génie mécanique [physics.class-ph]; Génie civil

Aicha Bessaim, Mohammed Sid Ahmed Houari, Fabrice Bernard, Abdelouahed Tounsi. A nonlocal quasi-3D trigonometric plate model for free vibration behaviour of micro/nanoscale plates. Structural Engineering and Mechanics, 2015, 56 (2), pp.223--240. ⟨10.12989/sem.2015.56.2.223⟩. ⟨hal-01302345⟩