https://univ-rennes.hal.science/hal-01302345Bessaim, AichaAichaBessaimUniversité Djilali Liabès [Sidi-Bel-Abbès]Houari, Mohammed Sid AhmedMohammed Sid AhmedHouariUniversité Djilali Liabès [Sidi-Bel-Abbès]Bernard, FabriceFabriceBernardLGCGM - Laboratoire de Génie Civil et Génie Mécanique - UR - Université de Rennes - INSA Rennes - Institut National des Sciences Appliquées - Rennes - INSA - Institut National des Sciences AppliquéesTounsi, AbdelouahedAbdelouahedTounsiUniversité Djilali Liabès [Sidi-Bel-Abbès]A nonlocal quasi-3D trigonometric plate model for free vibration behaviour of micro/nanoscale platesHAL CCSD2015bending 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[SPI.MECA.GEME] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Mechanical engineering [physics.class-ph][SPI.GCIV] Engineering Sciences [physics]/Civil EngineeringJonchère, Laurent2016-04-14 09:40:192023-05-10 08:39:332016-04-14 09:40:19enJournal articles10.12989/sem.2015.56.2.2231In 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