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

• Published in: Structural engineering and mechanics Vol. 56; no. 2; pp. 223 - 240
• Main Authors: Bessaim, Aicha, Houari, Mohammed Sid Ahmed, Bernard, Fabrice, Tounsi, Abdelouahed
• Format: Journal Article
• Language: English
• Published: Techno-press Ltd 25-10-2015; 국제구조공학회
• Subjects: Civil Engineering; Engineering Sciences; Mechanical engineering; Mechanics; 토목공학; nanoplates; Vibration; neutral surface position; normal deformation-theory; walled carbon nanotubes; boundary-conditions; graded sandwich plates; wave-propagation; graphene sheets; stretching effect; navier solution; nonlocal elasticity theory; bending analysis; higher-order shear; trigonometric shear deformation theory; elasticity theory
• ISSN: 1225-4568
• DOI: 10.12989/sem.2015.56.2.223

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