Analytical Procedure for Determining Natural Frequencies of Annular Single-Layered Graphene Sheet via Nonlocal Elasticity Theory
Publication: Journal of Engineering Mechanics
Volume 144, Issue 9
Abstract
This paper investigates the axisymmetric free vibrations of annular single-layered graphene sheets with different boundary conditions using nonlocal elasticity theory. The analysis procedure is based on the first-order shear deformation theory and small deflections assumption to derive the equations of motion which are a system of partial differential equations with variable coefficients. In order to determine the transverse natural frequencies as well as the radial natural frequencies analytically, the perturbation technique is applied to solve these equations. The transverse natural frequencies are calculated using classical plate theory. The results of both theories are compared with those obtained from the literature. A parametric study is performed and the effects of nonlocal parameter, geometry, and boundary conditions on the natural frequencies are investigated.
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Published In
Journal of Engineering Mechanics
Volume 144 • Issue 9 • September 2018
Copyright
©2018 American Society of Civil Engineers.
History
Received: Apr 11, 2018
Accepted: Apr 11, 2018
Published online: Jul 3, 2018
Published in print: Sep 1, 2018
Discussion open until: Dec 3, 2018
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