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Coupling effects of nonlocal and surface energy on vibration analysis of nanobeams
Faculty
Science
Year:
2013
Type of Publication:
Article
Pages:
760-774
Authors:
Eltaher, M. A, Mahmoud, F. F, Assie, A. E, Meletis, E. I
DOI:
10.1016/j.amc.2013.09.002
Journal:
APPLIED MATHEMATICS AND COMPUTATION ELSEVIER SCIENCE INC
Volume:
224
Research Area:
Mathematics
ISSN
ISI:000327734800069
Keywords :
Nonlocal elasticity, Surface effects, Nanobeam, Vibration analysis, Nonlocal finite element
Abstract:
This paper is proposed to study the coupled effects of surface properties and nonlocal elasticity on vibration characteristics of nanobeams by using a finite element method. Nonlocal differential elasticity of Eringen is exploited to reveal the long-range interactions of a nanoscale beam. To incorporate surface effects, Gurtin-Murdoch model is proposed to satisfy the surface balance equations of the continuum surface elasticity. Euler-Bernoulli hypothesis is used to model the bulk deformation kinematics. The surface layer and bulk of the beam are assumed elastically isotropic. Galerkin finite element technique is employed for the discretization of the nonlocal mathematical model with surface properties. An efficiently finite element model is developed to descretize the beam domain and solves the equation of motion numerically. The output results are compared favorably with those published works. The effects of nonlocal parameter and surface elastic constants on the vibration characteristics are presented. Also, the effectiveness of finite element method to handle a complex geometry is illustrated. The present model can be used for free vibration analysis of single-walled carbon nanotubes with essential, natural and nonlinear boundary conditions. (C) 2013 Elsevier Inc. All rights reserved.
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