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Vibration analysis of Euler-Bernoulli nanobeams by using finite element method
Faculty
Science
Year:
2013
Type of Publication:
Article
Pages:
4787-4797
Authors:
Eltaher, M. A, Mahmoud, F. F, Alshorbagy, Amal E
DOI:
10.1016/j.apm.2012.10.016
Journal:
APPLIED MATHEMATICAL MODELLING ELSEVIER SCIENCE INC
Volume:
37
Research Area:
Engineering; Mathematics; Mechanics
ISSN
ISI:000316579600017
Keywords :
Nonlocal elasticity, Nanobeams, Euler-Bernoulli beam, Free vibration, Finite element method
Abstract:
In the present study, an efficient finite element model for vibration analysis of a nonlocal Euler-Bernoulli beam has been reported. Nonlocal constitutive equation of Eringen is proposed. Equations of motion for a nonlocal Euler-Bernoulli are derived based on varitional statement. The finite element method is employed to discretize the model and obtain a numerical approximation of the motion equation. The model has been verified with the previously published works and found a good agreement with them. Vibration characteristics, such as fundamental frequencies, are illustrated in graphical and tabulated form. Numerical results are presented to figure out the effects of nonlocal parameter, slenderness ratios, rotator inertia, and boundary conditions on the dynamic characteristics of the beam. The above mention effects play very important role on the dynamic behavior of nanobeams. (C) 2012 Elsevier Inc. All rights reserved.
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