Journal
APPLIED MATHEMATICAL MODELLING
Volume 37, Issue 7, Pages 4787-4797Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.apm.2012.10.016
Keywords
Nonlocal elasticity; Nanobeams; Euler-Bernoulli beam; Free vibration; Finite element method
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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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