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Analytical Study for the Nonlinear Vibrations of Multiwalled Carbon Nanotubes using Homotopy Analysis Method |
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PP: 1675-1684 |
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Author(s) |
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M. M. Khader,
N. H. Sweilam,
Z. I. EL-Sehrawy,
S. A.Ghwail,
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Abstract |
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In this article, the homotopy analysis method (HAM) is implemented for obtaining semi-analytical solutions to the problem
of the nonlinear vibrations of multiwalled carbon nanotubes embedded in an elastic medium. A multiple-beam model is utilized in
which the governing equations of each layer are coupled with those of its adjacent ones via the Van der Waals inter layer forces.
The amplitude-frequency curves for large-amplitude vibrations of single-walled, double-walled and triple-walled carbon nanotubes
are obtained. The influence of changes in material constants of the surrounding elastic medium and the effect of changes in nanotube
geometrical parameters on the vibration characteristics are studied by comparing the results with those from the previous work. Series
solutions of the problem under consideration are developed by means of HAM and the recurrence relations are given explicitly. The
obtained numerical results show the rapid convergence of the series constructed by the proposed method to the exact solution. Test
problems have been considered to ensure that HAM is accurate and efficient compared with the Adomian decomposition method. |
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