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Volume 9, issue 2 | Copyright
Mech. Sci., 9, 349-358, 2018
https://doi.org/10.5194/ms-9-349-2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

Research article 01 Nov 2018

Research article | 01 Nov 2018

The computation of bending eigenfrequencies of single-walled carbon nanotubes based on the nonlocal theory

Jozef Bocko, Pavol Lengvarský, Róbert Huňady, and Juraj Šarloši Jozef Bocko et al.
  • Department of Applied Mechanics and Mechanical Engineering, Technical University of Košice, Košice, 04200, Slovakia

Abstract. In this work, a recently proposed nonlocal theory of bending is used in the analysis of eigenfrequencies of single-walled carbon nanotubes (SWCNTs). The nanotube vibration is analyzed in the form of a homogenized continuum. Classical treatment where a nanotube is approximated by standard beam theory, is replaced by the more sophisticated nonlocal method of material interactions where a nonlocal parameter is used. The eigenfrequencies are computed by the combination of analytical as well as numerical methods for four different carbon nanotube (CNT) supports. Various types of supports are considered for the analysis: fixed–simply supported, fixed–free, simply–simply supported and fixed–fixed. Due to the huge amount of computed data, only outcomes of eigenfrequency computations for the nanobeams of armchair type with fixed and simply supported ends, and different nonlocal parameters are represented in the form of graphs at the end of the article. The study shows how the nanotube eigenfrequencies depend on nonlocal parameters as well as on the length and diameter of CNTs. The obtained results are in good agreement with the results published in papers which were gained by different procedures.

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The paper is concerned to the computation of eigenfrequencies of single-walled carbon nanotubes (SWCNTs). Classical treatment, where the nanotube is approximated by beam theory, is replaced by the nonlocal theory of beam bending. The eigenfrequencies are computed by combination of analytical, as well as numerical methods for four types of boundary conditions. The results can be used for determination of Young’s modulus of homogenized SWCNTs from experimental measurements.
The paper is concerned to the computation of eigenfrequencies of single-walled carbon nanotubes...
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