Articles | Volume 9, issue 2
https://doi.org/10.5194/ms-9-349-2018
https://doi.org/10.5194/ms-9-349-2018
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

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Subject: Structural Mechanics | Techniques and Approaches: Numerical Modeling and Analysis
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Cited articles

Arash, B. and Wang, Q.: A review on the application of nonlocal elastic models in modeling of carbon nanotubes and graphenes, Comput. Mater. Sci., 51, 303–313, https://doi.org/10.1016/j.commatsci.2011.07.040, 2012. 
Asemi, S. R., Mohammadi, M., and Farajpour, A.: A study on the nonlinear stability of orthotropic single-layered graphene sheet based on nonlocal elasticity theory, Lat. Am. J. Solids Struct., 11, 1515–1540, https://doi.org/10.1590/S1679-78252014000900004, 2014. 
Bagdatli, S. M.: Non-linear transverse vibrations of tensioned nanobeams using nonlocal beam theory, Struct. Eng. Mech., 55, 281–298, https://doi.org/10.12989/sem.2015.55.2.281, 2015. 
Bocko, J. and Lengvarský, P.: Bending vibrations of carbon nanotubes by using nonlocal theory, Procedia Eng., 96, 21–27, https://doi.org/10.1016/j.proeng.2014.12.093, 2014a. 
Bocko, J. and Lengvarský, P.: The use of nonlocal theory for bending vibrations of single-walled carbon nanotubes, Appl. Mech. Mater., 611, 332–336, https://doi.org/10.4028/www.scientific.net/AMM.611.332, 2014b. 
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Short summary
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.