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.

Bocko, J. and Lengvarský, P.: Vibration of single-walled carbon nanotubes
by using nonlocal theory, Am. J. Mech. Eng., 2, 195–198,
https://doi.org/10.12691/ajme-2-7-5, 2014c.

Chakraverty, S. and Behera, L.: Small scale effect on the vibration of
non-uniform nanoplates, Struct. Eng. Mech., 55, 495–510,
https://doi.org/10.12989/sem.2015.55.3.495, 2015.

Eringen, A. C.: Nonlocal Continuum Field Theories, Springer-Verlag, New York,
2002.

Fu, Y. M., Zhou, H. Q., and Zhang, P.: Nonlinear free vibration of nanowires
including size effects, Micro Nano Lett., 7, 348–352,
https://doi.org/10.1049/mnl.2011.0689, 2012.

Gupta, S. S. and Batra, R. C.: Continuum structures equivalent in normal mode
vibrations to single-walled carbon nanotubes, Comput. Mater. Sci., 43,
715–723, https://doi.org/10.1016/j.commatsci.2008.01.032, 2008.

Harik, V. M.: Mechanics of carbon nanotubes: applicability of the
continuum-beam models, Comput. Mater. Sci., 24, 328–342,
https://doi.org/10.1016/S0927-0256(01)00255-5, 2002.

Hussain, M. and Naeem, M. N.: Vibration analysis of single-walled carbon
nanotubes using wave propagation approach, Mech. Sci., 8, 155–164,
https://doi.org/10.5194/ms-8-155-2017, 2017.

Hussain, M., Naeem, M. N., Shahzad, A., and He, M.: Vibrational behavior of
single-walled carbon nanotubes based on cylindrical shell model using wave
propagation approach, AIP Adv., 7, 045114, https://doi.org/10.1063/1.4979112, 2017.

Iijima, S.: Helical microtubules of graphitic carbon, Nat., 354, 56–58,
https://doi.org/10.1038/354056a0, 1991.

Imani Yengejeh, S., Akbar Zadeh, M., and Öchsner, A.: Numerical modeling
of eigenmodes and eigenfrequencies of hetero-junction carbon nanotubes with
pentagon–heptagon pair defects, Comput. Mater. Sci., 92, 76–83,
https://doi.org/10.1016/j.commatsci.2014.05.015, 2014.

Karličić, D., Murmu, T., Adhikari, S., and McCarthy, M.: Non-Local
Structural Mechanics, John Wiley & Sons, Inc., Hoboken, NJ, USA, 2015.

Kumar, D. and Srivastava, A.: Elastic properties of CNT- and
graphene-reinforced nanocomposites using RVE, Steel. Comp. Struct., 21,
1085–1103, https://doi.org/10.12989/scs.2016.21.5.1085, 2016.

Lee, H. L. and Chang, W. J.: Frequency analysis of carbon-nanotube-based mass
sensor using non-local Timoshenko beam theory, Micro Nano Lett., 7, 86–89,
https://doi.org/10.1049/mnl.2011.0469, 2012.

Lim, C. W., Li, C., and Yu, J.: Free vibration of pre-tensioned nanobeams
based on nonlocal stress theory, J. Zhejiang Univ. Sci. A, 11, 34–42,
https://doi.org/10.1631/jzus.A0900048, 2010.

Lü, J., Chen, H., Lü, P., and Zhang, P.: Research of natural
frequency of single-walled carbon nanotube, Chin. J. Chem. Phys., 20, 525,
https://doi.org/10.1088/1674-0068/20/05/525-530, 2007.

Narendar, S. and Gopalakrishnan, S.: Nonlocal continuum mechanics formulation
for axial, flexural, shear and contraction coupled wave propagation in single
walled carbon nanotubes, Lat. Am. J. Solids Struct., 9, 497–514,
https://doi.org/10.1590/S1679-78252012000400005, 2012.

Rahmani, O., Norouzi, S., Golmohammadi, H., and Hosseini, S. A. H.: Dynamic
response of a double, single-walled carbon nanotube under a moving
nanoparticle based on modified nonlocal elasticity theory considering surface
effects, Mech. Adv. Mater. Struc., 24, 1274–1291,
https://doi.org/10.1080/15376494.2016.1227504, 2017.

Rahmani, O., Shokrnia, M., Golmohammadi, H., and Hosseini, S. A. H.: Dynamic
response of a single-walled carbon nanotube under a moving harmonic load by
considering modified nonlocal elasticity theory, Eur. Phys. J. Plus., 133,
42, https://doi.org/10.1140/epjp/i2018-11868-4, 2018.

Reddy, J. N. and Pang, S. D.: Nonlocal continuum theories of beams for the
analysis of carbon nanotubes, J. Appl. Phys., 103, 023511,
https://doi.org/10.1063/1.2833431, 2008.

Şimşek, M.: Vibration analysis of a single-walled carbon nanotube
under action of a moving harmonic load based on nonlocal elasticity theory,
Physica E, 43, 182–191, https://doi.org/10.1016/j.physe.2010.07.003, 2010.

Şimşek, M.: Forced vibration of an embedded single-walled carbon
nanotube traversed by a moving load using nonlocal Timoshenko beam theory,
Steel. Comp. Struct., 11, 59–76, https://doi.org/10.12989/scs.2011.11.1.059, 2011.

Swain, A., Roy, T., and Nanda, B. K.: Vibration behaviour of single walled
carbon nanotube using finite element, Int. J. Theor. Appl. Res. Mech. Eng.,
2, 129–133, 2013.

Thongyothee, C., Chucheepsakul, S., and Li, T.: Nonlocal elasticity theory
for free vibration of single-walled carbon nanotubes, Adv. Mat. Res., 747,
257–260, https://doi.org/10.4028/www.scientific.net/AMR.747.257, 2013.

Wang, Y.-G., Song, H.-F., Lin, W.-H., Wang, J.-K., Wang, Y.-G., Song, H.-F.,
Lin, W.-H., and Wang, J.-K.: Large amplitude free vibration of micro/nano
beams based on nonlocal thermal elasticity theory, Lat. Am. J. Solids
Struct., 12, 1918–1933, https://doi.org/10.1590/1679-78251904, 2015.

Wu, A. S. and Chou, T.-W.: Carbon nanotube fibers for advanced composites,
Mat. Today, 15, 302–310, https://doi.org/10.1016/S1369-7021(12)70135-9, 2012.

Yang, J., Ke, L. L., and Kitipornchai, S.: Nonlinear free vibration of
single-walled carbon nanotubes using nonlocal Timoshenko beam theory, Physica
E, 42, 1727–1735, https://doi.org/10.1016/j.physe.2010.01.035, 2010.

Yayli, M. Ö.: On the axial vibration of carbon nanotubes with different
boundary conditions, Micro Nano Lett., 9, 807–811,
https://doi.org/10.1049/mnl.2014.0398, 2014.

Zhang, Y. Y., Wang, C. M., and Tan, V. B. C.: Assessment of Timoshenko beam
models for vibrational behavior of single-walled carbon nanotubes using
molecular dynamics, Adv. Appl. Math. Mech., 1, 89–106, 2009.