Journal of Theoretical
and Applied Mechanics

57, 1, pp. 193-205, Warsaw 2019
DOI: 10.15632/jtam-pl.57.1.193

On the eigenmodes and eigenfrequencies of low-dimensional degenerated carbon structures: obtaining natural frequencies of ideal and structurally defected systems

Sadegh Imani Yengejeh, Seyedeh Alieh Kazemi, Andreas Öchsner
We concentrated on evaluating the vibrational response of ideal and defected degenerated
carbon nanostructures under the influence of different boundary conditions. In addition,
an attempt has been made to investigate the relative deviation of the natural frequency of
imperfect systems and to study the effect of defected regions on vibrational stability of the
particles. It has been found that a single and pinhole vacancy defect have the least and the
most impact on the natural frequency of nanostructures. Furthermore, the effect of CNT
diameter on natural frequencies of low-dimensional systems has also been investigated in
this research.
Keywords: carbon nanostructures, finite element method, vibrational property, vacancy defect


Ardeshana B., Jani U., Patel A., Joahi A.Y., 2017, An approach to modelling and simulation

of single-walled carbon nanocones for sensing applications, AIMS Materials Science, 4, 1010-1028

Bogush I., Ciobu V., Paladi F., 2017, Advanced computational method for studying molecular

vibrations and spectra for symmetrical systems with many degrees of freedom, and its application

to fullerene, The European Physical Journal B, 90, 193

Chandra N., Namilae S., 2006, Tensile and compressive behavior of carbon nanotubes: effect

of functionalization and topological defects, Mechanics of Advanced Materials and Structures, 13, 115-127

Hollerer S., Celigoj C.C., 2013, Buckling analysis of carbon nanotubes by a mixed atomistic

and continuum model, Computational Mechanics, 51, 765-789

Iijima S., 1991, Helical microtubules of graphitic carbon, Nature, 354, 56

Imani Yengejeh S., Akbar Zadeh M., ¨ Ochsner A., 2014a, On the buckling behavior of

connected carbon nanotubes with parallel longitudinal axes, Applied Physics A, 115, 1335-1344

Imani Yengejeh S., Akbar Zadeh M., ¨ Ochsner A., 2015a, On the tensile behavior of heterojunction

carbon nanotubes, Composites Part B, 75, 274-280

Imani Yengejeh S., Kazemi S.A., ¨ Ochsner A., 2014b, A numerical evaluation of the influence

of atomic modification on the elastic and shear behavior of connected carbon nanotubes with

parallel longitudinal axes, Journal of Nano Research, 29, 93-104

Imani Yengejeh S., Kazemi S.A., ¨ Ochsner A., 2015b, On the buckling behavior of curved

carbon nanotubes, [In:] Mechanical and Materials Engineering of Modern Structure and Component

Design, A. ¨Ochsner, H. Altenbach (Eds.), Switzerland, Springer International Publishing, 70, 401-412

Imani Yengejeh S., Kazemi S.A., ¨ Ochsner A., 2016, Advances in mechanical analysis of

structurally and atomically modified carbon nanotubes and degenerated nanostructures: A review,

Composites Part B: Engineering, 86, 95-107

Imani Yengejeh S., ¨ Ochsner A., 2015, Influence of twisting and distortion on the mechanical

properties of carbon nanotubes, Journal of Computational and Theoretical Nanoscience, 12, 443-448

Kuang Y.D., He X.Q., 2009, Young’s moduli of functionalized single-wall carbon nanotubes

under tensile loading, Composites Science and Technology, 69, 169-175

Lu J.P., 1997, Elastic properties of carbon nanotubes and nanoropes, Physical Review Letters, 79, 1297-1300

Mohammadian M., Hosseini S.M., Abolbashari M.H., 2017, Free vibration analysis of dissimilar

connected CNTs with atomic imperfections and different locations of connecting region,

Physica B: Condensed Matter, 524, 34-46

Mylvaganam K., Vodenitcharova T., Zhang L.C., 2006, The bending-kinking analysis of a

single-walled carbon nanotube – a combined molecular dynamics and continuum mechanics technique,

Journal of Materials Science, 41, 3341-3347

Ruoff R.S., Lorents D.C., 1995, Mechanical and thermal properties of carbon nanotubes,

Carbon, 33, 925-930

Tserpes K.I., Papanikos P., 2007, The effect of Stone-Wales defect on the tensile behavior and

fracture of single-walled carbon nanotubes, Composite Structures, 79, 581-589

Yao X.-H., Han Q., Xin H., 2008, Bending buckling behaviors of single- and multi-walled carbon

nanotubes, Computational Materials Science, 43, 579-590