Carbon Nanotube Structure Vibration Based on Non-local Elasticity

Abdelkadir Belhadj; Abdelkrim Boukhalfa; Sid Ahmed Belalia

doi:10.21467/jmm.3.1.9-13

Authors

Abdelkadir Belhadj Computational Mechanics Laboratory Faculty of technology University of Tlemcen
Abdelkrim Boukhalfa Computational Mechanics Laboratory Department of Mechanical Engineering Faculty of Technology University of Tlemcen
Sid Ahmed Belalia Computational Mechanics Laboratory Department of Mechanical Engineering Faculty of Technology University of Tlemcen

DOI:

https://doi.org/10.21467/jmm.3.1.9-13

Abstract

This manuscript investigates the bending vibration dynamic of a single walled carbon nanotube (SWCNT) based on the theory of non-local elasticity. Fundamental natural frequencies and mode shapes of the SWCNT are computed by using a semi-analytical procedure called differential quadrature method (DQM), which gives accurate results in reference with the exact solution.

Keywords:

Carbon nanotube, vibration, non-local elasticity, frequency, Euler-Bernoulli, DQM

Downloads

Download data is not yet available.

References

S. Iijima, “Helical microtubules of graphitic carbon” Nature, vol.354, pp. 56-58, 1991.

S.N. Cha, J.E. Jang, Y. Choi, G.A.J. Amaratunga et al., “Fabrication of a nanoelectromechanical switch using a suspended carbon nanotube”, Applied Physics Letters, vol. 86, no.8, p083105, 2005.

J. Bernholc,D. Brenner, M. B. Nardelli, V. Meunier, C. Roland, “Mechanical and electrical properties of nanotubes” Annual Review of Materials Research, vol 32, no.1 pp347–375, 2002.

F. ChenXin, C. YunFei, J. JiWei, “Molecular dynamics simulation of the test of single-walled carbon nanotubes under tensile loading”, Science in China Series E: Technological Science, vol.50, no.1, pp7-17, 2007.

K. P. Chong, “Nano science and engineering in solid mechanics”. Acta Mechanica Solida Sinica, vol. 21, no2, pp 95–103, 2008.

A. C. Eringen, “Nonlocal polar elastic continua”. International Journal of Engineering and Science, vol.10, no.1, pp 1–16, 1972.

A.C. Eringen, “Relation between non-local elasticity and lattice dynamics”. Crystal lattice defects, vol. 7, pp. 51-57. 1977.

Q. Wang, “Wave propagation in carbon nanotubes via nonlocal continuum mechanics”, Journal of applied Physics. vol. 98, no 12, pp 124301, 2005.

L.F. Wang, H.Y. Hu, “Flexural wave propagation in single-walled carbon nanotubes,” Physical Review B, Vol. 71, no. 19, p.195412.2005.

Q. Wang, Q, Varadan, V.K., Quek, S.T., “Small scale effect on elastic buckling of carbon nanotubes with nonlocal continuum models», Physics Letters. A, vol.357, no.2, pp. 130-135., 2006.

J. Bocko, P. Lengvarský, “Vibration of Single-Walled Carbon Nanotubes by Using Nonlocal Theory”, American Journal of Mechanical Engineering, Vol. 2, no. 7, pp.195-198, 2014.

T. Natsuki, N. Matsuyama, Q.Ni, “Vibration analysis of carbon nanotube-based resonator using nonlocal elasticity theory”, Applied Physics A, vol.120, no.4, pp.1309–1313, 2015.

A. Houmat, “Nonlinear free vibration of non-prismatic single-walled carbon nanotubes by a non-local shear deformable beam p-element”, Acta Mechanica., vol 227. no.4, pp. 1051–1065, 2015.

S. Govind, S. Bansal, “Design of Mass-sensor Based on Resonant Frequency Analysis of a Single Walled Nanotube”, International Journal of Advanced Mechanical Engineering, vol.4, no.3, pp. 331-342,2014.

S.B. Coşkun, M.T. Atay, B. Öztürk, “Transverse Vibration Analysis of Euler-Bernoulli Beams Using Analytical Approximate Techniques”, Advances in Vibration Analysis Research, Dr. Farzad Ebrahimi (Ed.), InTech.

C.W. Bert, M. Malik, “Differential quadrature method in computational mechanics: A review”, Applied Mechanics Review, vol. 49, no.1, pp. 1-27. 1996.

W. Chen, A.G. Striz, C.W. Bert, “A new approach to the differential quadrature method for fourth-order equations”, International Journal for Numerical Methods in Engineering, vol. 40, no.11, pp. 1941–1956. 1997.

MATLAB and Statistics Toolbox Release 2012b, The MathWorks, Inc., Natick, Massachusetts, United States.