Buckling Behaviour and Natural Frequency of Zigzag and Armchair Single-Walled Carbon Nanotubes

Abstract:

In this study, single-walled carbon nanotubes were generated in their perfect state as finite element models in the MSC.Marc software. The buckling behaviour and resonant frequency modes of the two limiting cases of carbon nanotubes, i.e. the armchair and zigzag models, were studied. The obtained results were compared with the classical analytical solutions related to a similar continuum structure of a hollow cylinder. The buckling behaviour of single-walled carbon nanotubes under cantilever boundary conditions proved to be almost identical to the prediction of the classical Euler equation. Furthermore, there was very good agreement between the analytical and finite element results of the studied single-walled carbon nanotubes; though the achieved value of the first mode of frequency, obtained from the finite element results, was more accurate than the higher modes.

• Periodical: Journal of Nano Research (Volume 16)
• Pages: 153-160
• DOI: https://doi.org/10.4028/www.scientific.net/JNanoR.16.153
• Online since: January 2012
• Authors: Moones Rahmandoust, Andreas Öchsner
• Keywords: Buckling, Cantilever, Carbon Nanotube (CN), Finite Element Model (FEM), Natural Frequency, Resonance Frequency

References

[1] M.S. Dresselhaus, G. Dresselhaus, R. Saito, Physics of Carbon Nanotubes, Carbon 33 (7) (1995) 883–91.

DOI: 10.1016/0008-6223(95)00017-8

[2] E.T. Thostenson, Z. Ren, T.W. Chou, Advances in the Science and Technology of Carbon Nanotubes and Their Composites: A Review, Compos. Sci. Technol. 61 (2001) 1899–(1912).

DOI: 10.1016/s0266-3538(01)00094-x

[3] M. Rahmandoust and A. Öchsner, Influence of Structural Imperfections and Doping on the Mechanical Properties of Single-walled Carbon Nanotubes, J. Nano Res. 6 (2009) 185–196.

DOI: 10.4028/www.scientific.net/jnanor.6.185

[4] M. Rahmandoust and A. Öchsner, On Finite Element Modeling of Single and Multi-walled Carbon Nanotubes. J. Nanosci. Nanotech. 12 (2012) in press.

DOI: 10.1166/jnn.2012.4521

[5] C. Li, T.W. Chou, A Structural Mechanics Approach for the Analysis of Carbon Nanotubes, Int. J. Solids Struct. 40 (2003) 2487–2499.

[6] C.M. Wang, Y.Y. Zhang, Y. Xiang, and J.N. Reddy, Recent Studies on Buckling of Carbon Nanotubes, Appl. Mech. Rev. 63 (2010) 030804–1–18.

[7] W.S. To Cho, Bending and Shear Moduli of Single-walled Carbon Nanotubes, Finite Elem. Anal. Des. 42 (2006) 404–413.

DOI: 10.1016/j.finel.2005.08.004

[8] S.M. Mavalizadeh, M. Rahmandoust and A. Öchsner, Numerical Investigation of the Overall Stiffness of Carbon Nanotubebased Composite Materials, J. Nano Res. 13 (2011) 47–59.

DOI: 10.4028/www.scientific.net/jnanor.13.47

[9] C.W. Fan, Y.Y. Liu and C. Hwu, Finite Element Simulation for Estimating the Mechanical Properties of Multi-walled Carbon Nanotubes, Appl. Phys. A 95 (2009) 819–831.

DOI: 10.1007/s00339-009-5080-y

[10] I. Eslami Afrooz, A. Öchsner and M. Rahmandoust, Effects of the carbon nanotube distribution on the macroscopic stiffness of composite materials, Comp. Mater. Sci. 51 (2012) 422–429.

DOI: 10.1016/j.commatsci.2011.08.003

[11] H.J. De Los Santos, Introduction to Microelectromechanical Microwave Systems, Artech House Publishers, London (1999).

[12] P.J.F. Harris, Carbon Nanotubes Composites. Maney for the institute of materials, minerals and mining and ASM international, Int. Mater. Rev. 49 (2004) 31–43.

[13] T. Irvine, Application of the Newton-Raphson Method to Vibration Problems, Vibrationdata Publications, (1999).