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Wave Characteristics of Multi-Walled Carbon Nanotubes

Mira Mitra1, S. Gopalakrishnan2

Department of Aerospace Engineering, Indian Institute of Technology, Bombay, Mumbai 400 076. INDIA, e-mail:
Department of Aerospace Engineering, Indian Instituteof Science, Bangalore 560 012. INDIA, e-mail:, Fax: +91-80-2360-0134

Computer Modeling in Engineering & Sciences 2008, 27(1&2), 125-136.


In this paper, the wave characteristics, namely, the spectrum and dispersion relations of multi-wall carbon nanotubes (MWNTs) are studied. The MWNTs are modeled as multiple thin shells coupled through van der Waals force. Each wall of the MWNT has three displacements, i.e, axial, circumferential and radial with variation along the axial and circumferential directions. The wave characteristics are obtained by transforming the governing differential wave equations to frequency domain via Fourier transform. This transformation is first done in time using fast Fourier transform (FFT) and then in one spatial dimension using Fourier series. These transformed equations are solved by posing them as polynomial eigenvalue problem (PEP). The solution gives the wavenumbers and the wave speeds. First, the wave properties are studied for infinite length MWNT which does not have any variation along the axial direction. Next, the wavenumbers are studied for finite length MWNT with small and large radii. The analysis is done for single, double and three-walled carbon nanotubes.


Cite This Article

Mitra, M., Gopalakrishnan, S. (2008). Wave Characteristics of Multi-Walled Carbon Nanotubes. CMES-Computer Modeling in Engineering & Sciences, 27(1&2), 125–136.

cc This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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