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Group velocity of wave propagation in carbon nanotubes.
- Source :
-
Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences . Jun2008, Vol. 464 Issue 2094, p1423-1438. 16p. - Publication Year :
- 2008
-
Abstract
- The group velocities of longitudinal and flexural wave propagations in single- and multi-walled carbon nanotubes are studied in the frame of continuum mechanics. The dispersion relations between the group velocity and the wavenumber for flexural and longitudinal waves, described by a beam model and a cylindrical shell model, are established for both single- and multi-walled carbon nanotubes. The effect of microstructures in carbon nanotubes on the wave dispersion is revealed through the non-local elastic models of a beam and a cylindrical shell, including the second-order gradient of strain and a parameter of microstructure. It is shown that the microstructures in the carbon nanotubes play an important role in the dispersion of both longitudinal and flexural waves. In addition, the non-local elastic models predict that the cut-off wavenumber of the dispersion relation between the group velocity and the wavenumber is approximately 2×1010m−1 for the longitudinal and flexural wave propagations in both single- and multi-walled carbon nanotubes. This may explain why the direct molecular dynamics simulation cannot give a proper dispersion relation between the phase velocity and the wavenumber when the wavenumber approaches approximately 2×1010m−1, much lower than the cut-off wavenumber for the dispersion relation between the phase velocity and the wavenumber predicted by continuum mechanics. [ABSTRACT FROM AUTHOR]
- Subjects :
- *DISPERSION (Chemistry)
*OPTICS
*FULLERENES
*CARBON
Subjects
Details
- Language :
- English
- ISSN :
- 13645021
- Volume :
- 464
- Issue :
- 2094
- Database :
- Academic Search Index
- Journal :
- Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences
- Publication Type :
- Academic Journal
- Accession number :
- 32803445