Journal
PHYSICAL REVIEW B
Volume 65, Issue 23, Pages -Publisher
AMERICAN PHYSICAL SOC
DOI: 10.1103/PhysRevB.65.235402
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The classical vibrational modes are calculated for a thin-walled hollow cylinder of isotropic material. An analytical solution is obtained for all of the modes. The results are applied to calculate the low-frequency vibrational modes of a single-wall carbon nanotube. Analytical formulas are obtained for the Raman frequencies, and for the velocities of acoustical modes.
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