Using continuous models in the analysis of vibrational spectra for carbon nanotubes / G. L. Brovko, Z. G. Tunguskova. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2009. № 4. P. 53-56 [Moscow Univ. Mech. Bulletin. Vol. 72, N 2, 2017. P. 93-96].
Rod models of longitudinal, torsional, and bending vibrations are used to
find the natural vibration spectrum of a carbon nanotube. The spectrum of
natural radial vibrations is found using the membrane theory of cylindrical
shells. The coefficients of these models are chosen by comparing the results
obtained on the basis of the micromodel with the Keating interaction
potential in the framework of the long-wave approximation and the continuous
model. It is shown that the spectra of longitudinal, radial, and torsional
vibrations of the carbon nanotube are of the same order of magnitude (the
minimum frequency is about
Key words: carbon nanotube, natural vibrations, spectrum of natural frequencies.