radial breathing mode frequency of multi-walled carbon nanotube via multiple-elastic thin shell theory

in this paper, the radial breathing mode (rbm) frequencies of multi-walled carbon nanotubes (mwcnts) are  obtained based on the multiple-elastic thin shell model. for this purpose, mwcnt is considered as a multiple concentric elastic thin cylindrical shells, which are coupled through van der waals (vdw) forces between two adjacent tubes. lennard-jones potential is used to calculate the vdw forces between adjacent tubes. the rbm frequencies of mwcnts predicted by the present shell model are in excellent agreement with the available experimental and atomistic results with relative errors less than 2.5%. the results emphasize the utility of multiple-elastic thin shell theory for modelling the rbm vibrational behaviour of mwcnts.