Wall thickness and elastic moduli of single-walled carbon nanotubes from frequencies of axial, torsional and inextensional modes of vibration

We also compare higher vibrational modes of shells and hollow cylinders with those of the corresponding SWCNTs. For a shell we use a first-order shear deformable shell theory (FSDST). Frequencies of a shell using the FSDST and of the hollow cylinder using the three-dimensional linear elasticity theory are computed with the finite element method. It is found that for low to moderate circumferential and axial wave numbers frequencies and mode shapes of the shell and of the hollow cylinder agree well with those of the corresponding SWCNT computed with the MM simulations.