Mode transformation in single-walled carbon nanotubes

Mode transformations in single-walled carbon nanotubes (SWCNTs) are investigated analytically and numerically in the present paper. The analytical results based on a classical thin circular cylindrical shell theory for SWCNTs show that the effective thickness prescribed to SWCNTs has strong effect on mode transformation in SWCNTs. The use of different thickness values (i.e. 0.066 or 0.1 nm) may predict different flexural modes to be excited, and accordingly predict different internal resonance mechanisms (i.e. 2:1 or 1:1) in a SWCNT. In contrast, studies of mode transformations in SWCNTs based on finite element analysis, which does not rely on thin-walled shell assumptions, indicate that the thickness values influence the initiation time of the first mode transformation in a SWCNT, but not the excited flexural mode and accordingly the internal resonance mechanism in the SWCNT. It is shown that the analytical prediction of the critical initial radial velocity based on the Mathieu stability diagram for the occurrence of mode transformation is in the same order of the prediction based on finite element analysis.