Prediction of wave propagation in multi-walled carbon nanotubes examined using a multiple-elastic-shell model

A multiple-elastic-shell model is presented for wave propagation estimation along an individual MWCNT.The analysis shows that when the frequency is lower than the critical frequencies of the shells in MWCNT,the vibration mode is almost coaxial.However,when the frequency is higher than at least one of the critical frequencies,non-coaxial vibration modes emerge and these vibrations propagate at various speeds significantly higher or lower than the speed predicted by the single-elastic-shell model.Hence,tetra-hertz waves in MWCNTs are essentially non-coaxial with complex phenomena.Tetra-hertz waves in MWCNTs propagate at various speeds,which depend not only on the frequency,but also on the non-coaxial vibration mode.