Reduced vibrational frequencies of multiwall carbon nanotubes due to interlayer degrees of freedom

• We model MWCNTs as coupling beam systems by considering interlayer degrees of freedom of MWCNTs.
• Study vibration of MWCNTs with various outer and inner boundary constraints.
• The interlayer degrees of freedom of MWCNTs have a substantial effect on reducing natural frequencies.
• Offer a reasonable explanation of the discrepancy between experimental measured results and theoretical predicted results of MWCNTs.

Some recent experiments have showed that measured resonant frequencies of multi-walled carbon nanotubes (MWCNTs) were often much lower than the theoretical resonant frequencies predicted by the widely used elastic beam model which defines the whole MWCNTs as a single elastic beam. The present work aims at offering a reasonable explanation of this discrepancy by considering interlayer degrees of freedom of MWCNTs. To this end, vibration of MWCNts with various outer and inner boundary constraints is studied. MWCNTs are modeled as a coupling beam system in which the outermost tube(s) is simulated as a single beam while all other inner tubes are modeled as another single beam and the two beams are coupled through van der walls interlayer forces. To better fit typical experimental conditions, the outmost tube is assumed to be doubly clamped into the surrounding matrix while all other inner tubes are assumed to be free at their ends. Our results confirmed that the interlayer degrees of freedom of MWCNts have a substantial effect on reducing natural frequencies and thus offer a plausible explanation for the observed lower natural frequencies as compared to the theoretical predictions of the single beam model which ignored all interlayer degrees of freedom. Typically, the natural frequencies predicted by the present model are about 30% lower than those predicted by the single beam model, in good agreement with a few recently reported experimental data.