Analysis of wave propagation in carbon nanotubes via elastic shell theories

Abstract

This paper investigates wave propagation in both single-walled carbon nanotubes (SWNTs) and double-walled carbon nanotubes (DWNTs) via two developed elastic shell theories: Love’s thin cylindrical shell theory and the Cooper–Naghdi thick cylindrical shell theory. In studying DWNTs, the van der Waals effect is accounted for and modeled with the two theories. The elastic thick shell theory, in which the shear and inertia effects are taken into account, is developed first to investigate the wave propagations of CNTs to provide more accurate wave dispersions for higher modes. The material properties of the CNTs that are used in the two shell theories are proposed, and the expression of the inertia moment of the cross area in the thick shell theory is recommended. The dispersion results that are derived via the two theories are compared to show the feasibility of those theories in studying CNTs. Radius-dependent wave propagation results in SWNTs and DWNTs are also studied via the two theories.