Effects of axial load on wave propagation in double-walled carbon nanotubes used as a flexible tip in AFM

This paper is concerned with the effect of axial load, shear deformation and rotary inertia on wave propagation in double-walled carbon nanotubes (DWCNTs) within terahertz range. Our analysis is based on Timoshenko-beam model and Eulerbeam model. The present models predict some terahertz critical frequencies at which the number of wave speeds changes. In these models the amounts of wave speed is unique only when the frequency is below the lowest critical frequency. When the frequency is equal to the lowest critical frequency, there can be one or two (for CNTs of smaller radii) wave speeds. Furthermore, when the frequency is higher than the lowest critical frequency, more than one wave speed exists and waves of given frequency could propagate at various speeds. It can be seen that rotary inertia and shear deformation have a significant effect on both the wave speeds and the critical frequencies. Hence, terahertz wave propagation in CNTs should be better modeled by Timoshenko-beam model, instead of Euler-beam model.