A nonlocal rod model for axial vibration of double-walled carbon nanotubes including axial van der Waals force effects

In this study, the axial vibration of double-walled carbon nanotubes (DWCNTs) is studied using nonlocal elasticity theory. The nonlocal constitutive equations of Eringen are used in the formulations. The van der Waals forces are considered in the axial direction.An interaction coefficient is obtained in terms of the previously proposed van der Waals coefficient and effective thickness of the single-walled carbon nanotubes. The effect of various parameters like geometry of nanotubes, van der Waals forces and nonlocal parameters on the axial vibration of DWCNTs is discussed. Some mode shapes are also depicted in order to show the relative motion of the nested tubes. The van der Waals forces have strong effects on the axial vibration characteristics of DWCNTs. The present results can be used in the continuum modeling of nanoscale linear motors and oscillators.