Coupling analysis of screwing motion of double-walled carbon nanotubes

As the inner tube is excited from a rotation frequency at a separation distance, the inner tube will generate a reciprocating screwing motion. In this work, this coupling effect is investigated theoretically. The van der Waals force between two carbon nanotubes is expressed in a simple form of Fourier series so that the coupled nonlinear differential equations can be quickly solved. The proposed approach is thousands of times faster than the traditional method, which makes it possible to fit the coupling coefficients. As a result, expressions for the coefficients of the coupled equations are given. It is observed that a larger initial rotation frequency excitation will result in a higher dissipation rate of the axial oscillation, and vice versa.