Structure-preserving analysis on chaotic characteristics of transverse vibration for embedded double-walled carbon nanotube

Analysing the ultra-high frequency vibrational characteristics of carbon nanotubes, especially on the chaotic characteristics, is a key scientific problem in the dynamic design of the carbon nanotube devices. Considering the van der Waals force between the inner layer and the outer layer of the embedded double-walled carbon nanotube, and the effects of the elastic medium as well as the effects of the simple harmonic external excitation, the coupling dybamic model describing the transverse vibration of the embedded double-walled carbon nanotube is presented. The generalized multi-symplectic formulations with an explicit multi-symplectic structure residual are deduced by introducing the dual momenta. The Preissmann approach, which has been proved to be a structure-preserving method that can be used to reproduce the chaotic characteristics of carbon nanotubes, is employed to discrete the generalized multi-symplectic formulations. The numerical results imply that, the transverse vibration of the embedded double-walled carbon nanotube subjected to the external excitation larger than the critical external excitation will enter the chaotic state through a period-doubling bifurcation path. In addition, the critical external excitation for the chaos of the inner layer carbon nanotube's transverse vibration is larger than that of the outer layer carbon nanotube's transverse vibration. The above findings reported in this paper provide some guidance for the dynamic design of the carbon nanotube devices directly.