Stability Analysis of Double-Walled Carbon Nanotubes with Initial Stress

Abstract

In the paper, the stability of the double-walled carbon nanotubes (DWCNTs) under the initial axial stress are studied. Galerkin and harmonic balance method are used to analyze the relation between the amplitudes and the frequencies of the tubes. The results show that the critical initial stress plays a significant control role in the amplitude-frequency curves. When the initial axial stress is less than the critical initial stress, DWCNTs have twice dynamical mode transitions corresponding to twice noncoaxial vibrations, however, when the initial axial stress is larger than the critical initial stress, the topological forms of the amplitude-frequency curve are changeable, which are corresponding to coaxial vibration or three possible noncoaxial vibration type.