Abstract
The nonlinear vibration behaviors of double-walled carbon nanotubes (DWCNTs) are investigated based on Donnell’s cylindrical shell model with van der Waals (vdW) forces between the inner and outer tubes. The harmonic balance method is used to analyze the relationship between the amplitudes and the frequencies of natural vibrations of the tubes. Numerical analyses are carried out to understand the effects of vdW forces and nonlinearity on the carbon nanotubes (CNTs). The results show that the radial vibrational modes of the inner and outer tubes of simply supported DWCNTs have twice dynamical mode transitions as the frequency increases. The transitions correspond to twice the noncoaxial vibrations, which play a critical role in the electronic and transport properties of CNTs.
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