Vibration and buckling of a carbon nanotube inserted with a carbon chain
Paper in proceedings, 2008
An elastic string-elastic shell model is developed to study vibration behaviors of a carbon nanowire. The present model predicts that non-coaxial vibration between the C-chain and the innermost tube does not occur due to negligible bending rigidity of the C-chain. In addition, it is found that the C-chain has most significant effect on the lowest frequency associated with radial vibration mode for circumferential wave-number 2 (n=2). In particular, the effect of the C-chain on axisymmetric radial breathing frequencies (n=0) predicted by the present model is found to be in reasonable agreement with known experimental and modeling results available in the literature. To study the buckling of a carbon nanowire made of the C-chain inserted inside a CNT, not only the elastic string-elastic shell model that used above but also the molecular dynamics (MD) simulation are adopted. For radial buckling, both continuum model and MD simulation predict that C-chain increases buckling stress by more than 40% to (2, 8), (0, 9), (3, 7) and (5, 5) tube. The continuum model predicts that circumferential wave number n=2 at buckling. Related with this, MD simulation shows that the cross-section of CNT is an ellipse at buckling. In particular, the nonlinear effects of vdW interaction have significant influence on the critical buckling loading. For the buckling under axial compression, two different kinds of buckling have been observed and investigated, namely the C-chain's unconditional buckling, and the tube's wall buckling, respectively. After the unconditional buckling, all displacements on the C-chain are in the same plane, and, the wave amplitudes' localization phenomenon appears. To the tube's wall buckling, the C-chain could either increase or decrease axial buckling strain depending on specific CNT chirality and temperature.