Numerical simulation of the vibration behavior of curved carbon nanotubes

Several zigzag and armchair single-walled carbon nanotubes (CNTs) were modeled by a commercial finite element package and their vibrational behavior was studied. Numerous computational tests with different boundary conditions and different bending angles were performed. Both computational and analytical results were compared. It was shown that the computational results are in good agreement with the analytical calculations in the case of straight tubes. In addition, it was concluded that the natural frequency of straight armchair and zigzag CNTs increases by increasing the chiral number of both armchair and zigzag CNTs. It was also revealed that the natural frequency of CNTs with higher chirality decreases by introducing bending angles. Nevertheless, the influence of increasing bending angle on the natural frequency of armchair and zigzag CNTs with lower chiral number is almost negligible.