Abstract
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.
Highlights
Since the discovery of carbon nanotubes (CNTs) by Iijima in 1991 [1], these nanostructures have been the focus of many investigations
Since experimental observations show that CNTs are not usually straight, but rather have certain degree of curvature or waviness along the nanotubes length [7, 8], we focus in the following on the investigation of the effect of the curvature on the dynamic behavior
The vibrational behavior of different armchair and zigzag single-walled carbon nanotubes (SWCNTs) was investigated for different curvatures from 0∘ to 45∘ bending angle
Summary
Since the discovery of carbon nanotubes (CNTs) by Iijima in 1991 [1], these nanostructures have been the focus of many investigations. They could apply the molecular mechanics theory directly due to the modeling of atomic bonds, applying physical variables such as bond stretching Based on their results, new natural frequencies and mode shapes for numerous CNTs under different boundary conditions were found. They analyzed both armchair and zigzag CNTs with clamped-clamped and clamped-free boundary conditions in order to find their natural frequencies and corresponding mode shapes Their results indicated the appearance of these modes of vibration in the eigenvalues and eigenvectors without any distinction. All our simulations were performed with the commercial finite element code MSC.MARC (MSC Software Corporation, Santa Ana, CA, USA)
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