Carbon nanotubes, from single to 5-walled ones in their perfect form, were simulated on the basis of the finite element method. Their natural frequencies were obtained analytically and through a finite element approach and compared with each other. In the next step, three most likely and randomly scattered defects (Si-doping, carbon vacancy and perturbation) of different amounts were introduced to the perfect models and their vibrational behavior and the influence of these defects upon the vibrational stability of carbon nanotubes were investigated. According to the results, the existence and development of any type of defect in the structure of carbon nanotubes resulted in a reduction in the natural frequency and vibrational stability of the carbon nanotubes. These reductions were also expressed by simple general relationships that predicted and judged the influence of the defects upon the vibrational stability of carbon nanotubes.

Numerical Modeling of Eigenmodes and Eigenfrequencies of Single- and Multi-Walled Carbon Nanotubes under the Influence of Atomic Defects. A.Ghavamian, A.Öchsner: Computational Materials Science, 2013, 72, 42-8