{'fraction_non_alphanumeric': 0.01948051948051948, 'fraction_numerical': 0.0, 'mean_word_length': 5.391705069124424, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
The Effect of Atom Vacancy Defect on the Vibrational Behavior of Single-Walled Carbon Nanotubes: A Structural Mechanics Approach

An atomistic structural mechanics method, which is based on the exclusive use of spring elements, is developed in order to study the effect of imperfections due to atom vacancy on the vibrational characteristics of single-walled carbon nanotubes (SWCNTs). The developed elements simulate the relative translations and rotations between atoms as well as the mass of the atoms. In this way, molecular mechanics theory can be applied directly because the atomic bonds are modeled by using exclusively physical variables such as bond stretching. The method is validated for its predictability comparing with vibration results found in the open literature for pristine nanotubes. Then, it is used for the vibration analysis of defective nanotubes. Imperfections such as one-atom vacancy, two-atom vacancy, and one carbon hexagonal cell vacancy are investigated. Their effect on vibrational behavior is explored for different defect positions, nanotube diameters, and support conditions. According to the obtained results, the fundamental frequency is decreased as the size of imperfection increases, and the percentage reduction in fundamental frequency due to the atomic vacancy defect is more affected for a single-clamped SWCNT than for a double-clamped one.