{'fraction_non_alphanumeric': 0.013550135501355014, 'fraction_numerical': 0.0, 'mean_word_length': 5.595238095238095, '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}}
Dynamic Characteristics of Multi-Walled Carbon Nanotubes under Longitudinal Magnetic Fields

This article presented an analytical solution for the effect of longitudinal magnetic field on asymmetric dynamic characteristics of multi-walled carbon nanotubes (MWNTs). Based on the Maxwell equation and electrodynamic equation, asymmetric couple dynamic equations of MWNTs under a longitudinal magnetic field are solved. The effects of longitudinal magnetic field and elastic medium on the vibration frequencies and amplitude ratios between tube walls of MWNTs are discussed through numerical results. Results show that the longitudinal magnetic field exerted on double-walled carbon nanotubes (DWNTs) makes the lowest frequency of the DWNTs increase and the highest frequency of the DWNTs decrease; the two walls of DWNTs appear in radially coaxial vibration phenomena, two walls of DWNTs appear in a relative axial motion when the outer wall of the DWNTs is subjected to the effect of medium constrain, and the relative axial motion increases as the longitudinal magnetic field exerted on the DWNTs increases.