单壁碳纳米管振动特性有限元分析

Analysis of vibration properties of single-walled carbon nanotubes with finite element method

利用有限元方法对悬臂梁式单壁碳纳米管固有频率和手性角、长度、直径等几何参数之间的关系进行研究。C-C共价键作用通过等效梁单元来模拟,碳原子等效为质点,建立碳纳米管分子结构力学有限元模型,并引入了质量比例因子β来消除数值误差。数值结果表明,手性角对单壁碳纳米管的固有频率影响很小;固有频率随长度的增加而减小,但达到一定长度之后基频随长度的变化不再明显;前4阶固有频率随直径增大而增大,第5阶固有频率不随直径变化,而高阶固有频率随直径的变化不规律;在低阶模态时长度对固有频率的影响比直径的影响更加显著。

The nature frequencies versus the change of the geometry of the cantilever SWCNTs were investigated with the finite element method. A molecular structure model of SWCNTs was built with carbon-carbon（C-C） covalent bonds simulated by the equivalent beam elements and carbon atoms equivalent to mass points. A mass scale factor β is introduced to eliminate the numerical error. The results show that the chiral angle has no obvious effect on the nature frequency of SWCNTs with the same aspect ratio and similar diameter. The natural frequency of the SWCNTs with the same diameter decreases with the increase of the length; while the fundamental frequency changes little with the increase of length when it is long enough （Aspect ratio〉10）. The first four order frequencies increase with the increase of diameter and the fifth order frequency doesn＇t change with the diameter; while the trend is not regular for higher order nature frequencies of SWCNTs with the same length when the diameter increases. The length has a greater impact on nature frequency than the diameter does in the lower order modes.