基于能量法的载流单层碳纳米管振动特性研究

Analysis of the vibration characteristics of fluid-conveying single-walled carbon nanotubes based on the energy method

以非局部弹性理论为基础,考虑了碳纳米管的小尺度效应;采用欧拉-伯努利梁模型,基于能量法给出了载流单层碳纳米管的振动频率近似解;并通过具体算例,应用振动频率近似解公式求解了悬臂单层纳米管的频率值,进而研究了管内流体流速、碳纳米管小尺度参数对悬臂梁一阶振动频率及振型的影响,并将得到的结论与已有文献的结果进行比较,证明了振动频率近似解的正确性。

Approximated frequency expressions for a single-walled carbon nanotubes(SWCNTs) with conveying fluid are analyzed based on the energy method and using the nonlocal elastic theory with the Euler-Bernoulli beam theory. Through some numerical analysis, the influences of internal moving fluids, such as flow velocity, and the small size parameter on the first mode vibration frequency and mode shape of cantilever SWCNTs are investigated in detail. By comparison with the results reported in references, the accuracy and feasibility of the approximated expression are validated.