基于能量法的单层固支碳纳米管频率预测

以非局部弹性理论为基础,同时考虑碳纳米管小尺度效应,采用欧拉-伯努利梁模型建立有外加预应力情况下单层碳纳米管的动力学控制方程,并给出其振动频率精确解,进而基于能量法给出单层碳纳米管振动频率近似解,最后通过具体算例将其精确解与近似解进行比较。结果表明,外加预应力的大小、碳纳米管模态数以及小尺度参数均影响单层碳纳米管振动频率预测值的准确性。

Prediction of natural frequency of SWCNTs with clamped boundary based on energy method

Based on nonlocal elastic theory and with the size effect of carbon nanotubes considered, this paper used Euler-Bernoulli beam theory (EBT) to establish the dynamic governing equation of single-walled carbon nanotubes (SWCNTs) with clamped-clamped boundary under prestress. It gave the exact solution to the vibration frequency of SWCNTs, which was then compared with the approximate solution derived by the energy method. It is found that the accuracy of SWCNTs vibration frequency prediction is influenced by the value of prestress, modal number and small scale parameters of SWCNTs.