锥形纳米管纵向振动固有频率

Natural frequencies of longitudinal vibration of cone-shaped nanotubes

研究变截面锥形纳米管/棒的纵向振动问题。由于其控制方程涉及变系数微分方程,提出适用范围广、简单精确的积分方程方法求解该问题,基于经典弹性杆理论与非局部弹性杆理论分别给出几种边界条件下的固有频率计算。对一端固定一端附加集中质量的碳纳米管的纵向振动,给出共振基频的近似简单表达式。与其它方法所得数值结果对比表明该方法有效。

The longitudinal vibration of cone-shaped nanotubes/nanorods was studied. The governing equation involved in the problem is a partial differential equation with variable coefficients. A widely applicable, simple and accurate integral equation method was presented to solve the above-mentioned problem. Based on the classical and nonlocal theories of elastic rods, the natural frequencies were determined under various boundary conditions. In particular, a simple approximate expression for the resonant fundamental frequency of clamped-free carbon nanotubes carrying a concentrated mass at the free end was derived. The comparison of our results with the previous ones using different approaches indicates that the proposed method is effective and easy to implement.