Mohamed Selim Mahmoud, Musa Awad
Department of Mathematics, College of Science and Humanities in Al-Aflaj, Prince Sattam bin Abdul-Aziz university, Al-Aflaj 11912, Saudi Arabia.
Department of Mathematics, Suez Faculty of Science, Suez University, Suez 34891, Egypt.
Nanomaterials (Basel). 2020 May 18;10(5):974. doi: 10.3390/nano10050974.
This paper is an attempt to study the nonlinear vibration of a pre-stressed single-walled carbon nanotube (SWCNT) with water-filled and simply supported ends. A new analytical formula is obtained for the nonlinear model based on the simplified Donnell's shell theory. The effects of internal fluid on the coupling vibration of the SWCNT-water system are discussed in detail. Furthermore, the influence of the different nanotube thicknesses and radiuses on the nonlinear vibration frequencies is investigated according to the shell theory. Numerical calculations are done to show the effectiveness of the proposed schemes. The results show that the nonlinear frequency grew with the increasing nonlinear parameters (radius and thickness of nanotube). In addition, it is shown that the influence of the nonlinear parameters is greater at the lower mode in comparison with the higher mode for the same nanotube thickness and radius.
本文旨在研究两端简支且内部充水的预应力单壁碳纳米管（SWCNT）的非线性振动。基于简化的Donnell壳理论，得到了非线性模型的一个新解析公式。详细讨论了内部流体对SWCNT - 水系统耦合振动的影响。此外，根据壳理论研究了不同纳米管厚度和半径对非线性振动频率的影响。通过数值计算验证了所提方案的有效性。结果表明，非线性频率随非线性参数（纳米管半径和厚度）的增加而增大。此外，对于相同的纳米管厚度和半径，在较低模态下非线性参数的影响比在较高模态下更大。
