In this paper, the thermal effect on wave dispersion characteristic induced by the spinning and longitudinal motions in the viscoelastic carbon nanotubes (CNTs) conveying fluid is presented. Hamilton’s principle is utilized to derive the governing equation of this nanotube based on the non-local strain gradient and Euler–Bernoulli beam theories. Then, the dispersion solution is found by using the Naiver method. Based on this, the influences of the spinning and longitudinal motion velocities, structural damping, temperature and flow velocity on dispersion relation of the nanotubes are discussed according to numerical simulation. In view of the results of numerical examples, some interesting conclusions can be drawn. The existence of spinning motion leads to the coupling between the vibration in the [Formula: see text] and [Formula: see text] directions, which induces that the first-order transverse wave frequency increases/decreases for small/large wave number and the second-order one increases. The important solutions presented in the work will provide the useful information for the designation of the nanotubes conveying fluid with the spinning and longitudinal motion.

中文翻译：

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旋转和纵向运动对输送流体的粘弹性碳纳米管波传播行为的热效应

本文介绍了粘弹性碳纳米管 (CNT) 输送流体中旋转和纵向运动对波色散特性的热效应。汉密尔顿原理用于基于非局部应变梯度和欧拉-伯努利束理论推导该纳米管的控制方程。然后，使用 Naiver 方法找到分散溶液。在此基础上，通过数值模拟讨论了自旋和纵向运动速度、结构阻尼、温度和流速对纳米管色散关系的影响。鉴于数值例子的结果，可以得出一些有趣的结论。旋转运动的存在导致[公式：见正文]和[公式：见文本]方向，这导致小/大波数的一阶横波频率增加/减少，二阶横波频率增加。工作中提出的重要解决方案将为指定具有旋转和纵向运动的输送流体的纳米管提供有用的信息。