Abstract

This article is a comprehensive investigation into the equations of the size-dependent free vibration of a special type of fluid-conveying nanotubes, i.e., double-walled boron nitride nanotubes, in a thermal environment. The motion equations are obtained through the use of nonlocal strain gradient theory for piezoelectric materials combined with the first-order shear deformation theory and Hamilton’s principle. Lennard-Jones potential function imposes the coupling between the pair of nanotubes that are bound together via van der Waals forces. This study also considers softening and hardening effects to better understand important aspects of modeling. After setting proper boundary conditions, the differential quadrature method is exploited to solve the obtained equations. This numerical study allows us to evaluate the effects of many parameters that include delta-temperature, aspect ratio, size scale and boundary conditions on the nondimensional eigenfrequency of considered system and critical flow velocity.

摘要

本文全面研究了一种特殊类型的流体输送纳米管，即双壁氮化硼纳米管，在热环境中的尺寸相关自由振动方程。运动方程是利用压电材料的非局部应变梯度理论结合一阶剪切变形理论和哈密顿原理得到的。Lennard-Jones 势函数在通过范德华力结合在一起的一对纳米管之间施加耦合。本研究还考虑了软化和硬化效应，以更好地理解建模的重要方面。在设定合适的边界条件后，利用微分求积法求解得到的方程。