In this article, the vibration analysis of a double-walled carbon nanotube (DWCNT) conveying viscous flow with the aid of modified strain gradient theory has been investigated. The visco-Pasternak model is used to simulate the elastic medium. The force caused by viscous fluid is calculated by modified Navier–Stokes relation. The Gurtin-Murdoch surface elasticity theory has the capability to capture the size-dependent behavior of nanostructures due to the surface stress effect. The governing equations and the boundary conditions have been developed using Hamilton's principle and solved with the aid of generalized differential quadrature (GDQ) methods.

在本文中，利用改进的应变梯度理论研究了输送粘性流的双壁碳纳米管（DWCNT）的振动分析。粘滞-帕斯泰纳克模型用于模拟弹性介质。由粘性流体引起的力是通过修改的Navier–Stokes关系计算的。Gurtin-Murdoch表面弹性理论具有捕获由于表面应力效应而产生的纳米结构尺寸相关行为的能力。控制方程和边界条件是使用汉密尔顿原理开发的，并借助广义差分正交（GDQ）方法进行了求解。