Because of the importance of the analytical study of the vibration behavior of nanotubes delivering nanoparticles, in this study, the transverse vibration of these systems has been studied by analytical approach based on the homotopy perturbation method. The nonlocal Euler–Bernoulli beam theory is used for derivation of the equation of motion. The interaction between nanoparticle and the inner wall of nanotube has been modeled by using van der Waals forces and considering the effects of inertial forces caused by centrifugal and Coriolis acceleration components of nanoparticles. After evaluation of the implemented analytical method by numerical results, it is revealed that the obtained second-order approximation response gives high accurate vibration behavior of these systems for a wide range of parameters. As well, these results show that inertial forces caused by motion of nanoparticle increase vibration amplitude of nanotube and change nonlinear frequency of the system.

由于分析输送纳米管的纳米管的振动行为的分析研究的重要性，在这项研究中，已经通过基于同伦摄动法的分析方法研究了这些系统的横向振动。非局部Euler–Bernoulli束理论用于运动方程的推导。纳米粒子和纳米管内壁之间的相互作用已通过使用范德华力建模，并考虑了纳米粒子的离心力和科里奥利加速度分量引起的惯性力的影响。通过数值结果对所实施的分析方法进行评估后，发现所获得的二阶逼近响应可为各种参数的系统提供高精度的振动特性。还有