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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.

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