Theoretical analysis on nonlinear vibration of fluid flow in single-walled carbon nanotube

In this study, the concept of nonlocal continuumtheory is used to characterize the nonlinear vibrationof an embedded single-walled carbon nanotube. ThePasternak-type model is employed to simulate the interactionof the SWNTs. The parameterized perturbationmethod is used to solve the corresponding nonlinear differentialequation. The effects of the vibration amplitude,flow velocity, nonlocal parameter, and stiffness of themedium on the nonlinear frequency variation are presented.The result shows that by increasing the Winkler constant,the nonlinear frequency decreases, especially for lowvibration amplitudes. In addition, it is resulted that influenceof the nonlocal parameter is greater at higher flowvelocities in comparison with lower flow velocities.