Free vibration of anisotropic single-walled carbon nanotube based on couple stress theory for different chirality

In the present work, using the couple stress theory, a new model is provided for vibrating behavior of anisotropic carbon nanotubes. Carbon nanotubes have many applications, and careful analysis of their behavior is important. So far, using the isotropic models, several studies have been conducted on carbon nanotube vibration. According to the arrangement of carbon atoms on the nanotube walls, their properties will be different in various directions. Therefore, the behavior of carbon nanotubes must be considered as anisotropic materials. In this article, initially, using the Hamilton's principle, motion equations, and boundary conditions of carbon nanotubes are extracted based on couple stress theory. Afterwards, the equations are solved using the analytical solution method. In the results section, the effect of different parameters, particularly the anisotropic effect, on the carbon nanotube natural frequency is investigated.