Influence of the Environment on the Natural Frequencies of Vibrations of Carbon Nanotubes

In many applications, carbon nanotubes are in contact with a medium, which may be internal or external. In this work, the bending vibrations of a single-walled carbon nanotube are determined from the theory of elastic vibrations of a long cylindrical shell. The inner and outer surfaces of the shell are in contact with fluids. The dependence of natural frequencies on the ratios of the densities and pressures of the inner and outer media, as well as on the material, wall thickness and radius of the nanotube, is studied. The conditions of detachment-free and cavitation wall-medium interaction are discussed. The results obtained are important for the numerous nanotechnologies in which carbon nanotubes are in contact with fluids.