Abstract
<jats:p>The bending vibrations of a single-walled carbon nanotube are determined using the theory of elastic vibrations of a long cylindrical shell, with the condition of inextensibility of the middle surface being satisfied with high accu racy. The shell surfaces are in contact with media of different densities and pressures inside and outside the shell. The medium can be compressible during surface deformation or incompressible. For gases, an isothermal law is as sumed, and for the incompressible fluid model, a constant density is assumed. The specified static pressures do not change during tube deformation. The equations of motion for ideal incompressible and compressible fluids with dif ferent densities and pressures inside and outside the tube are used. An assumption of a separation-free interaction between the tube wall and the contacting medium is made. The transverse distributed force is determined taking into account the change in elementary lengths on the inner and outer surfaces of the curved shell in accordance with the Kirchhoff–Love hypothesis on the normal to the curved midsurface. The conditions of equality of the velocities of an ideal fluid along the normal and the tube wall are used. The spectrum of natural frequencies of radial bending vibra tions of a long closed shell with the parameters of a single-wall carbon nanotube and the influence of the media in side and outside it on them are investigated. The dependence of the natural frequencies on the ratios of the densities and pressures of the media, as well as the material, wall thickness, and radius of the tube, is studied. The natural fre quencies of bending vibrations of a nanotube in the presence of water and other liquids are always significantly low er than in a vacuum. This is explained by the influence of the added masses of liquids inside and outside the tube. Estimates of the conditions for the occurrence of cavitation interaction between the nanotube and the liquid are im portant, since this leads to a significant change in the oscillation frequencies of the system compared to a separation free interaction. Apparently, this complex phenomenon has not yet been considered. It requires experimental study. A more accurate description is possible using molecular physics and numerical modeling. Here, some estimates of this phenomenon are given for the case of a vibrating single-walled nanotube in contact with water. The results ob tained are also relevant for macroscopic cylindrical shells. The influence of the contacting medium on the oscillation frequency is significant for thin shells made of a material with a low elastic modulus.</jats:p>