Elastic vibrations of a cylindrical nanotube with the effect of surface stress and surface inertia

•Surface stress and surface inertia have been taken into account to study the acoustic vibration of a nanotube.•Both surface stress and surface inertia have significant influence on the vibration behavior of the nanotube.•Due to the surface effect, resonant frequency of some vibration modes may be the same as that of lower order by the classical elasticity.•The surface effect may either decrease or increase the Raman shift compared to the classical results.

Vibration frequency analysis of nanostructures may be essential for study of their thermal conductivity and mechanical characterization. Given the high surface-to-volume ratio, the elastic vibrations of an infinitely long cylindrical nanotube have been studied by considering both the effects of surface stress and that of surface inertia within the framework of surface elasticity. The phonon dispersion and the resonant frequencies for the specific vibration modes have been calculated. Numerical results have indicated that the surface stress and the surface inertia have equally important effect on the vibration behavior of the nanotube that may depend on the vibration modes as well. Due to the surface effect, the vibration modes of lower order by the classical elasticity may be indeed the modes of higher order. The surface effect on the low-frequency Raman shift has also been found.

Graphical abstractThe dispersion relation of torsion mode demonstrated that the effect of surface inertia may render the vibration frequency of the third order consistent with the lowest one in conventional elasticity.Figure optionsDownload full-size imageDownload as PowerPoint slide