Vibrations in cylindrical shells with transverse elastic isotropy: Application to III–V nitride nanotubes

The vibrational modes of cylindrical shells with transverse elastic isotropy and arbitrary thickness are calculated in the framework of the elasticity theory and a comparison with the isotropic approach is presented. Cylindrical shells are a good model for nanotubes and here an application for nanotubes of transversely isotropic elastic materials is given. We have obtained the expression for the frequency of the radial breathing mode and it is shown that calculated frequencies coming from that expression compare fairly well with those obtained from different ab initio, force constant model calculations and experimental results. Further, the dispersion relations depend on all the elastic coefficients and therefore they are quite different for nanotubes with hexagonal or wurtzite structure. This demonstrates the need to go beyond the isotropic model to investigate the vibrational spectrum of transversely isotropic elastic material nanotubes and nanowires.