General expressions for the dispersion relation of acoustic radial (breathing) modes in cylinders and cylindrical shells of general anisotropic crystals

摘要

We present here a study of the radial modes for infinitely long cylinders andcylindrical shells of general anisotropic crystals. The elastic coefficientsmatrix includes twenty-one independent constants. We obtain expressions inclosed form for the dispersion relation, valid for any anisotropic material. Inthe case of the lowest breathing mode of a thin cylindrical shell we obtain asimple analytical formula. This can be used to obtain a first estimate of thebreathing mode frequency in nanotubes for any material.