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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.

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