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

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

preprint2012arXivOpen access
D. Martínez-GutiérrezV. R. Velasco
cond-mat.mes-hallcond-mat.mtrl-sci
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D. Martínez-GutiérrezV. R. Velasco

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