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

2012/07/02 by D. Martínez-Gutiérrez, Martínez-Gutiérrez, D., V. R. Velasco +1
Physics and Astronomy · #FOS: Physical sciences #Materials Science (cond-mat.mtrl-sci) #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #cond-mat.mes-hall #cond-mat.mtrl-sci

paper · pdf · doi:10.48550/arxiv.1207.0379

9 pages

arxiv created 2012/07/02 · arxiv updated 2012/07/03

Abstract

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.

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