Wave propagation in micromorphic anisotropic continua with an application to tetragonal crystals

TL;DR

This paper investigates wave propagation in micromorphic anisotropic continua, focusing on tetragonal crystals, providing detailed dispersion relations and vibrational modes for different propagation directions.

Contribution

It offers a novel micromorphic continuum model for anisotropic crystals, with exact solutions for wave frequencies and modes in tetragonal crystals along specific directions.

Findings

Exact dispersion relations for acoustic and optic frequencies.

Detailed vibrational mode representations for tetragonal crystals.

Qualitative insights into wave frequencies in anisotropic micromorphic media.

Abstract

We study the coupled macroscopic and lattice wave propagation in anisotropic crystals seen as continua with affine microstructure (or micromorphic). In the general case we obtain qualitative informations on the frequencies and the dispersion realtions. These results are then specialized to crystals of the tetragonal point group for various propagation directions: exact representation for the acoustic and optic frequencies and for the coupled vibrations modes are obtained for propagation directions along the tetragonal c-axis.