Elastic waves in homogeneous and layered transversely isotropic media: Plane waves and Gaussian wave packets. A general approach. Spies, M. The Journal of the Acoustical Society of America, 95(4):1748–1760, 1994.
Elastic waves in homogeneous and layered transversely isotropic media: Plane waves and Gaussian wave packets. A general approach [link]Paper  doi  abstract   bibtex   
Solutions to the equation of motion are derived for transversely isotropic media such as fiber composites, ideally fiber‐textured austenitic steels, or extruded metal‐matrix composites. The approach is most general in that the orientation of the materials’ axis of rotational symmetry is arbitrary. Thus the results obtained using a coordinate‐free representation are particularly convenient in view of layered structures, where for the materials of interest the fiber axis is perpendicular to the surface normal, but variable in orientation. Plane elastic waves are characterized by the corresponding wave vectors, making especially possible a quantitative evaluation of the deviation of wave propagation direction and energy flux, which is characteristic for anisotropic materials. Reflection and refraction of plane waves at an interface between two arbitrarily oriented transversely isotropic media is examined yielding an algorithm that provides the respective reflection and transmission coefficients. The propagation of elastic waves of finite spatial and temporal extent is modeled using the concept of Gaussian wave packets. The relations given in the literature for general anisotropic media are specialized to the homogeneous and layered transversely isotropic cases. Numerical evaluation of the analytical results is included.
@article{spies_elastic_1994,
	title = {Elastic waves in homogeneous and layered transversely isotropic media: {Plane} waves and {Gaussian} wave packets. {A} general approach},
	volume = {95},
	issn = {0001-4966},
	shorttitle = {Elastic waves in homogeneous and layered transversely isotropic media},
	url = {http://asa.scitation.org.docelec.insa-lyon.fr/doi/10.1121/1.408694},
	doi = {10.1121/1.408694},
	abstract = {Solutions to the equation of motion are derived for transversely isotropic media such as fiber composites, ideally fiber‐textured austenitic steels, or extruded metal‐matrix composites. The approach is most general in that the orientation of the materials’ axis of rotational symmetry is arbitrary. Thus the results obtained using a coordinate‐free representation are particularly convenient in view of layered structures, where for the materials of interest the fiber axis is perpendicular to the surface normal, but variable in orientation. Plane elastic waves are characterized by the corresponding wave vectors, making especially possible a quantitative evaluation of the deviation of wave propagation direction and energy flux, which is characteristic for anisotropic materials. Reflection and refraction of plane waves at an interface between two arbitrarily oriented transversely isotropic media is examined yielding an algorithm that provides the respective reflection and transmission coefficients. The propagation of elastic waves of finite spatial and temporal extent is modeled using the concept of Gaussian wave packets. The relations given in the literature for general anisotropic media are specialized to the homogeneous and layered transversely isotropic cases. Numerical evaluation of the analytical results is included.},
	number = {4},
	urldate = {2017-01-09TZ},
	journal = {The Journal of the Acoustical Society of America},
	author = {Spies, M.},
	year = {1994},
	pages = {1748--1760}
}
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