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- Title
WAVE REFLECTION AND TRANSMISSION FROM ANISOTROPIC LAYERS THROUGH RICCATI EQUATIONS.
- Authors
CAVIGLIA, GIACOMO; MORRO, ANGELO
- Abstract
Reflection and transmission matrices, associated with obliquely-incident plane harmonic waves, are investigated for a planarly-stratified inhomogeneous layer. The material in the layer and in the half-spaces is a dissipative anisotropic solid. Upon establishing a Cauchy problem for the local impedance matrix in the layer, the condition is found for the determination of the initial value. Next reflection and transmission matrices of the layer are related to the final value of the impedance. Moreover the dependence of the reflection matrix on the thickness of the layer is found to satisfy a Riccati differential equation. This shows in turn that the local reflection and the reflection of the layer are the same in the sense of a principle of localization. As a result, the principle is generalized to anisotropic dissipative layers.
- Subjects
WAVE mechanics; ANISOTROPY; ELECTRICAL harmonics; RICCATI equation; SOLIDS
- Publication
Quarterly Journal of Mechanics & Applied Mathematics, 2002, Vol 55, Issue 1, p93
- ISSN
0033-5614
- Publication type
Article
- DOI
10.1093/qjmam/55.1.93