Geodesic
The matrix of the transforming of vibration waves
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 30, Tome 275 (2001), pp. 105-131

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Scattering of the linear vibration waves on a nodal junction of elastic plates is considered. For description of transforming (transmission, reflection, refraction and transformation into other types) of such waves we use the transformation matrix. We have proved for this matrix some usual properties related with the reciprocity principle and with conservation of energy. In the case when a source of field is evanescent wave we have found a new property of the generalized scattering matrix. This property reflects the conservation of energy at such process. 
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     author = {D. P. Kouzov and G. L. Nikitin and V. G. Yakovleva},
     title = {The matrix of the transforming of vibration waves},
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     pages = {105--131},
     publisher = {mathdoc},
     volume = {275},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2001_275_a9/}
}
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D. P. Kouzov; G. L. Nikitin; V. G. Yakovleva. The matrix of the transforming of vibration waves. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 30, Tome 275 (2001), pp. 105-131. http://geodesic.mathdoc.fr/item/ZNSL_2001_275_a9/