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Sibirskii Zhurnal Industrial'noi Matematiki, 2016, Volume 19, Number 1, Pages 27–36
DOI: https://doi.org/10.17377/sibjim.2016.19.103 (Mi sjim909) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Reflection of plane waves from a rigid wall and a free surface in a transverse isotropic medium

B. D. Anninab, N. I. Ostrosablina

a Lavrent'ev Institute of Hydrodynamics SB RAS, 15 Lavrent'ev av., 630090 Novosibirsk
b Novosibirsk State University, 2 Pirogova str., 630090 Novosibirsk
Full-text PDF (229 kB) Citations (2)
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DOI: https://doi.org/10.17377/sibjim.2016.19.103
Abstract: We provide a representation of the general solution to the two-dimensional equations of the dynamics of a transverse isotropic medium with the Carrier–Gassmann condition. The representation of the solution is based on two solving functions that satisfy two separate wave equations. The problem of the reflection of plane waves from a rigid wall and a free surface is solved. The reflection coefficients and transformations of plane waves are found. The obtained formulas imply the solution for an isotropic medium as well. Special cases are considered, where the forms (amplitudes) of the reflected waves are not determined uniquely but related to the form of a falling wave through a linear relation.
Keywords: transverse isotropy, plane wave, Carrier–Gassmann condition, coefficients of reflection and transformation.
Funding agency Grant number
Russian Foundation for Basic Research 15-41-05081
Received: 23.06.2015
English version:
Journal of Applied and Industrial Mathematics, 2016, Volume 10, Issue 1, Pages 29–36
DOI: https://doi.org/10.1134/S199047891601004X
Bibliographic databases:
Document Type: Article
UDC: 539.3+517.958
Language: Russian
Citation: B. D. Annin, N. I. Ostrosablin, “Reflection of plane waves from a rigid wall and a free surface in a transverse isotropic medium”, Sib. Zh. Ind. Mat., 19:1 (2016), 27–36; J. Appl. Industr. Math., 10:1 (2016), 29–36
Citation in format AMSBIB
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\by B.~D.~Annin, N.~I.~Ostrosablin
\paper Reflection of plane waves from a~rigid wall and a~free surface in a~transverse isotropic medium
\jour Sib. Zh. Ind. Mat.
\yr 2016
\vol 19
\issue 1
\pages 27--36
\mathnet{http://mi.mathnet.ru/sjim909}
\crossref{https://doi.org/10.17377/sibjim.2016.19.103}
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\elib{https://elibrary.ru/item.asp?id=25591888}
\transl
\jour J. Appl. Industr. Math.
\yr 2016
\vol 10
\issue 1
\pages 29--36
\crossref{https://doi.org/10.1134/S199047891601004X}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84961666350}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Сибирский журнал индустриальной математики
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