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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika
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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2008, Number 9, Pages 69–75 (Mi ivm1722)  
This article is cited in 4 scientific papers (total in 4 papers)

Brief communications

On the orthogonality of eigenwaves in a semi-open elastic waveguide

K. N. Vdovinaa, N. B. Pleschinskiia, D. N. Tumakovb

a Kazan State University
b Department of Applied Mathematical Physics, Chebotarev Institute of Mathematics and Mechanics, Kazan State University
Full-text PDF (167 kB) Citations (4)
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Abstract: We consider a two-layer elastic waveguide structure such that its one layer is unbounded in the lateral direction and at the boundary of the other one the standard boundary conditions are stated. We study several kinds of eigenwaves of this structure. In general, they have a complex-valued longitudinal propagation constant (the spectral parameter). On the base of the Green formula we introduce the scalar product of two waves and prove that the set of eigenwaves of the semiopen elastic waveguide is orthogonal. We construct families of waves which belong to discrete and continuous parts of the spectrum.
Keywords: elastic waves, waveguide, stratified medium, eigenwaves, Green formula, scalar product, discrete and continuous spectrum.
Received: 18.08.2007
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2008, Volume 52, Issue 9, Pages 60–64
DOI: https://doi.org/10.3103/S1066369X08090089
Bibliographic databases:
Document Type: Article
UDC: 517.958:539.3
Language: Russian
Citation: K. N. Vdovina, N. B. Pleschinskii, D. N. Tumakov, “On the orthogonality of eigenwaves in a semi-open elastic waveguide”, Izv. Vyssh. Uchebn. Zaved. Mat., 2008, no. 9, 69–75; Russian Math. (Iz. VUZ), 52:9 (2008), 60–64
Citation in format AMSBIB
\Bibitem{VdoPleTum08}
\by K.~N.~Vdovina, N.~B.~Pleschinskii, D.~N.~Tumakov
\paper On the orthogonality of eigenwaves in a semi-open elastic waveguide
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2008
\issue 9
\pages 69--75
\mathnet{http://mi.mathnet.ru/ivm1722}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2468308}
\zmath{https://zbmath.org/?q=an:05621386}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2008
\vol 52
\issue 9
\pages 60--64
\crossref{https://doi.org/10.3103/S1066369X08090089}
Linking options:
  • https://www.mathnet.ru/eng/ivm1722
  • https://www.mathnet.ru/eng/ivm/y2008/i9/p69
    • This publication is cited in the following 4 articles:
    1. A. V. Anufrieva, K. N. Stekhina, D. N. Tumakov, “O sobstvennykh volnakh transversalno-izotropnogo sloya, sopryazhennogo s izotropnoi poluploskostyu”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 156, no. 2, Izd-vo Kazanskogo un-ta, Kazan, 2014, 87–94  mathnet
    2. K.N. Stekhina, D.N. Tumakov, Proceedings of the International Conference Days on Diffraction 2013, 2013, 136  crossref
    3. A.V. Anufrieva, D.N. Tumakov, V.L. Kipot, Proceedings of the International Conference Days on Diffraction 2013, 2013, 11  crossref
    4. A. V. Anufrieva, D. N. Tumakov, “Difraktsiya ploskoi uprugoi volny na gradientnom sloe”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 154, no. 4, Izd-vo Kazanskogo un-ta, Kazan, 2012, 116–125  mathnet
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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    References:63
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