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Zh. Vychisl. Mat. Mat. Fiz., 2009, Volume 49, Number 2, Pages 332–343 (Mi zvmmf44)  

This article is cited in 7 scientific papers (total in 7 papers)

Gap detection in the spectrum of an elastic periodic waveguide with a free surface

S. A. Nazarov

Institute of Mechanical Engineering Problems, Russian Academy of Sciences, Vasil'evskii Ostrov, Bol'shoi pr. 61, St. Petersburg, 199178, Russia

Abstract: A three-dimensional periodic elastic waveguide is constructed whose continuous spectrum (the frequencies that admit propagating waves) contains a gap, i.e., an interval that has its ends in the continuous spectrum but contains at most a discrete spectrum. The waveguide consists of an infinite chain of massive bodies connected by short thin links, and its surface is assumed to be free. The method for detecting a gap also applies to plane problems, including scalar ones. Periodic elastic waveguides with different shapes or contrasting properties are indicated in which a gap can also be detected.

Key words: three-dimensional periodic waveguides, gap in an eigenvalue spectrum, Floquet waves, elasticity problems.

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English version:
Computational Mathematics and Mathematical Physics, 2009, 49:2, 323–333

Bibliographic databases:

UDC: 519.634
Received: 23.05.2008

Citation: S. A. Nazarov, “Gap detection in the spectrum of an elastic periodic waveguide with a free surface”, Zh. Vychisl. Mat. Mat. Fiz., 49:2 (2009), 332–343; Comput. Math. Math. Phys., 49:2 (2009), 323–333

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Cardone G., Minutolo V., Nazarov S.A., “Gaps in the essential spectrum of periodic elastic waveguides”, ZAMM Z. Angew. Math. Mech., 89:9 (2009), 729–741  crossref  mathscinet  zmath  isi  elib  scopus
    2. Nazarov S.A., Ruotsalainen K., Taskinen J., “Gaps in the essential spectrum of infinite periodic necklace-shaped elastic waveguide”, Comptes Rendus Mécanique, 337:3 (2009), 119–123  crossref  adsnasa  isi  scopus
    3. S. A. Nazarov, “An example of multiple gaps in the spectrum of a periodic waveguide”, Sb. Math., 201:4 (2010), 569–594  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. Nazarov S.A., Ruotsalainen K., Taskinen J., “Essential spectrum of a periodic elastic waveguide may contain arbitrarily many gaps”, Appl. Anal., 89:1 (2010), 109–124  crossref  mathscinet  zmath  isi  elib  scopus
    5. Nazarov S.A., “Trapped surface waves in a periodic layer of a heavy liquid”, J. Appl. Math. Mech., 75:2 (2011), 235–244  crossref  mathscinet  zmath  adsnasa  isi  elib  elib  scopus
    6. Nazarov S.A., “Localized elastic fields in periodic waveguides with defects”, J. Appl. Mech. Tech. Phys., 52:2 (2011), 311–320  crossref  mathscinet  zmath  adsnasa  isi  elib  elib  scopus
    7. Bakharev F.L., Taskinen J., “Bands in the Spectrum of a Periodic Elastic Waveguide”, Z. Angew. Math. Phys., 68:5 (2017), 102  crossref  mathscinet  zmath  isi  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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