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.
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
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\paper Gap detection in the spectrum of an elastic periodic waveguide with a~free surface
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\yr 2009
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\pages 332--343
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\jour Comput. Math. Math. Phys.
\yr 2009
\vol 49
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\pages 323--333
\crossref{https://doi.org/10.1134/S0965542509020122}
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Linking options:
https://www.mathnet.ru/eng/zvmmf44
https://www.mathnet.ru/eng/zvmmf/v49/i2/p332
This publication is cited in the following 8 articles:
Marcus Rosenberg, Jari Taskinen, “Some aspects of the Floquet theory for the heat equation in a periodic domain”, J. Evol. Equ., 24:2 (2024)
Bakharev F.L., Taskinen J., “Bands in the Spectrum of a Periodic Elastic Waveguide”, Z. Angew. Math. Phys., 68:5 (2017), 102
Nazarov S.A., “Trapped surface waves in a periodic layer of a heavy liquid”, J. Appl. Math. Mech., 75:2 (2011), 235–244
Nazarov S.A., “Localized elastic fields in periodic waveguides with defects”, J. Appl. Mech. Tech. Phys., 52:2 (2011), 311–320
S. A. Nazarov, “An example of multiple gaps in the spectrum of a periodic waveguide”, Sb. Math., 201:4 (2010), 569–594
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
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
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
Citation in format AMSBIB
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