Abstract:
Rayleigh waves are studied in an elastic half-layer with a periodic end and rigidly clamped faces. It is established that the essential spectrum of the corresponding problem of elasticity theory has a band structure, and an example of a waveguide is presented in which a gap opens in the essential spectrum, i.e., an interval arises that contains points of at most discrete spectrum.
Keywords:
Rayleigh waves, essential spectrum, band structure.
Citation:
S. A. Nazarov, “Opening a gap in the essential spectrum of the elasticity problem in a periodic semi-layer”, Algebra i Analiz, 21:2 (2009), 166–204; St. Petersburg Math. J., 21:2 (2010), 281–307
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\by S.~A.~Nazarov
\paper Opening a~gap in the essential spectrum of the elasticity problem in a~periodic semi-layer
\jour Algebra i Analiz
\yr 2009
\vol 21
\issue 2
\pages 166--204
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\jour St. Petersburg Math. J.
\yr 2010
\vol 21
\issue 2
\pages 281--307
\crossref{https://doi.org/10.1090/S1061-0022-10-01095-2}
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Linking options:
https://www.mathnet.ru/eng/aa1009
https://www.mathnet.ru/eng/aa/v21/i2/p166
This publication is cited in the following 4 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
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
Citation in format AMSBIB
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