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Zh. Vychisl. Mat. Mat. Fiz., 2008, Volume 48, Number 5, Pages 863–881 (Mi zvmmf142)  

This article is cited in 19 scientific papers (total in 19 papers)

Trapped modes in a cylindrical elastic waveguide with a damping gasket

S. A. Nazarov

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

Abstract: An infinite cylindrical body containing a three-dimensional heavy rigid inclusion with a sharp edge is considered. Under certain constraints on the symmetry of the body, it is shown that any prescribed number of eigenvalues of the elasticity operator can be placed on an arbitrary real interval $(0,l)$ by choosing suitable physical properties of the inclusion. In the continuous spectrum, these points correspond to trapped modes, i.e., to exponentially decaying solutions to the homogeneous problem. The results can be used to design filters and dampers of elastic waves in a cylinder.

Key words: cylindrical elastic waveguides, trapped modes, gaskets with a sharp edge, spectral asymptotics, filters and dampers of elastic waves.

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English version:
Computational Mathematics and Mathematical Physics, 2008, 48:5, 816–833

Bibliographic databases:

UDC: 519.634
Received: 26.04.2007
Revised: 24.07.2007

Citation: S. A. Nazarov, “Trapped modes in a cylindrical elastic waveguide with a damping gasket”, Zh. Vychisl. Mat. Mat. Fiz., 48:5 (2008), 863–881; Comput. Math. Math. Phys., 48:5 (2008), 816–833

Citation in format AMSBIB
\by S.~A.~Nazarov
\paper Trapped modes in a~cylindrical elastic waveguide with a~damping gasket
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2008
\vol 48
\issue 5
\pages 863--881
\jour Comput. Math. Math. Phys.
\yr 2008
\vol 48
\issue 5
\pages 816--833

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. A. Nazarov, “On the concentration of the point spectrum on the continuous one in problems of the linearized theory of water-waves”, J. Math. Sci. (N. Y.), 152:5 (2008), 674–689  mathnet  crossref  elib
    2. S. A. Nazarov, “Concentration of trapped modes in problems of the linearized theory of water waves”, Sb. Math., 199:12 (2008), 1783–1807  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. S. A. Nazarov, “Opening a gap in the essential spectrum of the elasticity problem in a periodic semi-layer”, St. Petersburg Math. J., 21:2 (2010), 281–307  mathnet  crossref  mathscinet  zmath  isi
    4. S. A. Nazarov, “Gap detection in the spectrum of an elastic periodic waveguide with a free surface”, Comput. Math. Math. Phys., 49:2 (2009), 323–333  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    5. Nazarov S.A., “Localized waves in a doubly periodic elastic plane with a periodic row of defects”, Dokl. Phys., 54:12 (2009), 540–545  mathnet  crossref  mathscinet  zmath  adsnasa  isi  elib  elib  scopus
    6. Cardone G., Nazarov S.A., Taskinen J., “A criterion for the existence of the essential spectrum for beak-shaped elastic bodies”, J. Math. Pures Appl. (9), 92:6 (2009), 628–650  crossref  mathscinet  zmath  isi  scopus
    7. 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
    8. F. L. Bakharev, S. A. Nazarov, “On the structure of the spectrum for the elasticity problem in a body with a supersharp spike”, Siberian Math. J., 50:4 (2009), 587–595  mathnet  crossref  mathscinet  isi  elib  elib
    9. Nazarov S.A., “Gap in a continuous spectrum of an elastic waveguide with a partly clamped surface”, J. Appl. Mech. Tech. Phys., 51:1 (2010), 114–124  crossref  mathscinet  zmath  adsnasa  isi  elib  elib  scopus
    10. S. A. Nazarov, “On the asymptotics of an eigenvalue of a waveguide with thin shielding obstacle and Wood's anomalies”, J. Math. Sci. (N. Y.), 178:3 (2011), 292–312  mathnet  crossref
    11. S. A. Nazarov, “Discrete spectrum of cranked, branchy, and periodic waveguides”, St. Petersburg Math. J., 23:2 (2012), 351–379  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    12. 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
    13. S. A. Nazarov, “Elastic waves trapped by a homogeneous anisotropic semicylinder”, Sb. Math., 204:11 (2013), 1639–1670  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    14. Nazarov S.A., “Elastic Waves Trapped by a Semi-Infinite Orthotropic Cylinder”, Dokl. Phys., 58:11 (2013), 491–495  crossref  crossref  mathscinet  adsnasa  isi  elib  elib  scopus
    15. Nazarov S.A., “Near-Threshold Effects of the Scattering of Waves in a Distorted Elastic Two-Dimensional Waveguide”, Pmm-J. Appl. Math. Mech., 79:4 (2015), 374–387  crossref  mathscinet  isi  scopus
    16. S. A. Nazarov, “Almost standing waves in a periodic waveguide with a resonator and near-threshold eigenvalues”, St. Petersburg Math. J., 28:3 (2017), 377–410  mathnet  crossref  mathscinet  isi  elib
    17. Nazarov S.A. Ruotsalainen K.M. Silvola M., “Trapped Modes in Piezoelectric and Elastic Waveguides”, J. Elast., 124:2 (2016), 193–223  crossref  mathscinet  zmath  isi  elib  scopus
    18. Buttazzo G., Cardone G., Nazarov S.A., “Thin Elastic Plates Supported Over Small Areas. i: Korn'S Inequalities and Boundary Layers”, J. Convex Anal., 23:2 (2016), 347–386  mathscinet  zmath  isi
    19. Kozlov V.A. Nazarov S.A. Orlof A., “Trapped Modes in Zigzag Graphene Nanoribbons”, Z. Angew. Math. Phys., 68:4 (2017), 78  crossref  mathscinet  zmath  isi  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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