Gaps in the essential spectrum of infinite periodic necklace-shaped elastic waveguide

Sergey A. Nazarov; Keijo Ruotsalainen; Jari Taskinen

doi:10.1016/j.crme.2009.03.014

Gaps in the essential spectrum of infinite periodic necklace-shaped elastic waveguide
[Gaps dans le spectre essentiel d'un guide d'onde élastique, infini et périodique, ayant la forme d'un collier]

Présenté par : Evariste Sanchez-Palencia

Sergey A. Nazarov ¹ ; Keijo Ruotsalainen ² ; Jari Taskinen ³

¹ Institute of Mechanical Engineering Problems, V.O., Bolshoi pr., 61, 199178, St. Petersburg, Russia
² University of Oulu, Department of Electrical and Information Engineering, Mathematics Division, P.O. Box 4500, 90401 Oulu, Finland
³ University of Helsinki, Department of Mathematics and Statistics, P.O. Box 68, 00014 Helsinki, Finland

Comptes Rendus. Mécanique, Volume 337 (2009) no. 3, pp. 119-123.

Résumé
Abstract

Nous décrivons un guide d'ondes élastique homogène et périodique, ayant la forme particulière de collier constitué de grains reliés par des ligaments de diamètre $O (h)$ de telle sorte que le spectre essentiel contienne des gaps dont le nombre augmente infiniment quand h tend vers zéro.

We describe a periodic homogeneous elastic waveguide of a particular shape of beads connected by ligaments of diameter $O (h)$ such that the essential spectrum contains gaps, the number of which grows unboundedly when h tends to +0.

Reçu le : 2009-02-19
Accepté le : 2009-03-30
Publié le : 2009-03-01

DOI : 10.1016/j.crme.2009.03.014

Keywords: Periodic elastic waveguide, Gap-band structure of the spectrum
Mots-clés : Guide d'onde périodique élastique, Faille dans le spectre

Affiliations des auteurs :

Sergey A. Nazarov ¹ ; Keijo Ruotsalainen ² ; Jari Taskinen ³

¹ Institute of Mechanical Engineering Problems, V.O., Bolshoi pr., 61, 199178, St. Petersburg, Russia
² University of Oulu, Department of Electrical and Information Engineering, Mathematics Division, P.O. Box 4500, 90401 Oulu, Finland
³ University of Helsinki, Department of Mathematics and Statistics, P.O. Box 68, 00014 Helsinki, Finland

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     author = {Sergey A. Nazarov and Keijo Ruotsalainen and Jari Taskinen},
     title = {Gaps in the essential spectrum of infinite periodic necklace-shaped elastic waveguide},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {119--123},
     publisher = {Elsevier},
     volume = {337},
     number = {3},
     year = {2009},
     doi = {10.1016/j.crme.2009.03.014},
     language = {en},
}

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Sergey A. Nazarov; Keijo Ruotsalainen; Jari Taskinen. Gaps in the essential spectrum of infinite periodic necklace-shaped elastic waveguide. Comptes Rendus. Mécanique, Volume 337 (2009) no. 3, pp. 119-123. doi : 10.1016/j.crme.2009.03.014. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2009.03.014/

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