Comptes Rendus
no. 3
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. Nazarov1  ; Keijo Ruotsalainen2  ; Jari Taskinen3
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.

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 :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2009.03.014
Keywords: Periodic elastic waveguide, Gap-band structure of the spectrum
Mot clés : Guide d'onde périodique élastique, Faille dans le spectre
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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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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