Comptes Rendus
A gap in the continuous spectrum of an elastic waveguide
[Un gap dans le spectre continu d'un guide d'onde élastique]
Comptes Rendus. Mécanique, Volume 336 (2008) no. 10, pp. 751-756.

On exhibe un guide périodique d'onde élastique tel que le spectre continu de l'opérateur du problème élastique contienne un gap. Cet effet peut être utilisé pour construire des filtres d'ondes elastiques.

A periodic elastic waveguide is found out such that the continuous spectrum of the elasticity problem operator contains a gap. This effect can be used for constructing elastic wave filters.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2008.07.002
Keywords: Elastic periodic waveguide, Gap in continuous spectrum
Mot clés : Guide périodique d'onde élastique, Gap dans un spectre continu
Sergey A. Nazarov 1

1 Institute of Mechanical Engineering Problems, V.O., Bol'shoi pr., 61, 199178, St.-Petersburg, Russia
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Sergey A. Nazarov. A gap in the continuous spectrum of an elastic waveguide. Comptes Rendus. Mécanique, Volume 336 (2008) no. 10, pp. 751-756. doi : 10.1016/j.crme.2008.07.002. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2008.07.002/

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[3] R. Hempel; K. Lineau Spectral properties of the periodic media inlarge coupling limit, Comm. Partial Differential Equations, Volume 25 (2000), pp. 1445-1470

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[5] P. Kuchment Floquet Theory for Partial Differential Equations, Birkhäuser, Basel, 1993

[6] S.A. Nazarov; B.A. Plamenevsky Elliptic Problems in Domains with Piecewise Smooth Boundaries, Walter de Gruyter, Berlin, 1994

[7] I.C. Gohberg; M.G. Krein Introduction to the Theory of Linear Nonselfadjoint Operators, Amer. Math. Soc., Providence, RI, 1969

[8] S.A. Nazarov Elliptic boundary value problems with periodic coefficients in a cylinder, Math. USSR Izvestija, Volume 18 (1982) no. 1, pp. 89-98

[9] J. Nečas Les méthodes in théorie des équations elliptiques, Masson–Academia, Paris–Prague, 1967

[10] V.A. Kondratiev; O.A. Oleinik Boundary-value problems for the system of elasticity theory in unbounded domains. Korn's inequalities, Russian Math. Surveys, Volume 43 (1988) no. 5, pp. 65-119

[11] S.A. Nazarov Korn's inequalities for elastic junctions of massive bodies, thin plates and rods, Russian Math. Surveys, Volume 63 (2008) no. 1, pp. 143-217

[12] M.Sh. Birman; M.Z. Solomyak Spectral Theory of Selfadjoint Operators in Hilbert Space, D. Reidel Publ. Co., Dordrecht, 1987

[13] S.A. Nazarov Asymptotics of infrequencies of an elastic body with a heavy and hard peak-shaped inclusion, C. R. Mecanique, Volume 335 (2007) no. 12, pp. 757-762

Cité par Sources :

The author gratefully acknowledges the support by N.W.O., the Netherlands Organization for Scientific Research.

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