A gap in the continuous spectrum of an elastic waveguide

Sergey A. Nazarov

doi:10.1016/j.crme.2008.07.002

A gap in the continuous spectrum of an elastic waveguide

Presented by: Évariste Sanchez-Palencia

Sergey A. Nazarov ¹

¹ Institute of Mechanical Engineering Problems, V.O., Bol'shoi pr., 61, 199178, St.-Petersburg, Russia

Comptes Rendus. Mécanique, Volume 336 (2008) no. 10, pp. 751-756.

Abstract
Résumé

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.

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.

Received: 2008-05-15
Accepted: 2008-05-30
Published online: 2008-09-11

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

Author's affiliations:

Sergey A. Nazarov ¹

¹ Institute of Mechanical Engineering Problems, V.O., Bol'shoi pr., 61, 199178, St.-Petersburg, Russia

@article{CRMECA_2008__336_10_751_0,
     author = {Sergey A. Nazarov},
     title = {A gap in the continuous spectrum of an elastic waveguide},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {751--756},
     publisher = {Elsevier},
     volume = {336},
     number = {10},
     year = {2008},
     doi = {10.1016/j.crme.2008.07.002},
     language = {en},
}

TY  - JOUR
AU  - Sergey A. Nazarov
TI  - A gap in the continuous spectrum of an elastic waveguide
JO  - Comptes Rendus. Mécanique
PY  - 2008
SP  - 751
EP  - 756
VL  - 336
IS  - 10
PB  - Elsevier
DO  - 10.1016/j.crme.2008.07.002
LA  - en
ID  - CRMECA_2008__336_10_751_0
ER  -

%0 Journal Article
%A Sergey A. Nazarov
%T A gap in the continuous spectrum of an elastic waveguide
%J Comptes Rendus. Mécanique
%D 2008
%P 751-756
%V 336
%N 10
%I Elsevier
%R 10.1016/j.crme.2008.07.002
%G en
%F CRMECA_2008__336_10_751_0

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/

References
Cited by

[1] S.A. Nazarov Asymptotic Theory of Thin Plates and Rods. Vol. 1. Dimension Reduction and Integral Estimates, Nauchnaya Kniga, Novosibirsk, 2001

[2] A. Figotin; P. Kuchment Band-gap structure of spectra of periodic dielectric and acoustic media. I. Scalar model, SIAM J. Appl. Math., Volume 56 (1996), pp. 68-88 (II. Two-dimensional photonic crystals SIAM J. Appl. Math., 56, 1996, pp. 1561-1620)

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

[4] I.M. Gel'fand Expansions in eigenfunctions of an equation with periodic coefficients, Dokl. Acad. Nauk SSSR, Volume 73 (1950), pp. 1117-1120

[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

Cited by Sources:

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

Comments - Policy