[Un gap dans le spectre continu d'un guide d'onde élastique]
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.
Accepté le :
Publié le :
Mot clés : Guide périodique d'onde élastique, Gap dans un spectre continu
Sergey A. Nazarov 1
@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}, }
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/
[1] Asymptotic Theory of Thin Plates and Rods. Vol. 1. Dimension Reduction and Integral Estimates, Nauchnaya Kniga, Novosibirsk, 2001
[2] 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] Spectral properties of the periodic media inlarge coupling limit, Comm. Partial Differential Equations, Volume 25 (2000), pp. 1445-1470
[4] Expansions in eigenfunctions of an equation with periodic coefficients, Dokl. Acad. Nauk SSSR, Volume 73 (1950), pp. 1117-1120
[5] Floquet Theory for Partial Differential Equations, Birkhäuser, Basel, 1993
[6] Elliptic Problems in Domains with Piecewise Smooth Boundaries, Walter de Gruyter, Berlin, 1994
[7] Introduction to the Theory of Linear Nonselfadjoint Operators, Amer. Math. Soc., Providence, RI, 1969
[8] Elliptic boundary value problems with periodic coefficients in a cylinder, Math. USSR Izvestija, Volume 18 (1982) no. 1, pp. 89-98
[9] Les méthodes in théorie des équations elliptiques, Masson–Academia, Paris–Prague, 1967
[10] 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] 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] Spectral Theory of Selfadjoint Operators in Hilbert Space, D. Reidel Publ. Co., Dordrecht, 1987
[13] 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.
Commentaires - Politique