Comptes Rendus
no. 8
Novel exact surface wave solutions for layered structures

Presented by: Évariste Sanchez-Palencia

Aleksei P. Kiselev1 ; Eric Ducasse2; Marc Deschamps2; Alexander Darinskii3
1 St. Petersburg Department of Steklov Mathematical Institute, Fontanka 27, St. Petersburg 191023, Russia
2 Université Bordeaux 1, CNRS, Laboratoire de Mécanique Physique, 351, cours Libération, 33405 Talence, France
3 Institute of Crystallography RAS, Leninskii pr. 59, Moscow 119333, Russia
Comptes Rendus. Mécanique, Volume 335 (2007) no. 8, pp. 419-422.

Novel exact solutions describing surface acoustic waves on general layered structures have been found by the method of variable separation. First, solutions have been constructed with plane wavefronts and involving polynomial dependence on lateral variables. Second, their inhomogeneous plane-wave analogues have been found. At last, beam-like solutions highly localized at large lateral distances in a given sector have also been considered.

De nouvelles solutions exactes, caractéristiques d'ondes acoustiques de surface dans un milieu stratifié quelconque, sont obtenues par séparation des variables. Nous nous attachons tout d'abord aux solutions présentant des fronts d'ondes plan mais dont l'amplitude varie de façon polynomiale selon les directions transversales, ensuite aux ondes planes hétérogènes qui leur sont analogues, et enfin aux solutions de type « rayon » qui sont fortement localisées dans un secteur angulaire donné et comportent une focalisation.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crme.2007.06.001
Keywords: Waves, Surface wave, Exact solution, Beam
Mot clés : Ondes, Onde de surface, Solution exacte, Rayon

Aleksei P. Kiselev 1; Eric Ducasse 2; Marc Deschamps 2; Alexander Darinskii 3

1 St. Petersburg Department of Steklov Mathematical Institute, Fontanka 27, St. Petersburg 191023, Russia
2 Université Bordeaux 1, CNRS, Laboratoire de Mécanique Physique, 351, cours Libération, 33405 Talence, France
3 Institute of Crystallography RAS, Leninskii pr. 59, Moscow 119333, Russia 
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Aleksei P. Kiselev; Eric Ducasse; Marc Deschamps; Alexander Darinskii. Novel exact surface wave solutions for layered structures. Comptes Rendus. Mécanique, Volume 335 (2007) no. 8, pp. 419-422. doi : 10.1016/j.crme.2007.06.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2007.06.001/

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[3] A.P. Kiselev Rayleigh wave with a transverse structure, Proc. Roy. Soc. London, Ser. A, Volume 460 (2002), pp. 3059-3064

[4] V.S. Vladimirov Equations of Mathematical Physics, Mir, Moscow, 1984

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[6] A.J. Hughes Elastic surface wave guidance by Δν/ν effect guidance structure, J. Appl. Phys., Volume 43 (1972) no. 6, pp. 2569-2586

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