Comptes Rendus
no. 7
An explicit asymptotic model for the Bleustein–Gulyaev wave

Presented by: Évariste Sanchez-Palencia

Julius Kaplunov1 ; Leonid Kossovich2; Alexis Zakharov1
1 Department of Mathematics, University of Manchester, Oxford Road, Manchester, M13 9PL, UK
2 Saratov State University, Astrakhanskaya 83, Saratov, 410026, Russian Federation
Comptes Rendus. Mécanique, Volume 332 (2004) no. 7, pp. 487-492.

The antiplane motion of a transversely isotropic piezoelectric half-space is considered. An explicit asymptotic model is derived for the far field of the surface wave. It involves, in particular, a 1D hyperbolic equation for surface shear deformation propagating with the finite wave speed predicted for the first time by J.L. Bleustein and Yu.V. Gulyaev. Neumann and Dirichlet problems are formulated to restore interior mechanical and electric fields. The derivation utilizes asymptotic arguments combined with Lourier symbolic integration. Comparison with the exact solution is presented for surface impact loading.

Le mouvement antiplane d'un demi-espace piézoélectrique transversalement isotrope est considéré. Un modèle asymptotique explicite est dérivé pour le champ lointain de l'onde de surface. Il implique, en particulier, une équation hyperbolique de dimension un pour la déformation de la surface de cisaillement se propageant avec vitesse d'onde finie predite pour la première fois par J.L. Bleustein et Yu.V. Gulyaev. Des problèmes de Neumann et de Dirichlet sont formulés pour reconstituer les champs mécaniques et électriques intérieurs. La dérivation utilise des arguments asymptotiques combinés avec l'intégration symbolique de Lourier. La comparaison avec la solution exacte est présentée pour le chargement d'impact de surface.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crme.2004.03.007
Keywords: Waves, Asymptotic, Model, Far field, Piezoelectric, Surface wave, Bleustein–Gulyaev wave
Mots-clés : Ondes, Asymptotique, Modèle, Champ lointain, Piézoélectrique, L'onde de surface, L'onde de Bleustein–Gulyaev

Julius Kaplunov 1; Leonid Kossovich 2; Alexis Zakharov 1

1 Department of Mathematics, University of Manchester, Oxford Road, Manchester, M13 9PL, UK
2 Saratov State University, Astrakhanskaya 83, Saratov, 410026, Russian Federation 
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Julius Kaplunov; Leonid Kossovich; Alexis Zakharov. An explicit asymptotic model for the Bleustein–Gulyaev wave. Comptes Rendus. Mécanique, Volume 332 (2004) no. 7, pp. 487-492. doi : 10.1016/j.crme.2004.03.007. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2004.03.007/

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