Comptes Rendus
no. 1-2
Solitary SH waves in two-layered traction-free plates
[Ondes SH isolées en plaques bicouches libres de contraintes]
Irini Djeran-Maigre1  ; Sergey Kuznetsov2
1 LGCIE, INSA-Lyon, 34, avenue des Arts, 69621 Villeurbanne cedex, France
2 Institute for Problems in Mechanics, Prosp. Vernadskogo 101, Moscow 119526, Russia
Comptes Rendus. Mécanique, Volume 336 (2008) no. 1-2, pp. 102-107.

Une onde isolée ressemblant à un soliton est décrite mathématiquement en analysant les problèmes linéaires pour des ondes de cisaillement de surface se propageant dans les plaques élastiques, anisotropes et stratifiées. Le modèle mathématique est basé sur un formalisme particulier dans un espace complexe et sur la méthode de la matrice modifiée de transfert (MTM). Les conditions d'existence des ondes isolées sont obtenues. La vitesse de phase de ces ondes est décrite par des solutions analytiques.

A solitary wave, resembling a soliton wave, is observed when analyzing the linear problem of polarized shear (SH) surface acoustic waves propagating in elastic orthotropic two-layered traction-free plates. The analysis is performed by applying a special complex formalism and the Modified Transfer Matrix (MTM) method. Conditions for the existence of solitary SH waves are obtained. Analytical expressions for the phase speed of the solitary wave are derived.

Publié le :
DOI : 10.1016/j.crme.2007.11.001
Keywords: Waves, SH wave, Shear wave, Surface wave, Soliton, Solitary wave
Mot clés : Ondes, Ondes SH, Onde de cisaillement, Onde de surface, Soliton, Onde isolée
Irini Djeran-Maigre 1 ; Sergey Kuznetsov 2

1 LGCIE, INSA-Lyon, 34, avenue des Arts, 69621 Villeurbanne cedex, France
2 Institute for Problems in Mechanics, Prosp. Vernadskogo 101, Moscow 119526, Russia 
@article{CRMECA_2008__336_1-2_102_0,
     author = {Irini Djeran-Maigre and Sergey Kuznetsov},
     title = {Solitary {SH} waves in two-layered traction-free plates},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {102--107},
     publisher = {Elsevier},
     volume = {336},
     number = {1-2},
     year = {2008},
     doi = {10.1016/j.crme.2007.11.001},
     language = {en},
}
TY  - JOUR
AU  - Irini Djeran-Maigre
AU  - Sergey Kuznetsov
TI  - Solitary SH waves in two-layered traction-free plates
JO  - Comptes Rendus. Mécanique
PY  - 2008
SP  - 102
EP  - 107
VL  - 336
IS  - 1-2
PB  - Elsevier
DO  - 10.1016/j.crme.2007.11.001
LA  - en
ID  - CRMECA_2008__336_1-2_102_0
ER  - 
%0 Journal Article
%A Irini Djeran-Maigre
%A Sergey Kuznetsov
%T Solitary SH waves in two-layered traction-free plates
%J Comptes Rendus. Mécanique
%D 2008
%P 102-107
%V 336
%N 1-2
%I Elsevier
%R 10.1016/j.crme.2007.11.001
%G en
%F CRMECA_2008__336_1-2_102_0
Irini Djeran-Maigre; Sergey Kuznetsov. Solitary SH waves in two-layered traction-free plates. Comptes Rendus. Mécanique, Volume 336 (2008) no. 1-2, pp. 102-107. doi : 10.1016/j.crme.2007.11.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2007.11.001/

[1] J. Scott Russell, Report on waves, in: Fourteenth Meeting of the British Association for the Advancement of Science, York, 1844 (London 1845), pp. 311–390

[2] A.D.D. Craik The origins of water wave theory, Ann. Rev. Fluid Mech., Volume 36 (2004), pp. 1-28

[3] D.J. Korteweg; F. de Vries On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves, Philos. Mag., Volume 39 (1895), pp. 422-443

[4] P. Lax Integrals of nonlinear evolution equations and solitary waves, Comm. Pure Appl. Math., Volume 21 (1968), pp. 467-490

[5] J.W. Miles The Korteweg–de Vries equation, a historical essay, J. Fluid Mech., Volume 106 (1981), pp. 131-147

[6] A.E.H. Love Some Problems of Geodynamics, Cambridge University Press, London, 1911

[7] S.V. Kuznetsov Subsonic Lamb waves in anisotropic plates, Quart. Appl. Math., Volume 60 (2002), pp. 577-587

[8] S.V. Kuznetsov Love waves in stratified monoclinic media, Quart. Appl. Math., Volume 62 (2004), pp. 749-766

[9] I. Djeran-Maigre; S.V. Kuznetsov Surface waves on a half-space with cubic symmetry, Int. J. Comp. Civil & Struct. Eng., Volume 2 (2005), pp. 21-27

[10] S.V. Kuznetsov SH-waves in laminated plates, Quart. Appl. Math., Volume 64 (2006), pp. 153-165

[11] K. Sezawa Dispersion of elastic waves propagated on the surface of stratified bodies and on curved surfaces, Bull. Earthquake Res. Inst. Tokyo, Volume 3 (1927), pp. 1-18

[12] M.E. Gurtin The Linear Theory of Elasticity, Handbuch Der Physik, vol. VIa/2, Springer, 1973

Cité par Sources :

Commentaires - Politique