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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 313207, 15 pages
http://dx.doi.org/10.1155/2012/313207
Research Article

Rayleigh's, Stoneley's, and Scholte's Interface Waves in Elastic Models Using a Boundary Element Method

1Sección de Estudios de Posgrado e Investigación, ESIA Zacatenco, Instituto Politécnico Nacional, Avenida Instituto Politécnico Nacional s/n, Lindavista, Del. Gustavo A. Madero, 07320 México, DF, Mexico
2Sección de Estudios de Posgrado e Investigación, ESIME Azcapotzalco, Instituto Politécnico Nacional, Avenida de las Granjas 682, Sta. Catarina, Del. Azcapotzalco, 02250 México, DF, Mexico
3Ciencias de la computación, Centro de Investigación en Matemáticas, Callejón Jalisco s/n, Mineral de Valenciana, 36240 Guanajuato, GTO, Mexico
4Programa de Investigación de Geofísica de Exploración y Explotación, Instituto Mexicano del Petróleo, Eje Central Lázaro Cárdenas 152, Gustavo A. Madero, 07730 México, DF, Mexico

Received 15 September 2011; Revised 5 December 2011; Accepted 7 December 2011

Academic Editor: Srinivasan Natesan

Copyright © 2012 Esteban Flores-Mendez et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This work is focused on studying interface waves for three canonical models, that is, interfaces formed by vacuum-solid, solid-solid, and liquid-solid. These interfaces excited by dynamic loads cause the emergence of Rayleigh's, Stoneley's, and Scholte's waves, respectively. To perform the study, the indirect boundary element method is used, which has proved to be a powerful tool for numerical modeling of problems in elastodynamics. In essence, the method expresses the diffracted wave field of stresses, pressures, and displacements by a boundary integral, also known as single-layer representation, whose shape can be regarded as a Fredholm's integral representation of second kind and zero order. This representation can be considered as an exemplification of Huygens' principle, which is equivalent to Somigliana's representation theorem. Results in frequency domain for the three types of interfaces are presented; then, using the fourier discrete transform, we derive the results in time domain, where the emergence of interface waves is highlighted.