Rayleigh's, Stoneley's, and Scholte's Interface Waves in Elastic Models Using a Boundary Element Method
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 perfor...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/313207 |
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| author | Esteban Flores-Mendez Manuel Carbajal-Romero Norberto Flores-Guzmán Ricardo Sánchez-Martínez Alejandro Rodríguez-Castellanos |
| author_facet | Esteban Flores-Mendez Manuel Carbajal-Romero Norberto Flores-Guzmán Ricardo Sánchez-Martínez Alejandro Rodríguez-Castellanos |
| author_sort | Esteban Flores-Mendez |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-4e00a623879f416ba80e4a3b5f433926 |
| institution | OA Journals |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-4e00a623879f416ba80e4a3b5f4339262025-08-20T02:38:46ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/313207313207Rayleigh's, Stoneley's, and Scholte's Interface Waves in Elastic Models Using a Boundary Element MethodEsteban Flores-Mendez0Manuel Carbajal-Romero1Norberto Flores-Guzmán2Ricardo Sánchez-Martínez3Alejandro Rodríguez-Castellanos4Sección 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, MexicoSección de Estudios de Posgrado e Investigación, ESIME Azcapotzalco, Instituto Politécnico Nacional, Avenida de las Granjas 682, Sta. Catarina, Del. Azcapotzalco, 02250 México, DF, MexicoCiencias de la computación, Centro de Investigación en Matemáticas, Callejón Jalisco s/n, Mineral de Valenciana, 36240 Guanajuato, GTO, MexicoSección de Estudios de Posgrado e Investigación, ESIME Azcapotzalco, Instituto Politécnico Nacional, Avenida de las Granjas 682, Sta. Catarina, Del. Azcapotzalco, 02250 México, DF, MexicoPrograma de Investigación de Geofísica de Exploración y Explotación, Instituto Mexicano del Petróleo, Eje Central Lázaro Cárdenas 152, Gustavo A. Madero, 07730 México, DF, MexicoThis 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.http://dx.doi.org/10.1155/2012/313207 |
| spellingShingle | Esteban Flores-Mendez Manuel Carbajal-Romero Norberto Flores-Guzmán Ricardo Sánchez-Martínez Alejandro Rodríguez-Castellanos Rayleigh's, Stoneley's, and Scholte's Interface Waves in Elastic Models Using a Boundary Element Method Journal of Applied Mathematics |
| title | Rayleigh's, Stoneley's, and Scholte's Interface Waves in Elastic Models Using a Boundary Element Method |
| title_full | Rayleigh's, Stoneley's, and Scholte's Interface Waves in Elastic Models Using a Boundary Element Method |
| title_fullStr | Rayleigh's, Stoneley's, and Scholte's Interface Waves in Elastic Models Using a Boundary Element Method |
| title_full_unstemmed | Rayleigh's, Stoneley's, and Scholte's Interface Waves in Elastic Models Using a Boundary Element Method |
| title_short | Rayleigh's, Stoneley's, and Scholte's Interface Waves in Elastic Models Using a Boundary Element Method |
| title_sort | rayleigh s stoneley s and scholte s interface waves in elastic models using a boundary element method |
| url | http://dx.doi.org/10.1155/2012/313207 |
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