Asymptotic Formulation for the Rayleigh Wave on a Nonlocally Elastic Half-Space
This paper deals with the Rayleigh wave, propagating on a nonlocally elastic, linearly isotropic half-space, excited by a prescribed surface loading. The consideration develops the methodology of hyperbolic–elliptic models for Rayleigh and Rayleigh-type waves, and relies on the effective boundary co...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-01-01
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| Series: | Vibration |
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| Online Access: | https://www.mdpi.com/2571-631X/6/1/5 |
| _version_ | 1827747340203589632 |
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| author | Danila A. Prikazchikov |
| author_facet | Danila A. Prikazchikov |
| author_sort | Danila A. Prikazchikov |
| collection | DOAJ |
| description | This paper deals with the Rayleigh wave, propagating on a nonlocally elastic, linearly isotropic half-space, excited by a prescribed surface loading. The consideration develops the methodology of hyperbolic–elliptic models for Rayleigh and Rayleigh-type waves, and relies on the effective boundary conditions formulated recently, accounting for the crucial contributions of the nonlocal boundary layer. A slow-time perturbation scheme is established, leading to the reduced model for the Rayleigh wave field, comprised of a singularly perturbed hyperbolic equation for the longitudinal wave potential on the surface, acting as a boundary condition for the elliptic equation governing the decay over the interior. An equivalent alternative formulation involving a pseudo-differential operator acting on the loading terms, with parametric dependence on the depth coordinate, is also presented. |
| first_indexed | 2024-03-11T05:47:06Z |
| format | Article |
| id | doaj.art-642ee2d49f2049b1b8df18173c155fc1 |
| institution | Directory Open Access Journal |
| issn | 2571-631X |
| language | English |
| last_indexed | 2024-03-11T05:47:06Z |
| publishDate | 2023-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Vibration |
| spelling | doaj.art-642ee2d49f2049b1b8df18173c155fc12023-11-17T14:21:17ZengMDPI AGVibration2571-631X2023-01-0161576410.3390/vibration6010005Asymptotic Formulation for the Rayleigh Wave on a Nonlocally Elastic Half-SpaceDanila A. Prikazchikov0School of Computer Science and Mathematics, Keele University, Keele ST5 5BG, UKThis paper deals with the Rayleigh wave, propagating on a nonlocally elastic, linearly isotropic half-space, excited by a prescribed surface loading. The consideration develops the methodology of hyperbolic–elliptic models for Rayleigh and Rayleigh-type waves, and relies on the effective boundary conditions formulated recently, accounting for the crucial contributions of the nonlocal boundary layer. A slow-time perturbation scheme is established, leading to the reduced model for the Rayleigh wave field, comprised of a singularly perturbed hyperbolic equation for the longitudinal wave potential on the surface, acting as a boundary condition for the elliptic equation governing the decay over the interior. An equivalent alternative formulation involving a pseudo-differential operator acting on the loading terms, with parametric dependence on the depth coordinate, is also presented.https://www.mdpi.com/2571-631X/6/1/5Rayleigh wavenonlocalboundary layerasymptotic |
| spellingShingle | Danila A. Prikazchikov Asymptotic Formulation for the Rayleigh Wave on a Nonlocally Elastic Half-Space Vibration Rayleigh wave nonlocal boundary layer asymptotic |
| title | Asymptotic Formulation for the Rayleigh Wave on a Nonlocally Elastic Half-Space |
| title_full | Asymptotic Formulation for the Rayleigh Wave on a Nonlocally Elastic Half-Space |
| title_fullStr | Asymptotic Formulation for the Rayleigh Wave on a Nonlocally Elastic Half-Space |
| title_full_unstemmed | Asymptotic Formulation for the Rayleigh Wave on a Nonlocally Elastic Half-Space |
| title_short | Asymptotic Formulation for the Rayleigh Wave on a Nonlocally Elastic Half-Space |
| title_sort | asymptotic formulation for the rayleigh wave on a nonlocally elastic half space |
| topic | Rayleigh wave nonlocal boundary layer asymptotic |
| url | https://www.mdpi.com/2571-631X/6/1/5 |
| work_keys_str_mv | AT danilaaprikazchikov asymptoticformulationfortherayleighwaveonanonlocallyelastichalfspace |