Acoustic waves in gas-filled structured porous media: Asymptotic tortuosity/compliability and characteristic-lengths reevaluated to incorporate the influence of spatial dispersion
This study extends efforts to incorporate spatial dispersion into Biot-Allard’s theory, with a focus on poroelastic media with intricate microgeometries where spatial dispersion effects play a significant role. While preserving Biot’s small-scale quasi-“en-bloc” frame motion to keep the structure of...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
EDP Sciences
2024-01-01
|
| Series: | Acta Acustica |
| Subjects: | |
| Online Access: | https://acta-acustica.edpsciences.org/articles/aacus/full_html/2024/01/aacus230106/aacus230106.html |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850247472929046528 |
|---|---|
| author | Lafarge D. |
| author_facet | Lafarge D. |
| author_sort | Lafarge D. |
| collection | DOAJ |
| description | This study extends efforts to incorporate spatial dispersion into Biot-Allard’s theory, with a focus on poroelastic media with intricate microgeometries where spatial dispersion effects play a significant role. While preserving Biot’s small-scale quasi-“en-bloc” frame motion to keep the structure of Biot-Allard’s theory intact, the paper challenges Biot’s quasi-incompressibility of fluid motion at that scale by introducing structurations in the form of Helmholtz’s resonators. Consequently, Biot-Allard’s theory undergoes a significant augmentation, marked by the arising of non-local dynamic tortuosity and compliability, which are associated with potentially resonant fluid behavior. Building on an acoustic-electromagnetic analogy, the study defines these non-local responses and suggests simplifying them into pseudo-local ones, now potentially resonant and reminiscent of Veselago-type phenomena. In the high-frequency limit of small boundary layers and as an extension of the classical Johnson-Allard’s findings, simple field-averaged formulas are demonstrated for pseudo-local ideal-fluid tortuosity and compliability (complex frequency-dependent) and viscous and thermal characteristic lengths (positive frequency-dependent). These formulations are grounded in the Umov-Heaviside-Poynting thermodynamic macroscopic acoustic stress concept, suggested by the analogy. Future computational investigations, spanning various fundamental microgeometries, are planned to assess assumed pseudo-local simplifications, encompass low- and intermediate frequencies, and unveil potential behavioral outcomes resulting from the incorporation of spatial dispersion effects. |
| format | Article |
| id | doaj-art-078f92ce8c314dc1913dcea5fb586e2f |
| institution | OA Journals |
| issn | 2681-4617 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | Acta Acustica |
| spelling | doaj-art-078f92ce8c314dc1913dcea5fb586e2f2025-08-20T01:58:55ZengEDP SciencesActa Acustica2681-46172024-01-0184110.1051/aacus/2024019aacus230106Acoustic waves in gas-filled structured porous media: Asymptotic tortuosity/compliability and characteristic-lengths reevaluated to incorporate the influence of spatial dispersionLafarge D.0https://orcid.org/0000-0001-6428-4629Laboratoire d’Acoustique de l’Université du Mans, UMR 6613This study extends efforts to incorporate spatial dispersion into Biot-Allard’s theory, with a focus on poroelastic media with intricate microgeometries where spatial dispersion effects play a significant role. While preserving Biot’s small-scale quasi-“en-bloc” frame motion to keep the structure of Biot-Allard’s theory intact, the paper challenges Biot’s quasi-incompressibility of fluid motion at that scale by introducing structurations in the form of Helmholtz’s resonators. Consequently, Biot-Allard’s theory undergoes a significant augmentation, marked by the arising of non-local dynamic tortuosity and compliability, which are associated with potentially resonant fluid behavior. Building on an acoustic-electromagnetic analogy, the study defines these non-local responses and suggests simplifying them into pseudo-local ones, now potentially resonant and reminiscent of Veselago-type phenomena. In the high-frequency limit of small boundary layers and as an extension of the classical Johnson-Allard’s findings, simple field-averaged formulas are demonstrated for pseudo-local ideal-fluid tortuosity and compliability (complex frequency-dependent) and viscous and thermal characteristic lengths (positive frequency-dependent). These formulations are grounded in the Umov-Heaviside-Poynting thermodynamic macroscopic acoustic stress concept, suggested by the analogy. Future computational investigations, spanning various fundamental microgeometries, are planned to assess assumed pseudo-local simplifications, encompass low- and intermediate frequencies, and unveil potential behavioral outcomes resulting from the incorporation of spatial dispersion effects.https://acta-acustica.edpsciences.org/articles/aacus/full_html/2024/01/aacus230106/aacus230106.htmlsound propagationhelmholtz resonatorsspatial dispersionbiot’s theoryporous media |
| spellingShingle | Lafarge D. Acoustic waves in gas-filled structured porous media: Asymptotic tortuosity/compliability and characteristic-lengths reevaluated to incorporate the influence of spatial dispersion Acta Acustica sound propagation helmholtz resonators spatial dispersion biot’s theory porous media |
| title | Acoustic waves in gas-filled structured porous media: Asymptotic tortuosity/compliability and characteristic-lengths reevaluated to incorporate the influence of spatial dispersion |
| title_full | Acoustic waves in gas-filled structured porous media: Asymptotic tortuosity/compliability and characteristic-lengths reevaluated to incorporate the influence of spatial dispersion |
| title_fullStr | Acoustic waves in gas-filled structured porous media: Asymptotic tortuosity/compliability and characteristic-lengths reevaluated to incorporate the influence of spatial dispersion |
| title_full_unstemmed | Acoustic waves in gas-filled structured porous media: Asymptotic tortuosity/compliability and characteristic-lengths reevaluated to incorporate the influence of spatial dispersion |
| title_short | Acoustic waves in gas-filled structured porous media: Asymptotic tortuosity/compliability and characteristic-lengths reevaluated to incorporate the influence of spatial dispersion |
| title_sort | acoustic waves in gas filled structured porous media asymptotic tortuosity compliability and characteristic lengths reevaluated to incorporate the influence of spatial dispersion |
| topic | sound propagation helmholtz resonators spatial dispersion biot’s theory porous media |
| url | https://acta-acustica.edpsciences.org/articles/aacus/full_html/2024/01/aacus230106/aacus230106.html |
| work_keys_str_mv | AT lafarged acousticwavesingasfilledstructuredporousmediaasymptotictortuositycompliabilityandcharacteristiclengthsreevaluatedtoincorporatetheinfluenceofspatialdispersion |