A time-harmonic/time-domain hybrid approach based on displacement-based formulations to compute the absorbing coefficient in alpha cabins
Abstract In the automotive industry, the absorption coefficient of a porous material layer is usually measured in an alpha cabin, a reverberant chamber of reduced dimensions where the operational frequency range is limited and the absorbent sample size is typically small. Those characteristics are w...
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| Language: | English |
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SpringerOpen
2025-05-01
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| Series: | Journal of Mathematics in Industry |
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| Online Access: | https://doi.org/10.1186/s13362-025-00173-0 |
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| author | Laura Río-Martín Andrés Prieto Alfredo Bermúdez |
| author_facet | Laura Río-Martín Andrés Prieto Alfredo Bermúdez |
| author_sort | Laura Río-Martín |
| collection | DOAJ |
| description | Abstract In the automotive industry, the absorption coefficient of a porous material layer is usually measured in an alpha cabin, a reverberant chamber of reduced dimensions where the operational frequency range is limited and the absorbent sample size is typically small. Those characteristics are well adapted to the requirements of automotive acoustics but far from the standard reverberant chambers used in building acoustics which ensures the conditions to perform measurements under a diffusive field. Since there are no standard norms to measure the absorption coefficient under non-diffusive fields, this work proposes a time-harmonic/time-domain hybrid approach to compute the absorption coefficient in alpha cabins. For this purpose, pointwise numerical predictions of the sound pressure level decay rate are used to calculate the absorption coefficient associated with a porous sample. To generate the pressure field acting inside the alpha cabin and, subsequently, approximate its decay rate, time-harmonic numerical simulations at a fixed frequency and a full time-dependent discretization of the wave problem have been considered. The proposed methodology is validated in a manufactured scenario where the exact solution is known in closed form. Finally, a realistic three-dimensional alpha cabin is deemed to predict the diffuse field absorption coefficient from the computed reverberation times using the proposed hybrid approach and the heuristic Sabine and Millington formulas. |
| format | Article |
| id | doaj-art-9c989fae6fcd49cd9bf90322ac1bfe27 |
| institution | DOAJ |
| issn | 2190-5983 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Mathematics in Industry |
| spelling | doaj-art-9c989fae6fcd49cd9bf90322ac1bfe272025-08-20T03:10:18ZengSpringerOpenJournal of Mathematics in Industry2190-59832025-05-0115112310.1186/s13362-025-00173-0A time-harmonic/time-domain hybrid approach based on displacement-based formulations to compute the absorbing coefficient in alpha cabinsLaura Río-Martín0Andrés Prieto1Alfredo Bermúdez2Laboratory of Applied Mathematics, DICAM, University of TrentoCITMAga, Departamento de Matemáticas, Universidade da CoruñaCITMAga, Departamento de Matemática Aplicada, Universidade de Santiago de CompostelaAbstract In the automotive industry, the absorption coefficient of a porous material layer is usually measured in an alpha cabin, a reverberant chamber of reduced dimensions where the operational frequency range is limited and the absorbent sample size is typically small. Those characteristics are well adapted to the requirements of automotive acoustics but far from the standard reverberant chambers used in building acoustics which ensures the conditions to perform measurements under a diffusive field. Since there are no standard norms to measure the absorption coefficient under non-diffusive fields, this work proposes a time-harmonic/time-domain hybrid approach to compute the absorption coefficient in alpha cabins. For this purpose, pointwise numerical predictions of the sound pressure level decay rate are used to calculate the absorption coefficient associated with a porous sample. To generate the pressure field acting inside the alpha cabin and, subsequently, approximate its decay rate, time-harmonic numerical simulations at a fixed frequency and a full time-dependent discretization of the wave problem have been considered. The proposed methodology is validated in a manufactured scenario where the exact solution is known in closed form. Finally, a realistic three-dimensional alpha cabin is deemed to predict the diffuse field absorption coefficient from the computed reverberation times using the proposed hybrid approach and the heuristic Sabine and Millington formulas.https://doi.org/10.1186/s13362-025-00173-0Alpha cabinReverberation timeAbsorbing coefficientFinite element method |
| spellingShingle | Laura Río-Martín Andrés Prieto Alfredo Bermúdez A time-harmonic/time-domain hybrid approach based on displacement-based formulations to compute the absorbing coefficient in alpha cabins Journal of Mathematics in Industry Alpha cabin Reverberation time Absorbing coefficient Finite element method |
| title | A time-harmonic/time-domain hybrid approach based on displacement-based formulations to compute the absorbing coefficient in alpha cabins |
| title_full | A time-harmonic/time-domain hybrid approach based on displacement-based formulations to compute the absorbing coefficient in alpha cabins |
| title_fullStr | A time-harmonic/time-domain hybrid approach based on displacement-based formulations to compute the absorbing coefficient in alpha cabins |
| title_full_unstemmed | A time-harmonic/time-domain hybrid approach based on displacement-based formulations to compute the absorbing coefficient in alpha cabins |
| title_short | A time-harmonic/time-domain hybrid approach based on displacement-based formulations to compute the absorbing coefficient in alpha cabins |
| title_sort | time harmonic time domain hybrid approach based on displacement based formulations to compute the absorbing coefficient in alpha cabins |
| topic | Alpha cabin Reverberation time Absorbing coefficient Finite element method |
| url | https://doi.org/10.1186/s13362-025-00173-0 |
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