Abstract
Acoustically absorbing materials such as acoustic foam can be described by the equivalent fluid model. The homogenized fluid’s acoustic behavior is thereby described by complex-valued, frequency-dependent material parameters (equivalent density and compression modulus).
In this case, convolution integrals of the material parameters and the acoustic pressure arise when the acoustic wave equation is transformed from frequency to time domain. We circumvent the direct calculation of these integrals by introducing auxiliary differential equations (ADEs), which are coupled to the wave equation according to the ADE method. The set of coupled differen-
tial equations is solved using the finite element method (FEM). The approach requires the equivalent fluid parameters to be modeled by a rational function representing the frequency-dependent material behavior (frequency response function, FRF). Thereby, the order of the FRF defines the number of additionally introduced ADEs and auxiliary variables. For the sake of simplicity,
the formulation’s derivation is presented for FRFs consisting of only one real pole. The passivity of the porous material is demonstrated, and it is validated against
a frequency-domain simluation in openCFS based on a two-dimensional duct containing an equivalent fluid.
In this case, convolution integrals of the material parameters and the acoustic pressure arise when the acoustic wave equation is transformed from frequency to time domain. We circumvent the direct calculation of these integrals by introducing auxiliary differential equations (ADEs), which are coupled to the wave equation according to the ADE method. The set of coupled differen-
tial equations is solved using the finite element method (FEM). The approach requires the equivalent fluid parameters to be modeled by a rational function representing the frequency-dependent material behavior (frequency response function, FRF). Thereby, the order of the FRF defines the number of additionally introduced ADEs and auxiliary variables. For the sake of simplicity,
the formulation’s derivation is presented for FRFs consisting of only one real pole. The passivity of the porous material is demonstrated, and it is validated against
a frequency-domain simluation in openCFS based on a two-dimensional duct containing an equivalent fluid.
Original language | English |
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Title of host publication | Fortschriftte der Akustik - DAGA 2023 |
Pages | 1023-1026 |
ISBN (Electronic) | 978-3-939296-21-8 |
Publication status | Published - 2023 |
Event | DAGA 2023 - 49. Jahrestagung für Akustik - Hamburg, Germany Duration: 6 Mar 2023 → 9 Mar 2023 |
Conference
Conference | DAGA 2023 - 49. Jahrestagung für Akustik |
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Abbreviated title | DAGA 2023 |
Country/Territory | Germany |
City | Hamburg |
Period | 6/03/23 → 9/03/23 |
Keywords
- Equivalent Fluid
- Computational Acoustics