Porous absorber

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Figure 1: Sketch of the geometry. The porous material is marked in blue, the acoustic source by

q

.

Figure 2: Frequency response function.

Description

The Porous absorber benchmark models the sound pressure in a cavity excited by a single harmonic load. One side of the cavity is covered by a layer of poroelastic material, which adds dissipation to the system. The geometry of this model follows ^[1]. Various projection-based model order reduction methods have been applied and compared using this example as a benchmark in ^[2].

The cavity has the dimensions $0.75 \times 0.6 \times 0.4\,\mathrm{m}$ and one wall is covered by a $0.05\,\mathrm{m}$ thick poroelastic layer acting as a sound absorber. The poroelastic material is described by the Biot theory^[3] and the system is excited by a point source located in a corner opposite of the porous layer.

References

↑ R. Rumpler, P. Göransson, J.-F. Deü. "A finite element approach combining a reduced-order system, Padé approximants, and an adaptive frequency windowing for fast multi-frequency solution of poro-acoustic problems", International Journal for Numerical Methods in Engineering, 97: 759-784, 2014.
↑ Q. Aumann, S. W. R. Werner. "Structured model order reduction for vibro-acoustic problems using interpolation and balancing methods", Journal of Sound and Vibration, 543: 117363, 2023.
↑ M. A. Biot. "Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low-frequency range", J. Acoust. Soc. Am., 28(2):168–178, 1956.

[rumpler14-1] R. Rumpler, P. Göransson, J.-F. Deü. "A finite element approach combining a reduced-order system, Padé approximants, and an adaptive frequency windowing for fast multi-frequency solution of poro-acoustic problems", International Journal for Numerical Methods in Engineering, 97: 759-784, 2014.

[aumann23-2] Q. Aumann, S. W. R. Werner. "Structured model order reduction for vibro-acoustic problems using interpolation and balancing methods", Journal of Sound and Vibration, 543: 117363, 2023.

[biot56-3] M. A. Biot. "Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low-frequency range", J. Acoust. Soc. Am., 28(2):168–178, 1956.

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