Porous absorber - Revision history

Aumann at 08:28, 29 June 2023

2023-06-29T08:28:56Z

← Older revision		Revision as of 08:28, 29 June 2023
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	==Data==		==Data==
	The data is available at [https://doi.org/10.5281/zenodo.8087341 Zenodo].		The data is available at [https://doi.org/10.5281/zenodo.8087341 Zenodo].

			==Remarks==
			* The numerical model resembles the results from<ref name="rumpler14"/> in a frequency range from <math>100\,\mathrm{Hz}</math> to <math>1000\,\mathrm{Hz}</math>. The frequency response in this range is also included in the dataset.
			* The finite element discretization has been performed with [https://github.com/KratosMultiphysics/Kratos Kratos Multiphysics].
			* A comparison of different interpolation-based MOR methods using this benchmark example is available in<ref name="aumann23"/>.

			==Citation==
			To cite this benchmark, use the following references:

			* For the benchmark itself and its data:
			@Misc{dataAum23,
			author = {Aumann, Q.},
			title = {Matrices for an acoustic cavity with poroelastic layer},
			howpublished = {hosted at {MORwiki} -- Model Order Reduction Wiki},
			year = 2023,
			doi = {10.5281/zenodo.8087341}
			}

			* For the background on the benchmark:

			@Article{AumW23,
			author = {Aumann, Q. and Werner, S.~W.~R.},
			title = {Structured model order reduction for vibro-acoustic problems using interpolation and balancing methods},
			journal = {Journal of Sound and Vibration},
			volume = 543,
			year = 2023,
			pages = {117363},
			doi = {10.1016/j.jsv.2022.117363},
			publisher = {Elsevier {BV}}
			}

Aumann at 08:25, 29 June 2023

2023-06-29T08:25:23Z

← Older revision		Revision as of 08:25, 29 June 2023
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	{{preliminary}} <!-- Do not remove -->		{{preliminary}} <!-- Do not remove -->
			[[Category:benchmark]]
			[[Category:linear]]
			[[Category:SISO]]

	<figure id="fig:plot1">		<figure id="fig:plot1">
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	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 <ref name="rumpler14"/>. Various projection-based model order reduction methods have been applied and compared using this example as a benchmark in <ref name="aumann23"/>.		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 <ref name="rumpler14"/>. Various projection-based model order reduction methods have been applied and compared using this example as a benchmark in <ref name="aumann23"/>.

	The cavity has the dimensions <math>0.75 \times 0.6 \times 0.4\,\mathrm{m}</math> and one wall is covered by a <math>0.05\,\mathrm{m}</math> thick poroelastic layer acting as a sound absorber. The poroelastic material is described by the Biot theory<ref name="biot56"/> and the system is excited by a point source located in a corner opposite of the porous layer. The material parameters for the acoustic fluid and the poroelastic material have been chosen according to<ref name="rumpler14"/>.		The cavity has the dimensions <math>0.75 \times 0.6 \times 0.4\,\mathrm{m}</math> and one wall is covered by a <math>0.05\,\mathrm{m}</math> thick poroelastic layer acting as a sound absorber. The poroelastic material is described by the Biot theory<ref name="biot56"/> and the system is excited by a point source located in a corner opposite of the porous layer. The material parameters for the acoustic fluid and the poroelastic material have been chosen according to<ref name="rumpler14"/>. The transfer function measures the mean acoustic pressure inside the cavity.

	==Dimensions==		==Dimensions==

Aumann at 15:25, 27 June 2023

2023-06-27T15:25:29Z

← Older revision		Revision as of 15:25, 27 June 2023
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	:<math>		:<math>
	\begin{align}		\begin{align}
	\left( ~~A_1~~ + \tilde{\gamma}(s) ~~A_2~~ + \tilde{\rho}_f(s) ~~A_3~~ + s^2 ~~A_4~~ + s^2 \tilde{\gamma}(s) ~~A_5~~ + s^2 \tilde{\rho}(s) ~~A_6~~ + \frac{s^2 \phi^2}{\tilde{R}(s)} ~~A_7~~ \right) x(s) &= B, \\		\left( K + \tilde{\gamma}(s) K_{p,1} + \tilde{\rho}_f(s) K_{p,2} + s^2 M + s^2 \tilde{\gamma}(s) M_{p,1} + s^2 \tilde{\rho}(s) M_{p,2} + \frac{s^2 \phi^2}{\tilde{R}(s)} M_{p,3} \right) x(s) &= B, \\
	y(s) &= C x(s),		y(s) &= C x(s),
	\end{align}		\end{align}
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	System dimensions:		System dimensions:

	<math>~~A_i~~, \in \mathbb{R}^{n \times n}~~</math>, with <math>i=1, \ldots, 7~~ </math>,		<math>K, K_{p,1}, K_{p,2}, M, M_{p,1}, M_{p,2}, M_{p,3} \in \mathbb{R}^{n \times n}</math>,
	<math>B \in \mathbb{R}^{n \times 1}</math>,		<math>B \in \mathbb{R}^{n \times 1}</math>,
	<math>C \in \mathbb{R}^{1 \times n}</math>,		<math>C \in \mathbb{R}^{1 \times n}</math>,

Aumann at 15:17, 27 June 2023

2023-06-27T15:17:55Z

@@ Line 12: / Line 12: @@
 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 <ref name="rumpler14"/>. Various projection-based model order reduction methods have been applied and compared using this example as a benchmark in <ref name="aumann23"/>.
-The cavity has the dimensions <math>0.75 \times 0.6 \times 0.4\,\mathrm{m}</math> and one wall is covered by a <math>0.05\,\mathrm{m}</math> thick poroelastic layer acting as a sound absorber. The poroelastic material is described by the Biot theory<ref name="biot56"/> and the system is excited by a point source located in a corner opposite of the porous layer.
+The cavity has the dimensions <math>0.75 \times 0.6 \times 0.4\,\mathrm{m}</math> and one wall is covered by a <math>0.05\,\mathrm{m}</math> thick poroelastic layer acting as a sound absorber. The poroelastic material is described by the Biot theory<ref name="biot56"/> and the system is excited by a point source located in a corner opposite of the porous layer. The material parameters for the acoustic fluid and the poroelastic material have been chosen according to<ref name="rumpler14"/>.
 ==References==

Aumann at 14:09, 27 June 2023

2023-06-27T14:09:14Z

← Older revision		Revision as of 14:09, 27 June 2023
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	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 <ref name="rumpler14"/>. Various projection-based model order reduction methods have been applied and compared using this example as a benchmark in <ref name="aumann23"/>.		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 <ref name="rumpler14"/>. Various projection-based model order reduction methods have been applied and compared using this example as a benchmark in <ref name="aumann23"/>.

			The cavity has the dimensions <math>0.75 \times 0.6 \times 0.4\,\mathrm{m}</math> and one wall is covered by a <math>0.05\,\mathrm{m}</math> thick poroelastic layer acting as a sound absorber. The poroelastic material is described by the Biot theory<ref name="biot56"/> and the system is excited by a point source located in a corner opposite of the porous layer.

	==References==		==References==
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	<ref name="aumann23">Q. Aumann, S. W. R. Werner. "<span class="plainlinks">[https://doi.org/10.1016/j.jsv.2022.117363 Structured model order reduction for vibro-acoustic problems using interpolation and balancing methods]</span>", Journal of Sound and Vibration, 543: 117363, 2023.</ref>		<ref name="aumann23">Q. Aumann, S. W. R. Werner. "<span class="plainlinks">[https://doi.org/10.1016/j.jsv.2022.117363 Structured model order reduction for vibro-acoustic problems using interpolation and balancing methods]</span>", Journal of Sound and Vibration, 543: 117363, 2023.</ref>

			<ref name="biot56">M. A. Biot. "<span class="plainlinks">[http://dx.doi.org/10.1121/1.1908239 Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low-frequency range]</span>", J. Acoust. Soc. Am., 28(2):168–178, 1956.</ref>

	</references>		</references>

Aumann at 14:01, 27 June 2023

2023-06-27T14:01:33Z

← Older revision		Revision as of 14:01, 27 June 2023
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	{{preliminary}} <!-- Do not remove -->		{{preliminary}} <!-- Do not remove -->

			<figure id="fig:plot1">
			[[File:Porous_absorber.png\|480px\|thumb\|right\|<caption>Sketch of the geometry. The porous material is marked in blue, the acoustic source by <math>q</math>.</caption>]]
			</figure>

			<figure id="fig:tf">
			[[File:Porous_absorber_frf.png\|480px\|thumb\|right\|<caption>Frequency response function.</caption>]]
			</figure>

	==Description==		==Description==

Aumann: Created page with "{{preliminary}} ==Description== The '''Porous absorber''' benchmark models the sound pressure in a cavity excited by a single harmonic load. One side o..."

2023-05-23T07:41:09Z

Created page with "{{preliminary}}  ==Description== The '''Porous absorber''' benchmark models the sound pressure in a cavity excited by a single harmonic load. One side o..."

New page

{{preliminary}} 

==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 <ref name="rumpler14"/>. Various projection-based model order reduction methods have been applied and compared using this example as a benchmark in <ref name="aumann23"/>.

==References==

<references>

<ref name="rumpler14"> R. Rumpler, P. Göransson, J.-F. Deü. "<span class="plainlinks">[http://dx.doi.org/10.1002/nme.4609 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]</span>", International Journal for Numerical Methods in Engineering, 97: 759-784, 2014.</ref>

<ref name="aumann23">Q. Aumann, S. W. R. Werner. "<span class="plainlinks">[https://doi.org/10.1016/j.jsv.2022.117363 Structured model order reduction for vibro-acoustic problems using interpolation and balancing methods]</span>", Journal of Sound and Vibration, 543: 117363, 2023.</ref>

</references>