Sound transmission through a plate - Revision history

Malhotra: infobox string edit

2023-11-30T09:41:24Z

infobox string edit

← Older revision		Revision as of 09:41, 30 November 2023
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	{{Infobox		{{Infobox
	\|Title = ~~Silicon Nitride Membrane~~		\|Title = Sound Transmission through a Plate
	\|Benchmark ID = ~~siliconNitrideMembrane_n60020m1q2~~		\|Benchmark ID = soundTransmission_n95480m1q1
	\|Category = misc		\|Category = misc
	\|System-Class = ~~AP-~~LTI-~~FOS~~		\|System-Class = LTI-SOS
	\|nstates = ~~60020~~		\|nstates = 95480
	\|ninputs = 1		\|ninputs = 1
	\|noutputs = 2		\|noutputs = 1
	\|nparameters = 2		\|nparameters = 0
	\|components = A, B, C, E		\|components = B, C, E, K, M
	\|License = NA		\|License = Creative Commons Attribution 4.0 International
	\|Creator = [[User:~~Feng~~]]		\|Creator = [[User:Aumann]]
	\|Editor =		\|Editor =
	* [[User:~~Feng]]~~		* [[User:Aumann]]
	* [[User:Himpe]]		\|Zenodo-link = https://zenodo.org/record/7670587/files/soundTransmission_n95480m1q1.mat
	\|Zenodo-link = NA
	}}		}}

Malhotra: infobox string

2023-11-30T09:40:56Z

infobox string

@@ Line 4: / Line 4: @@
 [[Category:second differential order]]
 [[Category:SISO]]
 <figure id="fig:plot1">

Aumann: Update doi

2023-02-23T13:47:29Z

Update doi

← Older revision		Revision as of 13:47, 23 February 2023
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	==Data==		==Data==
	The data is available at [https://doi.org/10.5281/zenodo.~~7300347~~ Zenodo].		The data is available at [https://doi.org/10.5281/zenodo.7300346 Zenodo].

	==Remarks==		==Remarks==
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	howpublished = {hosted at {MORwiki} -- Model Order Reduction Wiki},		howpublished = {hosted at {MORwiki} -- Model Order Reduction Wiki},
	year = 2022,		year = 2022,
	doi = {10.5281/zenodo.~~7300347~~}		doi = {10.5281/zenodo.7300346}
	}		}

Aumann at 16:07, 5 January 2023

2023-01-05T16:07:31Z

← Older revision		Revision as of 16:07, 5 January 2023
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	==Remarks==		==Remarks==
	* The numerical model resembles the experimental data<ref name="guy81"/> in a frequency range from <math>0\,\mathrm{Hz}</math> to <math>1000\,\mathrm{Hz}</math>. The frequency response in this range is also included in the dataset.		* The numerical model resembles the experimental data<ref name="guy81"/> in a frequency range from <math>1\,\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].		* The finite element discretization has been performed with [https://github.com/KratosMultiphysics/Kratos Kratos Multiphysics].
	* The system has unstable eigenvalues. This is common in interior acoustic problems where no damping is assumed for the acoustic fluid<ref name="cool22"/>.		* The system has unstable eigenvalues. This is common in interior acoustic problems where no damping is assumed for the acoustic fluid<ref name="cool22"/>.

Aumann at 09:52, 8 November 2022

2022-11-08T09:52:55Z

← Older revision		Revision as of 09:52, 8 November 2022
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	==Remarks==		==Remarks==
	* The numerical model resembles the experimental data<ref name="guy81"/> in a frequency range from <math>0\,\mathrm{Hz}</math> to <math>1000\,\mathrm{Hz}</math>.		* The numerical model resembles the experimental data<ref name="guy81"/> in a frequency range from <math>0\,\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].		* The finite element discretization has been performed with [https://github.com/KratosMultiphysics/Kratos Kratos Multiphysics].
	* The system has unstable eigenvalues. This is common in interior acoustic problems where no damping is assumed for the acoustic fluid<ref name="cool22"/>.		* The system has unstable eigenvalues. This is common in interior acoustic problems where no damping is assumed for the acoustic fluid<ref name="cool22"/>.

Aumann: Created page with "{{preliminary}} Category:benchmark Category:linear Category:second differential order Category:SISO
File:guy...."

2022-11-07T18:04:02Z

Created page with "{{preliminary}}  Category:benchmark Category:linear Category:second differential order Category:SISO <figure id="fig:plot1"> File:guy...."

New page

{{preliminary}} 
[[Category:benchmark]]
[[Category:linear]]
[[Category:second differential order]]
[[Category:SISO]]

<figure id="fig:plot1">
[[File:guy.png|480px|thumb|right|<caption>Sketch of the geometry.</caption>]]
</figure>

<figure id="fig:tf">
[[File:guy_tf.png|480px|thumb|right|<caption>Transfer function.</caption>]]
</figure>

==Description==
The '''Sound transmission through a plate''' benchmark models the radiation of a vibrating plate and the excitation of a structure by an oscillating acoustic fluid. It is based on an experiment by Guy<ref name="guy81"/>.

The system consists of a cuboid acoustic cavity, where one wall is considered a system of two parallel elastic brass plates with a <math>2\,\mathrm{cm}</math> air gap between them; all other walls are considered rigid. The plates measure <math>0.2 \times 0.2\,\mathrm{m}</math> and have a thickness of <math>t = 0.9144\,\mathrm{mm}</math>; the receiving cavity is <math>0.2\,\mathrm{m}</math> wide. The outer plate is excited by a uniform pressure load and the resulting acoustic pressure in the receiving cavity is measured at the middle of the rigid wall opposite to the elastic plate (<math>P_1</math> in the sketch).

The following material parameters have been considered for the brass plates and the acoustic fluid:
{| class="wikitable" style="margin: auto;"
|+ style="caption-side:bottom;"|
|-
|Part
|Parameter
|Value
|Unit
|-style="background-color:#FFFFFF;"
|Brass plates
|<math>E</math>
|<math>104</math>
|<math>\mathrm{GPa}</math>
|-style="background-color:#FFFFFF;"
|
|<math>\rho</math>
|<math>8500</math>
|<math>\mathrm{kg}\,\mathrm{m}^{-3}</math>
|-style="background-color:#FFFFFF;"
|
|<math>\nu</math>
|<math>0.37</math>
|<math>-</math>
|-
|Acoustic fluid
|<math>c</math>
|<math>343</math>
|<math>\mathrm{m}\,\mathrm{s}^{-1}</math>
|-
|
|<math> \rho</math>
|<math> 1.21</math>
|<math> \mathrm{kg}\,\mathrm{m}^{-3}</math>
|-
|}

==Dimensions==
System structure:

:<math>
\begin{align}
M \ddot{x}(t) + E \dot{x}(t) + K x(t) &= B u(t), \\
y(t) &= C x(t)
\end{align}
</math>

System dimensions:

<math>M \in \mathbb{R}^{n \times n}</math>,
<math>E \in \mathbb{R}^{n \times n}</math>,
<math>K \in \mathbb{R}^{n \times n}</math>,
<math>B \in \mathbb{R}^{n \times 1}</math>,
<math>C \in \mathbb{R}^{1 \times n}</math>,
with <math>n=95\,480</math>.

Proportional damping, i.e. <math>E=\alpha M + \beta K</math>, with <math>\alpha=0, \beta=1\cdot 10^{-7}</math> is considered.
The two-way coupling between the structure and the acoustic fluid results in non-symmetric matrices <math>M, E, K</math>.

==Data==
The data is available at [https://doi.org/10.5281/zenodo.7300347 Zenodo].

==Remarks==
* The numerical model resembles the experimental data<ref name="guy81"/> in a frequency range from <math>0\,\mathrm{Hz}</math> to <math>1000\,\mathrm{Hz}</math>.
* The finite element discretization has been performed with [https://github.com/KratosMultiphysics/Kratos Kratos Multiphysics].
* The system has unstable eigenvalues. This is common in interior acoustic problems where no damping is assumed for the acoustic fluid<ref name="cool22"/>.
* 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{dataAum22,
author = {Aumann, Q.},
title = {Matrices for a sound transmission problem},
howpublished = {hosted at {MORwiki} -- Model Order Reduction Wiki},
year = 2022,
doi = {10.5281/zenodo.7300347}
}

* 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}}
}

==References==

<references>

<ref name="guy81">R. W. Guy. "[https://www.ingentaconnect.com/content/dav/aaua/1981/00000049/00000004/art00010 The Transmission of Airborne Sound through a Finite Panel, Air Gap, Panel and Cavity Configuration – a Steady State Analysis ]", Acta Acustica united with Acustica, 49(4): 323--333, 1981.</ref>

<ref name="cool22">V. Cool, S. Jonckheere, E. Deckers, W. Desmet. "[http://dx.doi.org/10.1016/j.jsv.2022.116922 Black box stability preserving reduction techniques in the Loewner framework for the efficient time domain simulation of dynamical systems with damping treatments]", Journal of Sound and Vibration, 529: 116922, 2022.</ref>

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

</references>