Linear 1D Beam - Revision history

Schuetz2 at 05:32, 17 June 2025

2025-06-17T05:32:52Z

← Older revision		Revision as of 05:32, 17 June 2025
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	title = {Linear 1{D} Beam},		title = {Linear 1{D} Beam},
	howpublished = {hosted at {MORwiki} -- Model Order Reduction Wiki},		howpublished = {hosted at {MORwiki} -- Model Order Reduction Wiki},
	url = <nowiki>{~~http~~://modelreduction.org/~~index.php~~/Linear_1D_Beam}</nowiki>,		url = <nowiki>{https://modelreduction.org/morwiki/Linear_1D_Beam}</nowiki>,
	year = 2004		year = 2004
	}		}

Malhotra: infobox string

2023-11-30T09:33:38Z

infobox string

← Older revision		Revision as of 09:33, 30 November 2023
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	[[Category:SISO]]		[[Category:SISO]]
	[[Category:Sparse]]		[[Category:Sparse]]

			{{Infobox
			\|Title = Linear 1D Beam
			\|Benchmark ID =
			* linear1DBeam_n14m1q1
			* linear1DBeam_n18m1q1
			* linear1DBeam_n19994m1q1
			* linear1DBeam_n19998m1q1
			\|Category = oberwolfach
			\|System-Class = LTI-SOS
			\|nstates =
			* 14
			* 18
			* 19994
			* 19998
			\|ninputs = 1
			\|noutputs = 1
			\|nparameters = 0
			\|components = B, C, E, K, M
			\|License = NA
			\|Creator = [[User:Himpe]]
			\|Editor =
			* [[User:Himpe]]
			* [[User:Mlinaric]]
			* [[User:Hund]]
			\|Zenodo-link = NA
			}}

Lund: Correct dof

2022-06-29T11:46:33Z

Correct dof

← Older revision		Revision as of 11:46, 29 June 2022
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	\|[https://csc.mpi-magdeburg.mpg.de/mpcsc/MORWIKI/Oberwolfach/Linear1dBeam-dim1e5-LFAT5000.zip Linear1dBeam-dim1e5-LFAT5000.zip]		\|[https://csc.mpi-magdeburg.mpg.de/mpcsc/MORWIKI/Oberwolfach/Linear1dBeam-dim1e5-LFAT5000.zip Linear1dBeam-dim1e5-LFAT5000.zip]
	\|flexural (<math>y</math> and <math>\theta_z</math>), axial, torsional		\|flexural (<math>y</math> and <math>\theta_z</math>), axial, torsional
	\|~~50000~~		\|5000
	\|19994		\|19994
	\|5532532		\|5532532

Mitchell: grammar

2022-03-15T10:16:24Z

grammar

← Older revision		Revision as of 10:16, 15 March 2022
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	Accurate modelling of such a system typically leads to high order models.		Accurate modelling of such a system typically leads to high order models.
	The tasks of simulation, analysis and controller design of high order nonlinear control systems can be simplified by reducing the order of the original system and ~~approximate~~ it by a lower order model.		The tasks of simulation, analysis and controller design of high order nonlinear control systems can be simplified by reducing the order of the original system and approximating it by a lower order model.

	A application of electrostatic moving structures are e.g. [[wikipedia:RF_switch\|RF switches]] or filters.		A application of electrostatic moving structures are e.g. [[wikipedia:RF_switch\|RF switches]] or filters.

Mitchell: wrong word

2022-03-15T10:15:35Z

wrong word

← Older revision		Revision as of 10:15, 15 March 2022
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	<figure id="fig4">[[File:Beam4.gif\|490px\|thumb\|right\|Figure 4]]</figure>		<figure id="fig4">[[File:Beam4.gif\|490px\|thumb\|right\|Figure 4]]</figure>

	Moving structures are an essential part ~~for~~ many microsystem devices, among them fluidic components like pumps and electrically controllable valves, sensing cantilevers, and optical structures.		Moving structures are an essential part of many microsystem devices, among them fluidic components like pumps and electrically controllable valves, sensing cantilevers, and optical structures.

	Several actuation principles can be employed on microscopic length scales, the most frequent certainly the electromagnetic forces.		Several actuation principles can be employed on microscopic length scales, the most frequent certainly the electromagnetic forces.

Saak: /* Data */

2021-12-14T08:57:47Z

Data

← Older revision		Revision as of 08:57, 14 December 2021
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	\|Compressed size [B]		\|Compressed size [B]
	\|-		\|-
	\|[https://~~www~~.mpi-magdeburg.mpg.de/mpcsc/MORWIKI/Oberwolfach/Linear1dBeam-dim1e1-LF10.zip Linear1dBeam-dim1e1-LF10.zip]		\|[https://csc.mpi-magdeburg.mpg.de/mpcsc/MORWIKI/Oberwolfach/Linear1dBeam-dim1e1-LF10.zip Linear1dBeam-dim1e1-LF10.zip]
	\|flexural (<math>y</math> and <math>\theta_z</math>)		\|flexural (<math>y</math> and <math>\theta_z</math>)
	\|10		\|10
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	\|2384		\|2384
	\|-		\|-
	\|[https://~~www~~.mpi-magdeburg.mpg.de/mpcsc/MORWIKI/Oberwolfach/Linear1dBeam-dim1e4-LF10000.zip Linear1dBeam-dim1e4-LF10000.zip]		\|[https://csc.mpi-magdeburg.mpg.de/mpcsc/MORWIKI/Oberwolfach/Linear1dBeam-dim1e4-LF10000.zip Linear1dBeam-dim1e4-LF10000.zip]
	\|flexural (<math>y</math> and <math>\theta_z</math>)		\|flexural (<math>y</math> and <math>\theta_z</math>)
	\|10000		\|10000
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	\|716807		\|716807
	\|-		\|-
	\|[https://~~www~~.mpi-magdeburg.mpg.de/mpcsc/MORWIKI/Oberwolfach/Linear1dBeam-dim1e1-LFAT5.zip Linear1dBeam-dim1e1-LFAT5.zip]		\|[https://csc.mpi-magdeburg.mpg.de/mpcsc/MORWIKI/Oberwolfach/Linear1dBeam-dim1e1-LFAT5.zip Linear1dBeam-dim1e1-LFAT5.zip]
	\|flexural (<math>y</math> and <math>\theta_z</math>), axial, torsional		\|flexural (<math>y</math> and <math>\theta_z</math>), axial, torsional
	\|5		\|5
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	\|2255		\|2255
	\|-		\|-
	\|[https://~~www~~.mpi-magdeburg.mpg.de/mpcsc/MORWIKI/Oberwolfach/Linear1dBeam-dim1e5-LFAT5000.zip Linear1dBeam-dim1e5-LFAT5000.zip]		\|[https://csc.mpi-magdeburg.mpg.de/mpcsc/MORWIKI/Oberwolfach/Linear1dBeam-dim1e5-LFAT5000.zip Linear1dBeam-dim1e5-LFAT5000.zip]
	\|flexural (<math>y</math> and <math>\theta_z</math>), axial, torsional		\|flexural (<math>y</math> and <math>\theta_z</math>), axial, torsional
	\|50000		\|50000

Himpe: Fix CrossRefs

2021-08-27T07:44:52Z

Fix CrossRefs

← Older revision		Revision as of 07:44, 27 August 2021
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	\|}		\|}

	See ~~<xr id="fig2"/>~~ for Degree of Freedom <math>x</math>, ~~<xr id="fig3"/>~~ for Degree of Freedom <math>\theta_x</math> and ~~<xr id="fig4"/>~~ for Degrees of freedom <math>y</math> and <math>\theta_z</math>.		See Fig. 2 for Degree of Freedom <math>x</math>, Fig. 3 for Degree of Freedom <math>\theta_x</math> and Fig. 4 for Degrees of freedom <math>y</math> and <math>\theta_z</math>.

	The beam is supported either on the left side or on both sides. For the left side (fixed) support,		The beam is supported either on the left side or on both sides. For the left side (fixed) support,

Himpe: minor fix.

2018-07-26T07:59:04Z

minor fix.

← Older revision		Revision as of 07:59, 26 July 2018
Line 27:		Line 27:
	The tasks of simulation, analysis and controller design of high order nonlinear control systems can be simplified by reducing the order of the original system and approximate it by a lower order model.		The tasks of simulation, analysis and controller design of high order nonlinear control systems can be simplified by reducing the order of the original system and approximate it by a lower order model.

	A application of electrostatic moving structures are e.g. RF switches or filters.		A application of electrostatic moving structures are e.g. [[wikipedia:RF_switch\|RF switches]] or filters.
	Given a simple enough shape, they often can be modelled as one-dimensional beams embedded in two or three dimensional space.		Given a simple enough shape, they often can be modelled as one-dimensional beams embedded in two or three dimensional space.

Himpe: /* Data */ Update benchmark data file links

2018-07-17T10:32:45Z

Data: Update benchmark data file links

← Older revision		Revision as of 10:32, 17 July 2018
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	\|Compressed size [B]		\|Compressed size [B]
	\|-		\|-
	\|[https://~~portal~~.~~uni~~-~~freiburg~~.de/~~imteksimulation~~/~~downloads~~/~~benchmark~~/~~Linear%201D%20Beam%20%2838861%29/files/fileinnercontentproxy~~.~~2010~~-01-~~31.3349728177~~ LF10.zip]		\|[https://www.mpi-magdeburg.mpg.de/mpcsc/MORWIKI/Oberwolfach/Linear1dBeam-dim1e1-LF10.zip Linear1dBeam-dim1e1-LF10.zip]
	\|flexural (<math>y</math> and <math>\theta_z</math>)		\|flexural (<math>y</math> and <math>\theta_z</math>)
	\|10		\|10
Line 125:		Line 125:
	\|2384		\|2384
	\|-		\|-
	\|[https://~~portal~~.~~uni~~-~~freiburg~~.de/~~imteksimulation~~/~~downloads~~/~~benchmark~~/~~Linear%201D%20Beam%20%2838861%29/files/fileinnercontentproxy~~.~~2010~~-01-~~31.3358570716~~ LF10000.zip]		\|[https://www.mpi-magdeburg.mpg.de/mpcsc/MORWIKI/Oberwolfach/Linear1dBeam-dim1e4-LF10000.zip Linear1dBeam-dim1e4-LF10000.zip]
	\|flexural (<math>y</math> and <math>\theta_z</math>)		\|flexural (<math>y</math> and <math>\theta_z</math>)
	\|10000		\|10000
Line 132:		Line 132:
	\|716807		\|716807
	\|-		\|-
	\|[https://~~portal~~.~~uni~~-~~freiburg~~.de/~~imteksimulation~~/~~downloads~~/~~benchmark~~/~~Linear%201D%20Beam%20%2838861%29/files/fileinnercontentproxy~~.~~2010~~-01-~~31.3367011092~~ LFAT5.zip]		\|[https://www.mpi-magdeburg.mpg.de/mpcsc/MORWIKI/Oberwolfach/Linear1dBeam-dim1e1-LFAT5.zip Linear1dBeam-dim1e1-LFAT5.zip]
	\|flexural (<math>y</math> and <math>\theta_z</math>), axial, torsional		\|flexural (<math>y</math> and <math>\theta_z</math>), axial, torsional
	\|5		\|5
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	\|2255		\|2255
	\|-		\|-
	\|[https://~~portal~~.~~uni~~-~~freiburg~~.de/~~imteksimulation~~/~~downloads~~/~~benchmark~~/~~Linear%201D%20Beam%20%2838861%29/files/fileinnercontentproxy~~.~~2010~~-01-~~31.3373723032~~ LFAT5000.zip]		\|[https://www.mpi-magdeburg.mpg.de/mpcsc/MORWIKI/Oberwolfach/Linear1dBeam-dim1e5-LFAT5000.zip Linear1dBeam-dim1e5-LFAT5000.zip]
	\|flexural (<math>y</math> and <math>\theta_z</math>), axial, torsional		\|flexural (<math>y</math> and <math>\theta_z</math>), axial, torsional
	\|50000		\|50000
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	where <math>B</math> is a <math>n \times 1</math> matrix and <math>C</math> is a <math>1 \times n</math> matrix with the only nonzero entry at the <math>y</math> DOF of the middle node.		where <math>B</math> is a <math>n \times 1</math> matrix and <math>C</math> is a <math>1 \times n</math> matrix with the only nonzero entry at the <math>y</math> DOF of the middle node.

	Details of the implementation are available in a separate [https://~~portal~~.~~uni~~-~~freiburg~~.de/~~imteksimulation/downloads/benchmark~~/~~Linear%201D%20Beam%20%2838861%29~~/~~files~~/~~fileinnercontentproxy.2010-01-31~~.~~3407950776~~ report]. A typical input to this system is a step response; periodic on/off switching is also possible.		Details of the implementation are available in a separate [https://www.mpi-magdeburg.mpg.de/mpcsc/MORWIKI/Oberwolfach/Linear1dBeam.pdf report]. A typical input to this system is a step response; periodic on/off switching is also possible.
	The reduced model should thus both represent the step response as well as the possible influence of higher order harmonics.		The reduced model should thus both represent the step response as well as the possible influence of higher order harmonics.
	See also <ref name="lienemann2006"/>.		See also <ref name="lienemann2006"/>.

Werner: Updated BibTeX entry.

2018-04-24T09:03:07Z

Updated BibTeX entry.

← Older revision		Revision as of 09:03, 24 April 2018
Line 192:		Line 192:

	* For the benchmark itself and its data:		* For the benchmark itself and its data:
	:: Oberwolfach Benchmark Collection '''Linear 1D Beam'''. hosted at MORwiki - Model Order Reduction Wiki, 2004. http://modelreduction.org/index.php/Linear_1D_Beam		:: Oberwolfach Benchmark Collection, '''Linear 1D Beam'''. hosted at MORwiki - Model Order Reduction Wiki, 2004. http://modelreduction.org/index.php/Linear_1D_Beam

	@MISC{morwiki_linear_beam,		@MISC{morwiki_linear_beam,
	author = {Oberwolfach Benchmark Collection},		author = <nowiki>{{Oberwolfach Benchmark Collection}}</nowiki>,
	title = {Linear 1{D} Beam},		title = {Linear 1{D} Beam},
	howpublished = {hosted at {MORwiki} -- Model Order Reduction Wiki},		howpublished = {hosted at {MORwiki} -- Model Order Reduction Wiki},
	url = {<nowiki>http://modelreduction.org/index.php/Linear_1D_Beam</nowiki>},		url = <nowiki>{http://modelreduction.org/index.php/Linear_1D_Beam}</nowiki>,
	year = 2004		year = 2004
	}		}

	* For the background on the benchmark:		* For the background on the benchmark:

	@TechReport{morLieRK06,		@TechReport{morLieRK06,
	title = {MST MEMS Model Order Reduction: Requirements and Benchmarks},		title = {MST MEMS Model Order Reduction: Requirements and Benchmarks},
	author = {J. Lienemann, E.B. Rudnyi and J.G. Korvink},		author = {J. Lienemann, E.B. Rudnyi and J.G. Korvink},
	journal = {Linear Algebra and its Applications},		journal = {Linear Algebra and its Applications},
	year = 2006,		year = 2006,
	volume = 415,		volume = 415,
	issue = 2--3,		issue = 2--3,
	pages = {469--498},		pages = {469--498},
	month = {June},		month = {June},
	publisher = {Elsevier},		publisher = {Elsevier},
	doi = {10.1016/j.laa.2005.04.002}		doi = {10.1016/j.laa.2005.04.002}
	}		}