The balanced proper orthogonal decomposition applied to a class of frequency-dependent damped structures.
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| Title: | The balanced proper orthogonal decomposition applied to a class of frequency-dependent damped structures. |
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| Authors: | Berthet, Alexandre1 (AUTHOR) alexandre.berthet@utc.fr, Perrey-Debain, Emmanuel1 (AUTHOR) emmanuel.perrey-debain@utc.fr, Chazot, Jean-Daniel1 (AUTHOR) jean-daniel.chazot@utc.fr, Germès, Sylvain2 (AUTHOR) sylvain.germes@saint-gobain.com |
| Source: | Mechanical Systems & Signal Processing. Feb2023, Vol. 185, pN.PAG-N.PAG. 1p. |
| Subjects: | Proper orthogonal decomposition, Laplacian matrices, Transfer matrix, Transfer functions, Data reduction, Matrix functions |
| Abstract: | A model reduction technique aimed at computing efficiently Frequency Response Functions of damped structures is presented. The frequency-dependent complex moduli are approximated by a mini-oscillators model, known as the Golla–Hughes–MacTavish (GHM) model, which permits to recast the original problem as a more familiar second-order, constant-coefficient system of equations. The matrix system, although much larger, is then treated by application of the Balanced Proper Orthogonal Decomposition (BPOD) which aims at approximating the transfer function matrix, or equivalently the admittance matrix, connecting forces and displacements at a specified set of points of the vibrating structure. All the necessary ingredients of the reduction strategy as well as its efficiency measured in terms of data reduction, accuracy and computational cost are shown. Two illustrative examples of increasing complexity involving a clamped cantilever beam and a realistic windshield are presented. It is shown that the admittance matrix can be approximated by matrices of very small size which computation can be speeded up via diagonalization. It is concluded that the application of BPOD combined with the GHM decomposition of the frequency-dependent algebraic system proves extremely efficient for the modeling of vibrating structures made of different materials, either viscoelastic or purely elastic. [ABSTRACT FROM AUTHOR] |
| Copyright of Mechanical Systems & Signal Processing is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 160213949 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: The balanced proper orthogonal decomposition applied to a class of frequency-dependent damped structures. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Berthet%2C+Alexandre%22">Berthet, Alexandre</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> alexandre.berthet@utc.fr</i><br /><searchLink fieldCode="AR" term="%22Perrey-Debain%2C+Emmanuel%22">Perrey-Debain, Emmanuel</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> emmanuel.perrey-debain@utc.fr</i><br /><searchLink fieldCode="AR" term="%22Chazot%2C+Jean-Daniel%22">Chazot, Jean-Daniel</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> jean-daniel.chazot@utc.fr</i><br /><searchLink fieldCode="AR" term="%22Germès%2C+Sylvain%22">Germès, Sylvain</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> sylvain.germes@saint-gobain.com</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Mechanical+Systems+%26+Signal+Processing%22">Mechanical Systems & Signal Processing</searchLink>. Feb2023, Vol. 185, pN.PAG-N.PAG. 1p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Proper+orthogonal+decomposition%22">Proper orthogonal decomposition</searchLink><br /><searchLink fieldCode="DE" term="%22Laplacian+matrices%22">Laplacian matrices</searchLink><br /><searchLink fieldCode="DE" term="%22Transfer+matrix%22">Transfer matrix</searchLink><br /><searchLink fieldCode="DE" term="%22Transfer+functions%22">Transfer functions</searchLink><br /><searchLink fieldCode="DE" term="%22Data+reduction%22">Data reduction</searchLink><br /><searchLink fieldCode="DE" term="%22Matrix+functions%22">Matrix functions</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: A model reduction technique aimed at computing efficiently Frequency Response Functions of damped structures is presented. The frequency-dependent complex moduli are approximated by a mini-oscillators model, known as the Golla–Hughes–MacTavish (GHM) model, which permits to recast the original problem as a more familiar second-order, constant-coefficient system of equations. The matrix system, although much larger, is then treated by application of the Balanced Proper Orthogonal Decomposition (BPOD) which aims at approximating the transfer function matrix, or equivalently the admittance matrix, connecting forces and displacements at a specified set of points of the vibrating structure. All the necessary ingredients of the reduction strategy as well as its efficiency measured in terms of data reduction, accuracy and computational cost are shown. Two illustrative examples of increasing complexity involving a clamped cantilever beam and a realistic windshield are presented. It is shown that the admittance matrix can be approximated by matrices of very small size which computation can be speeded up via diagonalization. It is concluded that the application of BPOD combined with the GHM decomposition of the frequency-dependent algebraic system proves extremely efficient for the modeling of vibrating structures made of different materials, either viscoelastic or purely elastic. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Mechanical Systems & Signal Processing is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.ymssp.2022.109746 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 1 StartPage: N.PAG Subjects: – SubjectFull: Proper orthogonal decomposition Type: general – SubjectFull: Laplacian matrices Type: general – SubjectFull: Transfer matrix Type: general – SubjectFull: Transfer functions Type: general – SubjectFull: Data reduction Type: general – SubjectFull: Matrix functions Type: general Titles: – TitleFull: The balanced proper orthogonal decomposition applied to a class of frequency-dependent damped structures. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Berthet, Alexandre – PersonEntity: Name: NameFull: Perrey-Debain, Emmanuel – PersonEntity: Name: NameFull: Chazot, Jean-Daniel – PersonEntity: Name: NameFull: Germès, Sylvain IsPartOfRelationships: – BibEntity: Dates: – D: 15 M: 02 Text: Feb2023 Type: published Y: 2023 Identifiers: – Type: issn-print Value: 08883270 Numbering: – Type: volume Value: 185 Titles: – TitleFull: Mechanical Systems & Signal Processing Type: main |
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