Fast vibro-acoustic response computations for finite periodic metamaterial plates using a generalized Bloch Mode Synthesis based sub-structuring approach
Metamaterials have recently emerged and shown great potential for noise and vibration reduction in specific frequency ranges, called stop bands. To predict stop bands, their often periodic nature is exploited and dispersion curves are calculated based on a single representative unit cell, typically...
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2022-11-01
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| Series: | Frontiers in Mechanical Engineering |
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| Online Access: | https://www.frontiersin.org/articles/10.3389/fmech.2022.1031899/full |
| _version_ | 1798015372791644160 |
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| author | Lucas Van Belle Lucas Van Belle Claus Claeys Claus Claeys Wim Desmet Wim Desmet Elke Deckers Elke Deckers |
| author_facet | Lucas Van Belle Lucas Van Belle Claus Claeys Claus Claeys Wim Desmet Wim Desmet Elke Deckers Elke Deckers |
| author_sort | Lucas Van Belle |
| collection | DOAJ |
| description | Metamaterials have recently emerged and shown great potential for noise and vibration reduction in specific frequency ranges, called stop bands. To predict stop bands, their often periodic nature is exploited and dispersion curves are calculated based on a single representative unit cell, typically modeled using the finite element method. Since their sub-wavelength nature and often intricate design can lead to large unit cell models, model reduction methods such as the Generalized Bloch Mode Synthesis have been proposed to greatly accelerate dispersion curve calculations. In order to calculate forced vibro-acoustic responses of finite periodic elastic metamaterial plates composed of an assembly of unit cells, however, full order finite element models rapidly become computationally unaffordable. Therefore, in this work the Generalized Bloch Mode Synthesis is incorporated in a sub-structuring approach, which enables fast forced vibration response calculations of finite elastic metamaterial plates based on a single reduced order unit cell model. The main advantage as compared to a regular Craig-Bampton approach is the additional local reduction of unit cell boundary degrees of freedom, whereby a compatible basis for the identical neighboring unit cells is incorporated. In addition, by combining this Generalized Bloch Mode Synthesis based sub-structuring approach with the Elementary Radiator Approach, efficient sound transmission loss computations of finite periodic metamaterial plates are enabled. The performance of the proposed approach for fast vibro-acoustic response predictions is demonstrated for different cases. |
| first_indexed | 2024-04-11T15:33:20Z |
| format | Article |
| id | doaj.art-42c39dc9da944f0db44a554ff0755dfd |
| institution | Directory Open Access Journal |
| issn | 2297-3079 |
| language | English |
| last_indexed | 2024-04-11T15:33:20Z |
| publishDate | 2022-11-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Mechanical Engineering |
| spelling | doaj.art-42c39dc9da944f0db44a554ff0755dfd2022-12-22T04:16:05ZengFrontiers Media S.A.Frontiers in Mechanical Engineering2297-30792022-11-01810.3389/fmech.2022.10318991031899Fast vibro-acoustic response computations for finite periodic metamaterial plates using a generalized Bloch Mode Synthesis based sub-structuring approachLucas Van Belle0Lucas Van Belle1Claus Claeys2Claus Claeys3Wim Desmet4Wim Desmet5Elke Deckers6Elke Deckers7Department of Mechanical Engineering, KU Leuven, Heverlee, BelgiumDMMS Core Lab, Flanders Make, Heverlee, BelgiumDepartment of Mechanical Engineering, KU Leuven, Heverlee, BelgiumDMMS Core Lab, Flanders Make, Heverlee, BelgiumDepartment of Mechanical Engineering, KU Leuven, Heverlee, BelgiumDMMS Core Lab, Flanders Make, Heverlee, BelgiumDMMS Core Lab, Flanders Make, Heverlee, BelgiumDepartment of Mechanical Engineering, KU Leuven, Campus Diepenbeek, Diepenbeek, BelgiumMetamaterials have recently emerged and shown great potential for noise and vibration reduction in specific frequency ranges, called stop bands. To predict stop bands, their often periodic nature is exploited and dispersion curves are calculated based on a single representative unit cell, typically modeled using the finite element method. Since their sub-wavelength nature and often intricate design can lead to large unit cell models, model reduction methods such as the Generalized Bloch Mode Synthesis have been proposed to greatly accelerate dispersion curve calculations. In order to calculate forced vibro-acoustic responses of finite periodic elastic metamaterial plates composed of an assembly of unit cells, however, full order finite element models rapidly become computationally unaffordable. Therefore, in this work the Generalized Bloch Mode Synthesis is incorporated in a sub-structuring approach, which enables fast forced vibration response calculations of finite elastic metamaterial plates based on a single reduced order unit cell model. The main advantage as compared to a regular Craig-Bampton approach is the additional local reduction of unit cell boundary degrees of freedom, whereby a compatible basis for the identical neighboring unit cells is incorporated. In addition, by combining this Generalized Bloch Mode Synthesis based sub-structuring approach with the Elementary Radiator Approach, efficient sound transmission loss computations of finite periodic metamaterial plates are enabled. The performance of the proposed approach for fast vibro-acoustic response predictions is demonstrated for different cases.https://www.frontiersin.org/articles/10.3389/fmech.2022.1031899/fullmetamaterialsunit cellsub-structuringmodel order reductionvibrationsound transmission |
| spellingShingle | Lucas Van Belle Lucas Van Belle Claus Claeys Claus Claeys Wim Desmet Wim Desmet Elke Deckers Elke Deckers Fast vibro-acoustic response computations for finite periodic metamaterial plates using a generalized Bloch Mode Synthesis based sub-structuring approach Frontiers in Mechanical Engineering metamaterials unit cell sub-structuring model order reduction vibration sound transmission |
| title | Fast vibro-acoustic response computations for finite periodic metamaterial plates using a generalized Bloch Mode Synthesis based sub-structuring approach |
| title_full | Fast vibro-acoustic response computations for finite periodic metamaterial plates using a generalized Bloch Mode Synthesis based sub-structuring approach |
| title_fullStr | Fast vibro-acoustic response computations for finite periodic metamaterial plates using a generalized Bloch Mode Synthesis based sub-structuring approach |
| title_full_unstemmed | Fast vibro-acoustic response computations for finite periodic metamaterial plates using a generalized Bloch Mode Synthesis based sub-structuring approach |
| title_short | Fast vibro-acoustic response computations for finite periodic metamaterial plates using a generalized Bloch Mode Synthesis based sub-structuring approach |
| title_sort | fast vibro acoustic response computations for finite periodic metamaterial plates using a generalized bloch mode synthesis based sub structuring approach |
| topic | metamaterials unit cell sub-structuring model order reduction vibration sound transmission |
| url | https://www.frontiersin.org/articles/10.3389/fmech.2022.1031899/full |
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