On a Non-Symmetric Eigenvalue Problem Governing Interior Structural–Acoustic Vibrations
Small amplitude vibrations of a structure completely filled with a fluid are considered. Describing the structure by displacements and the fluid by its pressure field, the free vibrations are governed by a non-self-adjoint eigenvalue problem. This survey reports on a framework for taking advantage o...
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| Format: | Article |
| Language: | English |
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MDPI AG
2016-06-01
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| Series: | Aerospace |
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| Online Access: | http://www.mdpi.com/2226-4310/3/2/17 |
| _version_ | 1818483588002217984 |
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| author | Heinrich Voss |
| author_facet | Heinrich Voss |
| author_sort | Heinrich Voss |
| collection | DOAJ |
| description | Small amplitude vibrations of a structure completely filled with a fluid are considered. Describing the structure by displacements and the fluid by its pressure field, the free vibrations are governed by a non-self-adjoint eigenvalue problem. This survey reports on a framework for taking advantage of the structure of the non-symmetric eigenvalue problem allowing for a variational characterization of its eigenvalues. Structure-preserving iterative projection methods of the the Arnoldi and of the Jacobi–Davidson type and an automated multi-level sub-structuring method are reviewed. The reliability and efficiency of the methods are demonstrated by a numerical example. |
| first_indexed | 2024-12-10T15:43:51Z |
| format | Article |
| id | doaj.art-4b4e6593ffb34320b8cc3c70d459cec3 |
| institution | Directory Open Access Journal |
| issn | 2226-4310 |
| language | English |
| last_indexed | 2024-12-10T15:43:51Z |
| publishDate | 2016-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Aerospace |
| spelling | doaj.art-4b4e6593ffb34320b8cc3c70d459cec32022-12-22T01:43:01ZengMDPI AGAerospace2226-43102016-06-01321710.3390/aerospace3020017aerospace3020017On a Non-Symmetric Eigenvalue Problem Governing Interior Structural–Acoustic VibrationsHeinrich Voss0Institute of Mathematics, Hamburg University of Technology, Am Schwarzenberg Campus 1, Hamburg D-21071, GermanySmall amplitude vibrations of a structure completely filled with a fluid are considered. Describing the structure by displacements and the fluid by its pressure field, the free vibrations are governed by a non-self-adjoint eigenvalue problem. This survey reports on a framework for taking advantage of the structure of the non-symmetric eigenvalue problem allowing for a variational characterization of its eigenvalues. Structure-preserving iterative projection methods of the the Arnoldi and of the Jacobi–Davidson type and an automated multi-level sub-structuring method are reviewed. The reliability and efficiency of the methods are demonstrated by a numerical example.http://www.mdpi.com/2226-4310/3/2/17fluid–solid vibrationvariational characterizationstructure-preserving iterative projection methodsautomated multi-level sub-structuring |
| spellingShingle | Heinrich Voss On a Non-Symmetric Eigenvalue Problem Governing Interior Structural–Acoustic Vibrations Aerospace fluid–solid vibration variational characterization structure-preserving iterative projection methods automated multi-level sub-structuring |
| title | On a Non-Symmetric Eigenvalue Problem Governing Interior Structural–Acoustic Vibrations |
| title_full | On a Non-Symmetric Eigenvalue Problem Governing Interior Structural–Acoustic Vibrations |
| title_fullStr | On a Non-Symmetric Eigenvalue Problem Governing Interior Structural–Acoustic Vibrations |
| title_full_unstemmed | On a Non-Symmetric Eigenvalue Problem Governing Interior Structural–Acoustic Vibrations |
| title_short | On a Non-Symmetric Eigenvalue Problem Governing Interior Structural–Acoustic Vibrations |
| title_sort | on a non symmetric eigenvalue problem governing interior structural acoustic vibrations |
| topic | fluid–solid vibration variational characterization structure-preserving iterative projection methods automated multi-level sub-structuring |
| url | http://www.mdpi.com/2226-4310/3/2/17 |
| work_keys_str_mv | AT heinrichvoss onanonsymmetriceigenvalueproblemgoverninginteriorstructuralacousticvibrations |