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Aerospace 2016, 3(2), 17; doi:10.3390/aerospace3020017

On a Non-Symmetric Eigenvalue Problem Governing Interior Structural–Acoustic Vibrations

Institute of Mathematics, Hamburg University of Technology, Am Schwarzenberg Campus 1, Hamburg D-21071, Germany
Academic Editors: Hossein Zare-Behtash and Kiran Ramesh
Received: 22 April 2016 / Revised: 30 May 2016 / Accepted: 3 June 2016 / Published: 17 June 2016
(This article belongs to the Special Issue Fluid-Structure Interactions)
View Full-Text   |   Download PDF [348 KB, uploaded 17 June 2016]   |  

Abstract

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. View Full-Text
Keywords: fluid–solid vibration; variational characterization; structure-preserving iterative projection methods; automated multi-level sub-structuring fluid–solid vibration; variational characterization; structure-preserving iterative projection methods; automated multi-level sub-structuring
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Voss, H. On a Non-Symmetric Eigenvalue Problem Governing Interior Structural–Acoustic Vibrations. Aerospace 2016, 3, 17.

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