Aerospace (Jun 2016)

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

  • Heinrich Voss

DOI
https://doi.org/10.3390/aerospace3020017
Journal volume & issue
Vol. 3, no. 2
p. 17

Abstract

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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.

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