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Applications of Mathematics

, Volume 59, Issue 1, pp 1–13 | Cite as

Variational characterization of eigenvalues of a non-symmetric eigenvalue problem governing elastoacoustic vibrations

  • Markus StammbergerEmail author
  • Heinrich Voss
Article

Abstract

Small amplitude vibrations of an elastic structure completely filled by a fluid are considered. Describing the structure by displacements and the fluid by its pressure field one arrives at a non-selfadjoint eigenvalue problem. Taking advantage of a Rayleigh functional we prove that its eigenvalues can be characterized by variational principles of Rayleigh, minmax and maxmin type.

Keywords

eigenvalue problem fluid-solid vibration variational characterization min-max principle maxmin principle 

MSC 2010

35P05 47A75 65N25 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2014

Authors and Affiliations

  1. 1.Hamburg University of TechnologyHamburgGermany

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