Journal of Applied Mathematics
Volume 2005 (2005), Issue 1, Pages 37-48
doi:10.1155/JAM.2005.37
Locating real eigenvalues of a spectral problem in fluid-solid type structures
Department of Mathematics, Technical University of Hamburg-Harburg, Hamburg 21071, Germany
Received 11 August 2003; Revised 16 August 2004
Copyright © 2005 Heinrich Voss. 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.
Abstract
Exploiting minmax characterizations for nonlinear and nonoverdamped eigenvalue problems, we prove the existence of a countable set of eigenvalues converging to ∞ and inclusion theorems for a rational spectral problem governing mechanical vibrations of a tube bundle immersed in an incompressible viscous fluid. The paper demonstrates that the variational characterization of eigenvalues is a powerful tool for studying nonoverdamped eigenproblems, and that the appropriate enumeration of the eigenvalues is of predominant importance, whereas the natural ordering of the eigenvalues may yield false conclusions.