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

Heinrich Voss

 Department of Mathematics, Technical University of Hamburg-Harburg, Hamburg 21071, Germany
Received 11 August 2003; Revised 16 August 2004

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.