Locating real eigenvalues of a spectral problem in fluid-solid type structures

2018/02/27 by Voß, Heinrich
#Mathematik #eigenvalue bounds #fluid structure interaction #minmax principle #nonlinear eigenvalue problem

paper · doi:10.15480/882.1555

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.

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