Curve veering for the parameter-dependent clamped plate

Abstract

The computation of vibrations of a thin rectangular clamped plate results in an eigenvalue problem with a partial differential equation of fourth order. If we change the geometry of the plate for fixed area, this results in a parameter-dependent eigenvalue problem. For certain parameters, the eigenvalue curves seem to cross. We give a numerically rigorous proof of curve veering, which is based on the Lehmann-Goerisch inclusion theorems and the Rayleigh-Ritz procedure.