Numerical Dispersion Error in Finite Methods, Exemplified by the Perfectly Straight Beam Undergoing Bending Oscillations

Abstract

In chapter (1) we present numerical simulations of the eigenstates of a MBS-model (Multi-Body-System) for a continuous ring structure. Both eigenfrequencies and eigenforms show a systematic error for high mode numbers. In order to understand the source of this error, in chapter (2) we calculate analytical solutions for the eigenfrequencies of a MBS- and a FEM-model (Finite-Element-Method) for the straight beam undergoing bending oscillations. We summarize our results in chapter (3).