The discretization of vibrating continuum models by multi-body systems
is a powerful approximation method for studying the natural frequencies of
almost all systems. The theory of this method is explained in detail and
also applied to several examples. This bachelor-thesis proves that the
atypical properties of viscoelastic supported beams, as described in
[BWS14], also occur during the investigation using an approximation by
multi-body systems. This behavior is presented and displayed in a sudden
change of the natural frequencies ('jump'). If, for example, the spring
constant is increased and the damping constant remains the same, the first
natural frequency jumps from zero to a fixed value, whereby the other
frequencies exhibit a similar unlike behavior. Furthermore, for some spring
constant, the natural frequencies increase by increasing the damper
constant. Minor discrepancies between the natural frequencies of continuum
and multi-body systems are observed, but this depends on the rate of
discretization. Since the focus of this work is on approximating
calculations, a lot of calculations concerning parameter changes are done,
e.g., variation of the length distribution of the discrete elements to
achieve `the best' approximation.