Based on the theoretical analysis defining the characteristics of the
state of motion a one-sided elastically mounted rotor system displays on
parametrical variation, the stability of the anticipated motion is
discussed and evaluated. For this methods of numerical mathematics in
MATLAB and the perturbation theory are applied. The following tasks are
processed: 1. Literary research on the characteristics of rotor dynamics
and the stability of rotor motions is conducted; 2. Implementation of a
mechanical model and determination of the differential equation system
based on the Lagrange equation of second kind; 3. Development of a
numerical solution in MATLAB and calculation of the natural frequencies of
the mechanical system; 4. Development of a stability diagram for the
differential equation system and analysis of consequences resulting from
parametrical variations. By implementation of specially developed MATLAB
programs the equation system can be determined and solved automatically.
The integrated calculation of the eigenvalues shows a clear functional
correlation of the natural frequencies to the speed of the rotor. Based on
the perturbation theory approximated solutions for the stability limits of
the mechanical system are calculated. They are visualized as a stability
diagram. Parametrical variation allows for the stability of the system to
be assessed for different conditions.