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T. Kniffka, H. Ecker:
"Observations regarding numerical results obtained by the Floquet-method";
in: "Proceedings DETC2013", issued by: ASME; ASME, New York, 2013, Paper ID DETC2013-13292, 10 pages.

Stability studies of parametrically excited systems are
frequently carried out by numerical methods. Especially for
LTP-systems, several such methods are known and in practical
use. This study investigates and compares two methods
that are both based on Floquet´s theorem.
As an introductary benchmark problem a 1-dof system
is employed, which is basically a mechanical representation
of the damped Mathieu-equation. The second problem to be
studied in this contribution is a time-periodic 2-dof vibrational
system. The system equations are transformed into a
modal representation to facilitate the application and interpretation
of the results obtained by different methods.
Both numerical methods are similar in the sense that a
monodromy matrix for the LTP-system is calculated numerically.
However, one method uses the period of the parametric
excitation as the interval for establishing that matrix.
The other method is based on the period of the solution,
which is not known exactly.
Numerical results are computed by both methods and
compared in order to work out how they can be applied efficiently.

Parametric Excitation