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component mode synthesis (CMS) have the best overall
performance. The results are sufficient accurate in terms
of statics and dynamics, independently of the applied
boundary conditions. Another practical feature is a clear
selection criterion for the number of considered modes as
a function of the excitations frequency content.
The observed accuracy in case of moment matching
(MM) cannot compete with one obtained by the CMS
method. The absence of a correlation between the con-
sidered modes and the covered frequency range is an-
other drawback for industrial use where no convergence
analysis with respect of the number of trial vectors will
Finally it can be reported, that BT in principle cannot
be recommended for model reduction in the investigated
framework at all. The reasons are manifold:
If the overall system response contains a static portion,
the accuracy in terms of displacement and stress is ques-
Due to the absence of static correction vectors in the
mode base, BT delivers bad results when the I/O DOF in
the reduced system face different boundary conditions as
at the time of trial vector generation.
Vibration modes can be missed as a consequence of
the I/O focused approach and its unity sensitivity. This
can lead to unpredictable full system response in case of
varying boundary conditions in the reduced system.
There is no correlation between the trial vectors and
the covered frequency range.
As a final conclusion it can clearly be stated that the
most reliable reduction method for metallic structures
and for a wide range of industrial application in me-
chanical engineering is still the Component Mode Syn-
thesis and its variants. Balanced truncation can be rec-
ommended, when the reduced system is not mistuned,
when the influence of statics is clarified and when just
the I/O behavior is of interest.
One of the most important fields where model reduc-
tion of flexible bodies needs to be applied is elastic multi
body system simulation (MBSS). As already mentioned
MBSS is characterized by the importance of statics, over-
all system response and varying boundary conditions at
the I/O DOF of flexible bodies. For the reasons shown in
this paper, CMS seems to be the best choice.
The feature of predictable error in case of balanced
truncation (BT) may be valuable when the displacement
I/O behavior of the non reduced system has to be ap-
proximated. The practical significance of such an a-priori
error estimation is questionable when viscous damping is
used as an approximation of real damping, when the
boundary conditions in the reduced model differ from the
one of the trial vectors and when stresses or statics are of
Finally it is mentioned once again, that the focus of the
current work is on mechanical engineering. The drawn
conclusions may not be valid for other disciplines like
control or electrical engineering, where the objectives
may be somehow different.
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On the Modal and Non-Modal Model Reduction of Metallic Structures with Variable Boundary Conditions