Dear engineers and physicists,(adsbygoogle = window.adsbygoogle || []).push({});

I would like to ask you a question about Component Mode Synthesis (CMS), which is the topic of my bachelor thesis. My primary resource is the classical AIAA article "Coupling of Substructures for Dynamic Analyses: an Overview" by Prof. Craig.

For now I am considering a simple mechanical system consisting of two connected bodies (arms) according to the first picture. The individual bodies have been modeled in ANSYS and their mass, stiffness, nodal coordinates and adjacency matrices were imported to Matlab, where reduction and interconnection themselves are carried out.

First the FEM solution without reduction (i.e. in physical coordinates) is calculated for reference and then two CMS methods are implemented, namely the Craig-Bampton's (fixed-interface normal modes & constraint modes) and Rubin's (free-interface normal modes, rigid-body modes & residual flexibility modes).

Now to my question, which might be a bit funny, bacause I am complaining about the methods being too precise. :) It seems that the natural frequencies of both methods correspond exactly (!) to the FEM solution, errors being of the order 0.01% which can be accounted to numerical round-offs. If I keep 30 natural modes for each body corresponding to 30 lowest frequencies, the first 50 natural frequencies of the connected system are exact! Then the error increases and the last calculated frequency (60th) has an error of 20% (talking about the Craig-Bampton now). I was really surprised by this, do you somebody have an insight where this "exact" corresponence comes from? If I compare the normal modes of the assembled reduced model with the reference solution by the Modal Assurance Criterion (MAC), I get the expected inaccuracies (please see 2nd included picture for the 20 lowest freq. normal shapes).

Thank you very much for any answers, tips, further questions or any other form of reactions. All the best from the Czech Republic.

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# Model Reduction and Substructuring in Dynamics, CMS

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