If there is 2 DOF (Translational, Rotational) Cantilever beam, and it has 7 elements, I want to use System reduction technique to get rid of the rotational Dof, Do I expect to obtain the same first seven natural frequencies?
Because I tried to use SEREP technique and I did not get the first seven natural frequencies, I got the 1,3,5,7,9,11,13 natural frequencies?
Does anyone has explanations please?
In our example, we used planar finite elements with two displacements per node (x and y) and therefore considered only the first 7 bending modes in the xy plane. For the expansion process, the numerical mode shapes were further reduced to 29 displacement DOFs in the y-direction.
From your description, I assume you are trying to use spatial linear finite elements. In this case, bending modes in the xz-plane (and possibly torsional modes) are also present in the numerical solution.
In our experimental model, the excitation was only performed in the y-direction, and the response was also measured in the y-direction using uniaxial accelerometers. Thus, only xy-plane bending was excited and observed.
Due to the lack of observability and controllability for the xz bending and torsional modes, an expansion to a spatial FEM model is unlikely to be successful.
If you are interested in a comparison of different expansion methods (SEREP, SEMM, and M-SEMM), open-source code and an example can be found in the Python library pyFBS (https://gitlab.com/pyFBS/pyFBS/-/blob/master/examples/21_expansion_methods.ipynb).
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