## Abstract

Goal
The course Numerical and Experimental Analysis of Linear Dynamical Systems at Eindhoven
University of Technology discusses the topic indicated by its name. However, despite that
there is quite an emphasis on the experimental analysis, the course is finished by doing only
numerical assignments. It would be nice if students also could practice with the experimental
part of the course. Therefore some kind of experimental setup, consisting of a relatively
simple structure, is needed. In this work, a proposal for such an experiment is made. All the
necessary steps for the proposed experiment for model updating are investigated theoretically
to verify the feasibility of the proposed experiment.
The proposed experiment
The proposed experimental setup consists of two clamped-free-free-free (CFFF) plates: one
with a saw-cut, one without. First, students will make a finite element model of the CFFF
plate and verify its correctness by comparing its natural frequencies with the analytic solution
and measurements on the CFFF plate. Second, students will do measurements on the CFFF
plate with saw-cut to find its natural frequencies. Finally, students will update the CFFF plate
model using the natural frequencies of the CFFF plate with saw-cut by updating the
thicknesses of the elements in the saw-cut. Since the plate thickness in the saw-cut is zero, the
thickness of the saw-cut elements should converge to this value during the model update. This
means that students can easily verify the results of the model update, which is a nice feature
of the proposed experiment.
Results
First, finite element models have been made for both plates. The models have been verified by
comparing their natural frequencies and mode shapes with the analytic solution (when
available) and Marc Mentat. Second, optimal sensor location to simulate FRF measurements
have been determined. Third, simulated FRF measurements have been done. The results have
been verified by comparing them with the analytic FRFs of modal superposition. Fourth, a
modal parameter fit procedure in the frequency domain has been used to extract the modal
parameters from the simulated FRF measurements. Fifth, the extracted natural frequencies of
the CFFF plate with saw-cut are used by a model update algorithm that updates the CFFF
plate model by updating the saw-cut thicknesses. During the model update, the saw-cut
thicknesses go to zero, which means that the CFFF plate model is successfully updated to a
CFFF plate with saw-cut model. Finally, the influence of noise, which will always be present
in a real world experiment, is investigated. Noise causes the simulated FRF measurements to
become less accurate, which results in less accurate natural frequencies found by the model
parameter fit procedure. Despite this, the model update will still converge to a thickness of
zero for the saw-cut elements, although more iterations are necessary.
Conclusions
The results in this work have shown that all the necessary steps for the proposed experiment
for model updating can be taken successfully in theory. Therefore, it is recommended to
fabricate the proposed experimental setup, make it ready for FRF measurements and perform
the proposed experiment. This be a good topic for a work of a next student. If that would not
reveal any problems, the experiment for model updating would be ready to be done by
students of the NEALDS course.

Original language | English |
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Place of Publication | Eindhoven |

Publisher | Eindhoven University of Technology |

Publication status | Published - 2011 |