A plate with a saw-cut : simulated experimental modal analysis and model updating

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

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