KEY RESULTS AND DISCUSSION As mentioned in the previous section, the planning of the first experiment began with the creation of a finite element model. Before performing any experiments, this model was created because it provided a means to predict the experimental results given a certain set of measurement degrees of freedom. By knowing what outcome to expect, the experiment was designed to meet the expectations of algorithms that were planned in areas like impact force identification. For this particular experiment, a finite element model was used to predict the undamped natural frequencies and real normal mode shapes. By knowing the modal frequencies and mode shapes, an appropriate measurement frequency range and spatial modal test grid was chosen. The finite element model was created using Abaqus. Properties were determined for the material that comprised the fixture: 4140 alloy steel. In order to account for the likelihood of relative motion across the bolted interface, a thin layer of lower stiffness material was inserted between the two components of the fixture in the model. The intermediate layer had properties similar to those of aluminum. It was understood that this approach was an approximation for modeling the bolted interface. The results could then be compared between the model and the experiment to determine the validity of the method. Table 1 contains pictures and descriptions of the six mode shapes that were estimated experimentally and were the focus of this analysis. Note that all of the shapes except Mode B had repeated roots present in the experimental data. Table 2 contains a comparison of the average frequency at which each of the six modes occurred in the tests alongside the predicted frequency from the finite element model. Differences in modal frequency from test to test are discussed later in this section. The largest percent difference in natural frequency of 5.88% was for Mode D. Considering the difficulty of modeling the bolted interface, the model was considered to be reasonable for predicting the modal properties of the test fixture. The mode shapes predicted by the model were also very close to what was observed experimentally. Once the model was determined to be adequate, the effects of nonlinearity due to preload level in the bolts was analyzed in the test data. Table 1 Mode Shapes Found in Experiment with Descriptions Mode A: Saddle Shape in Circular plate with little motion in square plate. This corresponds to the first mode of the circular plate.* Mode B: Bowl shape of the circular plate, while square plate moves rigidly with circular plate. This corresponds to the second mode of the circular plate. Mode C: Rigid tilting of the square plate with undulations at attachment points, resembling second bending across the diameter of plate.* Mode D: Six point sine wave around edge of circular plate, with little motion in square plate. This corresponds to the third mode of the circular plate.* Mode E: Eight point sine wave around edge of circular plate, with little motion in square plate. This corresponds to the fourth mode of the circular plate.* Mode F: First bending along the diagonal of the square plate with undulations at attachment points, resembling second bending across the diameter of plate.* *Repeated Root Exists for this Shape 570
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