20 T. Roberts and P. J. Cornwell pretension. Intuitively, one would imagine that the higher the pretension in the joint, the stiffer the system will be and the higher the natural frequencies will become. This possibility poses an interesting question from the perspective of structural health monitoring. If changing pretension has an effect on the modal properties of a system, then those properties could be used to detect the severity and location of a loosened connection. In order to simulate loosened connections, the size of the contact zone (i.e. area where elements are bonded together) was varied and modal properties were extracted for each different size contact zone. Table 2.8 shows the natural frequencies of the bolted structure from experimental data and from two different FE models – Bolted FE with 10-mm contact regions and Bolted FE with 17-mm contact regions. As expected, the model with the larger contact region resulted in higher natural frequencies. However, the FE model results still vary from the experimental results significantly (up to about 6%), especially when comparing higher frequency modes. Since the FE natural frequencies are consistently lower than those from the experimental modal tests, it is possible that the material properties of the bolts should be adjusted. By increasing the stiffness of the bolts, the natural frequencies of the models would likely increase, but these adjustments may lead to a model that is falsely accurate. The bolted connection creates much more variability within the model than material properties do, so it is more likely that the connection parameters are modeled incorrectly rather than the material model being the source of error. The last of the FE studies were two models with one bolt missing – 10-mm and 17-mm contact regions with a bolt and its contact region missing. The mass properties of the model as well as the stiffness from pretension will be affected by removing a bolt. Table 2.9 lists the natural frequencies of the undamaged and damaged FE models with 10-mm contact regions. Table 2.10 lists the natural frequencies of the undamaged and damaged FE models with 17-mm contact regions. From Tables 2.9 and 2.10, it is apparent that natural frequencies change in the damaged vs. undamaged models; however, the results are counterintuitive. Overall, the damaged structures had slightly lower natural frequencies than the undamaged structures, especially in the 1st Torsion, 3rd Bending, and 1st O.P. Bending modes. The damaged model with 17-mm contact Table 2.8 Natural frequencies and percent differences for the bolted structure, bolted structure FE model with 10-mm contact regions, and the bolted structure FE model with 17-mm contact regions Undamaged natural frequencies [Hz] Percent difference [%] Mode Bolted Bolted FE 10 mm Bolted FE 17 mm Bolted vs. FE 10 mm Bolted vs. FE 17 mm 1st bending 275.88 260.13 269.85 5.70 2.18 2nd bending 713.38 693.10 697.27 2.84 2.25 1st torsion 1225.5 1167.0 1195.7 4.77 2.43 3rd bending 1459.9 1388.2 1438.6 4.91 1.46 1st O.P. bending 1823.7 1754.3 1812.2 3.80 0.63 2nd torsion 1891.1 1777.9 1790.9 5.98 5.29 Table 2.9 Natural frequencies and percent differences for the undamaged and damaged bolted structure FE model with 10-mm contact regions Bolted FE model 10-mm contact region Natural frequencies [Hz] Percent differences [%] Mode Undamaged Damaged Damaged vs. undamaged 1st bending 260.13 254.20 2.14 2nd bending 693.10 693.39 0.04 1st torsion 1167.0 1121.1 3.74 3rd bending 1388.2 1348.4 2.72 1st O.P. bending 1754.3 1690.7 3.48 2nd torsion 1777.9 1775.6 0.12 Table 2.10 Natural frequencies and percent differences for the undamaged and damaged bolted structure FE model with 17-mm contact regions Bolted FE model 17-mm contact region Natural frequencies [Hz] Percent differences [%] Mode Undamaged Damaged Damaged vs. undamaged 1st bending 269.85 248.29 7.81 2nd bending 697.27 695.21 0.28 1st torsion 1195.7 1096.4 8.10 3rd bending 1438.6 1314.1 8.52 1st O.P. bending 1812.2 1644.6 9.18 2nd torsion 1790.9 1785.3 0.29
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