18 T. Roberts and P. J. Cornwell Table 2.3 Average natural frequencies and respective percent differences for the undamaged and damaged bolted structures. The O.P. direction was not tested for the damaged structure Natural frequencies [Hz] Percent differences [%] Mode Bolted (Undamaged) Bolted (Damaged) Damaged vs. Undamaged 1st bending 275.88 273.17 0.97 2nd bending 713.38 713.38 0.001 1st torsion 1225.5 1217.6 0.65 3rd bending 1459.9 1445.4 0.99 1st O.P. bending N/A N/A N/A 2nd torsion 1891.1 1904.6 0.71 Table 2.4 Average damping ratios and standard deviations for each structure Solid damping ratios Bolted damping ratios Welded damping ratios Mode Avg. Std. Dev Avg. Std. Dev Avg. Std. Dev 1st bending 0.00366 0.00093 0.00390 0.00112 0.00299 0.00100 2nd bending 0.00119 0.00053 0.00101 0.00013 0.00135 0.00047 1st torsion 0.00108 0.00017 0.00086 0.00035 0.00113 0.00025 3rd bending 0.00071 0.00019 0.00090 0.00024 0.00103 0.00007 1st O.P. bending 0.00172 0.00011 0.00108 0.00021 0.00109 0.00015 2nd torsion 0.00086 0.00035 0.00085 0.00039 0.00105 0.00024 Table 2.5 Percent differences in the average damping ratios for each of the three structures Damping ratio percent differences [%] Mode Solid vs. Welded Solid vs. Bolted Welded vs. Bolted 1st bending 7.40 18.32 23.94 2nd bending 15.45 13.03 33.68 1st torsion 20.50 5.35 32.52 3rd bending 26.49 44.44 14.19 1st O.P. bending 36.82 36.73 0.13 2nd torsion 1.67 22.10 24.18 A successive set of experimental modal data was taken from the bolted structure to examine the feasibility of using natural frequencies to detect damage in a structure. As with previous tests, the bolts in the structure were tightened to 25 in-lbs, but in this test, one bolt was removed from the structure. Table 2.3 summarizes the natural frequencies of the undamaged and damaged bolted structures from experimental modal testing. It is obvious from Table 2.3 that natural frequencies alone are not effective in distinguishing the undamaged structure from the damaged one. As this is a reasonably small structure with very tight connections, it is unlikely that removing a single bolt will have much effect on the natural frequencies. Removing the mass of a single bolt changes the overall mass of the structure by 1.6%, and the existing pretension in the model is still too significant to effectively loosen the joint. Contrary to the results from comparing different structures via natural frequencies, damping ratios for the three structures did not provide consistent results. Table 2.4 is a compiled list of the average damping ratios for each structure along with respective standard deviations. Table 2.5 contains the percent differences between the average damping ratios of the structures. On average, the standard deviations of the damping ratios for all structures was 26% of the average damping ratio value. In some cases, such as the 2nd Torsion mode for the welded structure, the standard deviation in the damping ratios was over 45% of the damping ratio average value. These statistics suggest that there is too much variability between damping ratios for each individual structure to allow for a meaningful comparison of results between structures. To reinforce this observation, Fig. 2.11 shows the individual damping ratio results from each test of each structure. Consider the results of the 1st Bending mode. There is more variability in the individual damping ratios for the bolted structure than there is between the averages of all three structures. Figure 2.11 shows that the variability between structures is not significant enough to consider damping a proper metric for distinguishing between different structures or damaged/undamaged structures.
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