Dynamic Properties of Stay Cables on The Penobscot Narrows Bridge

CHAPTER 6. SUMMARY OF COMPARISONS

FREQUENCY

The frequencies obtained from phase 1 and phase 2 testing for the cables in fans A and C were nearly equivalent, confirming that damper installation did not affect frequency. Phase 2 testing also showed that frequencies compared well between similar cables from the symmetrically matching fans. The graphs comparing the first two modes between the two phases are shown in figure 51 and figure 52. The remaining graphs for modes 3 through 7 can be found in appendix B. On average, the frequencies match within 3 percent, although the frequencies on some of the shorter cables in the higher modes differed as much as 8 percent.

Figure 51. Graph. First mode frequencies.

Figure 52. Graph. Second mode frequencies.

First mode theoretical frequencies were calculated for each cable using the string theory equation whose solution is shown in figure 4. These frequencies were then plotted against the field data and the results are shown in figure 53 and figure 54, from phase 1 and phase 2 testing, respectively. Results compared favorably between field and theory, however the longest cables found in fans B and C varied by a small percentage. Complete tables of the numerical values of the first mode theoretical frequencies are presented in appendix A.

Figure 53. Graph. First mode theoretical frequencies versus phase 1 field data.

Figure 54. Graph. First mode theoretical frequencies versus phase 2 field data.

DAMPING

Differences in damping between phase 1 and phase 2 data were readily apparent. Cable vibrations comparatively lasted only a fraction of the time after damper installation, which was clearly evident in the damping curves. Figure 55 shows a comparison of the decay curves before and after damper installation.

Figure 55. Graph. Comparison of the decay curves between phase 1 and phase 2 for
cable 19A.

The installation of dampers on the cable-stays had a tremendous impact on the damping ratio values, causing the damping ratios to increase by at least a factor of 5, and sometimes as high as 15. In general, first mode damping ratios for phase 1 testing were between 0.10 and 0.39 percent, where in phase 2 they ranged from 1.22 to 2.21 percent. Second mode damping ratios increased from 0.17 to 0.46 percent in phase 1 to 1.41 to 2.48 percent in phase 2. Figure 56 and figure 57 show the comparison of the damping ratios obtained from the cables tested in fan A between the two phases.

Figure 56. Graph. Comparison of first mode damping ratios.

Figure 57. Graph. Comparison of second mode damping ratios.

SCRUTON NUMBER

Before the installation of dampers, Scruton numbers for the cable stays were much lower than the recommended minimum value of 10 for controlling rain/wind-induced vibrations, even falling below the reduced value of 5 allowed for cables with an aerodynamic surface treatment. Phase 1 testing produced Scruton numbers ranging between 0.6 and 2.0. In phase 2 testing, the Scruton numbers climbed to acceptable levels, ranging between 7 and 12. A comparison of the values for the two phases of testing in fan A is shown in figure 58.

Figure 58. Graph. Comparison of Scruton numbers.