# Field Measurement Study on Dynamic Characteristics of the Shanghai World Financial Center
## 3 Dynamic Response of the SWFC
### Damping Ratio Amplitude Dependency  
Estimation of the structural damping ratio is essential for the selection of dynamic parameters and the detection of structural damage in the design stage. Similar to identifying natural frequency, the same E-RDT method was employed to attain the correlation and normalization curves of the first two orders of damping ratio with amplitude variation of the top structure of the SWFC under four earthquakes (Figures 10 and 11, respectively). It can be seen that the damping ratios of the first two orders in the X and Y directions of the SWFC under the four earthquakes increase to varying degrees with the increase of the structural amplitude. However, with a further increase of the amplitude, the increase rate of the damping ratio gradually slows down, and the damping ratio is discrete at low amplitudes. This stems from the increased amplitude of the structure, which causes more cracks in the structure, thereby increasing its energy dissipation due to a larger dampening ratio. When comparing the four earthquakes, it is worth mentioning that the damping ratio magnitudes in the X and Y directions are substantially different, and the normalized curves fluctuate considerably. In particular, the first-order damping ratio in  
Figure 9: Normalized natural frequency.  
the X-direction is 0.77% (E3) and the second-order damping ratio is 0.68% (E1). In the Y-direction, the first-order damping ratio is 0.86% (E1), and the second-order damping ratio is 0.65% (E2). This indicates a difference in the energy dissipation of super-tall buildings in response to earthquakes.  
Figure 10: SWFC damping ratio under earthquake.  
Table 4 shows the comparison between the HPBW method and E-RDT method to identify the damping ratio. As shown, the recognition results of the two methods are close, but there are some differences between the individual results, with X-1 st (E4) having a maximum error value of 9.7% and Y-2 nd (E2) having a minimum error value of only 0.9%. This discrepancy may be caused by noise, which causes the HPBW method to pick up the feature frequency, and thus, can blur the recognition of frequency differences, resulting in some recognition errors.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Earthquake**} & \multirow{2}{*}{**Direction**} & \multirow{2}{*}{**Mode**} & \multicolumn{3}{c}{**Ratio (\%)**} \\ \cline{4-6}  & & & **HPBW** & **E-RDT** & **Difference (\%)** \\ \hline \multirow{4}{*}{E1} & X-direction & Mode 1 & 0.6514 & 0.6041 & 7.30 \\  & & Mode 2 & 0.6091 & 0.6366 & 4.51 \\  & Y-direction & Mode 1 & 0.6942 & 0.7041 & 1.42 \\  & & Mode 2 & 0.5679 & 0.5512 & 2.94 \\  & & Mode 1 & 0.6995 & 0.7075 & 1.14 \\  & X-direction & Mode 2 & 0.6103 & 0.5630 & 7.75 \\  & & Mode 1 & 0.7165 & 0.6522 & 8.97 \\  & Y-direction & Mode 2 & 0.6384 & 0.6442 & 0.90 \\  & & Mode 1 & 0.6293 & 0.6762 & 6.93 \\  & & Mode 2 & 0.5775 & 0.5473 & 5.23 \\  & & Mode 1 & 0.6867 & 0.6674 & 2.81 \\  & & Mode 2 & 0.5474 & 0.5684 & 3.84 \\  & & Mode 1 & 0.6339 & 0.6029 & 4.89 \\  & & Mode 2 & 0.5217 & 0.5778 & 9.70 \\  & & Mode 1 & 0.6565 & 0.6200 & 5.56 \\  & & Mode 2 & 0.5370 & 0.5018 & 6.55 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Damping ratio of sway modes.  
Figure 11: Normalized damping ratio.