# Field Measurement Study on Dynamic Characteristics of the Shanghai World Financial Center
## 3 Dynamic Response of the SWFC
### Natural Frequency Amplitude Dependency  
Natural frequency is one of the important parameters used to describe the dynamic characteristics of high-rise buildings, and it is very important to accurately determine the size of the natural frequency in the structural design to evaluate the safety of the structure [36]. To improve the data utilization, the correlation curves of the first two orders of the natural frequency with amplitude in the X and Y directions of the SWFC under four earthquakes were determined. This was achieved by using the E-RDT method based on time-range data of the 101F acceleration response obtained in Figure 4, and by setting 20 intercepts from 0.1 times the standard deviation to 2.5 times the standard deviation (see Figure 8).  
Figure 8 shows that the first two orders of natural frequencies of the building decrease with an increase in structural amplitude under each of the four earthquakes, among which the decreasing trend of natural frequencies is most apparent under the earthquake of E3. This is in agreement with [PERSON] et al. [37] and [PERSON] et al. [9]. This phenomenon can be explained by the stick-slip model proposed by [PERSON] and [PERSON] [38]. When the amplitude of the structural response is at a low level, the contact surfaces between the structural members do not move, but when the amplitude of the structural response increases to a specific value, a nonlinear response is generated and the contact surface steel nodes begin to slip, thus resulting in weakened structural stiffness. With an increase in structural amplitude, the number of sliding contact surfaces increases, leading to a decrease in the natural frequency of the structure.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Earthquake**} & \multirow{2}{*}{**Direction**} & \multirow{2}{*}{**Mode**} & \multicolumn{3}{c}{**Frequency (Hz)**} \\ \cline{4-6}  & & & **PP** & **E-RDT** & **Difference (\%)** \\ \hline \multirow{4}{*}{E1} & \multirow{2}{*}{X\(-\)direction} & Mode 1 & 0.1494 & 0.1540 & 3.0 \\  & & Mode 2 & 0.5497 & 0.4879 & 11.2 \\  & \multirow{2}{*}{Y\(-\)direction} & Mode 1 & 0.1531 & 0.1532 & 0.0  
Figure 8: SWFC natural frequency under earthquake.  
To compare the related characteristics of structural natural frequency amplitudes under different earthquakes, the acceleration amplitudes under four earthquakes were normalized by modal shapes, and the normalized amplitude-related natural frequencies are shown in Figure 9. It can be observed that the differences in the magnitudes of the structural natural frequencies during different earthquakes are minor. Except for the earthquake of E3, the normalized curves of the natural frequencies of each order in other directions have a gentle trend, and the maximum decrease rate is smaller than 0.9%, indicating that the structure remains safe and stable under earthquake impact. There is a notable decrease of 1.14% in the first-order natural frequency in the Y-direction under the influence of the earthquake of E3, which may be because of the large amplitude of E3 with an intensity class of 7.2, resulting in a greater fluctuation in natural frequency.