16 Ambient Vibration Testing of a Super Tall Building in Shanghai 159 Fig. 16.5 Detailed TROMINO location near the brace 16.4 Natural Frequencies and Mode Shapes Operational modal analysis was performed using the software ARTeMIS Modal V3.6 [8]. The software is capable to perform high quality modal analysis through various analysis techniques, including the Frequency Domain Decomposition (FDD) technique and several Stochastic Subspace Identification (SSI) approaches. For this project, a simplified spatial representation of the Shanghai Tower shear wall system was established and two methods of modal identification were adopted for analysis: the Frequency Domain Decomposition (FDD) technique and the Enhanced Frequency Domain Decomposition (EFDD) technique. By incorporating the tested and processed data in the ARTeMIS from the 38 accelerometers, both the lateral and torsional modes were estimated FDD. This method provides an efficient and quick manner for user to obtain the dynamic properties of the structure by peak-picking rules. The power spectral densities (PSD) of the above measurements were averaged to give the Averaged Normalized Power Spectral Density. This technique is based on decomposing the PSD function matrix using Singular Value Decomposition (SVD) where the spectral matrix is decomposed into a set of Single Degree of Freedom (SDOF) system with one corresponding individual mode. As an extension of FDD, EFDD allows users to identify the damping properties of the corresponding modes, which are of significant important to the performance of super tall building. More information could be found in Brincker, et al. [9]. Figure 16.6 presents the picked peak values of the natural frequencies estimations. It should be noted that not all of the peaks in Fig. 16.6 necessarily corresponded to a natural frequency. The mode shapes were generally well consistent in the North–South (N–S) and East–West (E–W) lateral directions. The first three lateral frequencies in each direction were quite close since the Shanghai Tower is a relatively uniform structure. No significant irregular layouts were constructed for structural component except the architectural outer facade with rotational shape. In total, ten modes have been recognized in the frequency range of 0.1–1 Hz (PeriodD1–10 s), including six lateral mode shapes and four torsional mode shapes. The testing results were highly compatible with the finite element (FE) simulation results in other technical publications [2, 10]. As expected, the very fundamental period of the Shanghai Tower is as long as 9.43 s with the corresponding damping ratio of 1.734 %, as seen in Table 16.2. There are also some higher modes have been identified in this study. However, due to the complex geometry and long period characteristics, only the first ten modes were presented and discussed in this paper. In the following section, each mode is shown in a 3-D surface view of the entire structure. For better comparison and understanding, the mode shapes are shown in the order of frequency listed below. 16.5 Discussions In total, ten modes have been well determined in Fig. 16.7. It should be noticed that some localized coupled torsional modes could also be observed in 2nd and 5th mode shapes. The resolution of higher modes are not as good as lower modes due to the imperfect GPS synchronization where the internal clock of the instruments shifted unexpectedly during the test. As stated previously in the spectral density plot, the first three translational mode shapes in both North–South (1st, 4th and 7th mode shapes) and East–West (2nd, 5th and 8th mode shapes) directions are highly identical due to the uniform structural layout of the Shanghai Tower.
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