## 5 Experimental Results and Analysis
### Simple Harmonic Excitation Analysis  
According to the modal analysis results, a 111.3 Hz simple harmonic wave was used as the excitation frequency to apply a vibration signal to the structure to simulate pressure pulsation and structural high-frequency resonance. The peak acceleration (PA) is related to the safety of the structure, and the root mean square acceleration (RMSA) is the index of vibration energy. Therefore, to study the damping effect of the tuned mass damper, the variation of vibration energy was analyzed, and the attenuation rate of peak acceleration and root mean square acceleration were used as the evaluation indices, defined as:  
\[AT_{PA}=\frac{PA_{O}-PA_{D}}{PA_{O}} \tag{9}\]  
\[AT_{RMSA}=\frac{RMSA_{O}-RMSA_{D}}{RMSA_{O}} \tag{10}\]  
Figure 5: Modal parameter identification of structures: (**a**) time–history curve of acceleration and (**b**) frequency response curves of the structure. Figure 6: Parameter identification of controlled modal: (**a**) time–history curve of acceleration and (**b**) frequency response curves of the structure. Here, \(PA_{O}\) and \(RMSA_{O}\) and \(PA_{D}\) and \(RMSA_{D}\) represent the peak and root mean square values of the acceleration response of the original structure and the damping structure, respectively. Figure 7 shows the uncontrolled and controlled responses for the tested structure. The effectiveness of the proposed control strategy is clearly seen; the PA and RMSA at the top and bottom of the structure are significantly reduced compared to the uncontrolled responses. Table 3 summarizes the results of different control strategies under simple harmonic excitation tests. Taking the top layer as an example, the RMSA decay rates of STMD, DTMD, MTMD, and MDTMD are 47.56%, 59.08%, 60.24%, and 77.62%, respectively. A simple harmonic load is characterized by a single excitation frequency, while TMD is particularly sensitive to fixed frequency vibration. Hence, the designed TMD device reduces the structure high-frequency vibration significantly. DTMD and MTMD are the same number of design forms, and there is no substantial difference, so it can be found from the chart that the vibration reduction effect of the two is basically the same. In engineering practice, the layout scheme can be selected according to the actual situation. MDTMD had the best vibration reduction performance among the four conditions. The increase of TMD not only further improves the performance, but also the robustness of the system, which is particularly important for the occurrence of unstable excitation in practical engineering. In the above four cases, TMD equipment was installed at the bottom of the structure. It can be seen from the results that the overall response of the model structure was obviously reduced. Therefore, to further study the influence of different arrangement positions on the high-frequency vibration control of the structure, the TMD devices of the four cases were arranged on the top floor \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Location**} & \multicolumn{2}{c}{**Top**} & \multicolumn{2}{c}{**Bottom**} \\ \cline{2-5}  & **PA** & **RMSA** & **PA** & **RMSA** \\ \hline STMD-B & 47.87 & 47.56 & 49.62 & 48.96 \\ STMD-T & 29.95 & 31.59 & 24.35 & 25.76 \\ DTMD-B & 59.22 & 59.08 & 62.33 & 62.16 \\ DTMD-T & 44.54 & 44.22 & 36.72 & 36.14 \\ MTMD-B & 59.45 & 60.24 & 61.46 & 61.40 \\ MTMD-T & 32.43 & 34.60 & 29.34 & 29.13 \\ MDTMD-B & 77.57 & 77.62 & 79.03 & 78.88 \\ MDTMD-T & 61.21 & 61.13 & 55.68 & 54.74 \\
4 MTMD-T & 62.26 & 62.16 & 63.19 & 56.15 \\ Spatial multi-point TMD & 73.00 & 73.89 & 72.93 & 73.51 \\
4 MTMD-B & 77.13 & 80.73 & 73.65 & 78.02 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Attenuation rates of TMD under various conditions (%). Figure 7: Structural responses of original structure and vibration-damping structure under simple harmonic excitation in various conditions: (**a**) peak acceleration and (**b**) root mean square (RMS) acceleration. of the structure to measure the response under simple harmonic excitation.