## 4 Experiment Results and Discussion
### Vibration Control Experiments Based on Multiple Frequency Excitations  
Multi-frequency excitations were simulated by fan airflow, acting on the surface of flexible plate. Three groups of experiments were carried out. The vibration suppression effects are shown in Figure 13 and summarized in Table 5. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Experiment** & **Amplitude** & \multicolumn{4}{c}{**Major Frequency**} \\ \hline \multirow{4}{*}{**I**} & Without control & \(-\)26.27\({}^{\circ}\)-30.78\({}^{\circ}\) & \multicolumn{2}{c}{0.06 Hz} & 0.13 Hz & 0.19 Hz \\ \cline{3-6}  & \multirow{2}{*}{With control-6 A} & \(-\)7.13\({}^{\circ}\)-5.58\({}^{\circ}\) & Amplitude & 3.77\({}^{\circ}\) & 15.84\({}^{\circ}\) & 5.39\({}^{\circ}\) \\ \cline{3-6}  & & Amplitude & 0.72\({}^{\circ}\) & 4.63\({}^{\circ}\) & 0.31\({}^{\circ}\) \\ \cline{3-6}  & \multirow{2}{*}{With control-6 A} & \(-\)7.13\({}^{\circ}\)-5.58\({}^{\circ}\) & \multicolumn{2}{c}{Control effect} & 80.90\% & 70.77\% & 94.25\% \\  & & & \(-\)14.38 dB & \(-\)10.68 dB & \(-\)24.80 dB \\ \hline \multirow{4}{*}{**II**} & Without control & \(-\)43.95\({}^{\circ}\)-41.44\({}^{\circ}\) & \multicolumn{2}{c}{0.06 Hz} & 0.12 Hz & 0.18 Hz \\ \cline{3-6}  & & Amplitude & 10.89\({}^{\circ}\) & 28.15\({}^{\circ}\) & 6.07\({}^{\circ}\) \\ \cline{3-6}  & & Amplitude & 2.01\({}^{\circ}\) & 6.74\({}^{\circ}\) & 0.32\({}^{\circ}\) \\ \cline{3-6}  & \multirow{2}{*}{With control-6 A} & \(-\)11.46\({}^{\circ}\)-10.26\({}^{\circ}\) & \multicolumn{2}{c}{Control effect} & 81.54\% & 76.06\% & 94.73\% \\  & & & \(-\)14.68 dB & \(-\)12.42 dB & \(-\)25.56 dB \\ \hline \multirow{4}{*}{**III**} & Without control & \(-\)44.20\({}^{\circ}\)-42.41\({}^{\circ}\) & \multicolumn{2}{c}{0.06 Hz} & 0.12 Hz & 0.18 Hz \\ \cline{3-6}  & \multirow{2}{*}{With control-6 A} & \(-\)13.18\({}^{\circ}\)-9.03\({}^{\circ}\) & Amplitude & 11.31\({}^{\circ}\) & 32.42\({}^{\circ}\) & 8.33\({}^{\circ}\) \\ \cline{3-6}  & & Amplitude & 1.51\({}^{\circ}\) & 7.31\({}^{\circ}\) & 0.84\({}^{\circ}\) \\ \cline{3-6}  & & & \(-\)13.18\({}^{\circ}\)-9.03\({}^{\circ}\) & \multicolumn{2}{c}{Control effect} & 86.65\% & 77.45\% & 89.92\% \\ \cline{3-6}  & & & \(-\)17.49 dB & \(-\)12.94 dB & \(-\)19.93 dB \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Vibration control effect based on fans airflow excitation. Figure 13: Vibration control experiments: (**a**) Experiment I, (**b**) Experiment II and (**c**) Experiment III. The interference frequency is within 0.2 Hz. This frequency includes three main frequency signals: 0.06, 0.13 and 0.19 Hz. Specifically, 0.06 Hz is the fan rotation frequency; 0.13 and 0.19 Hz are close to frequency doubling. The interference amplitude is relatively large (within 25-45\({}^{\circ}\)), which is due to the very low interference frequency excitations. The frequency domain results show that the disturbance amplitude around 0.12 Hz is the largest, rather than 0.06 Hz, which is mainly due to the large flexibility of the plate. Especially, the full frequency band vibration suppression effect within 0.2 Hz is obvious, and the vibration suppression effect at 0.12 Hz (dominant frequency) is the best up to 12.94 dB (Experiment III). The previous single-frequency excitation experiment was effective. However, the passive damping between the two permanent magnets may affect the vibration control effect of dual joints. Therefore, to highlight the performance of dual joints, it is of great necessity to investigate the semi-active vibration control effect under passive damping. The experimental process still uses the fan airflow excitation. In Figure 9, the motor output shaft is locked and PM1 remains stationary. The vibration control effect is depicted in Figure 14. The experimental results are summarized and compared in Table 6  
Experimental results show that the interference frequency contains multiple frequency components. The frequency range is below 0.2 Hz; the interference amplitude is 14-30\({}^{\circ}\).