## 4 Shaking Table Experiment
### Forced Sinusoidal Vibration  
We carried out 11 sets of experiments at different frequencies and the excitation magnitude was 10 mm. Moreover, the numerical analyses were correspondingly carried out using Simulink. The swing angle time history curves are shown in Figure 10. \(\lambda\) is defined as before. \(\beta\) is defined by \(\beta=\omega_{a}/\omega_{m}\). \(\omega_{a}\) is the peak frequency obtained by frequency domain analysis. Figure 8: Sketch of experimental system: (**a**) photo of experiment setup; (**b**) control structure interaction loop of the ARID system. Figure 9: Schematic of the experiment system. Figure 10a,c show that the swing angle of the structure with ARID control was smaller. The control effect is obvious. And the numerical analysis results agree well with the experimental results, which can further prove the good control effect of the ARID system. Figure 10b,d show that there were two peaks in the frequency domain without a control case, while in the ARID control case, there was only one peak. The results of the numerical analysis also agree well with the experimental results. The 11 sets of frequency domain analysis results are shown in Figure 11.  
Figure 10: Comparison of experiment and numerical analysis results: **(a)** Experiment swing angle time history of \(\lambda=0.7\); **(b)** Experiment swing angle time history of \(\lambda=1\); **(c)** Numerical analysis swing angle time history of \(\lambda=0.7\); **(d)** Numerical analysis swing angle time history of \(\lambda=1\); **(e)** Amplitude-frequency curve of \(\lambda=0.7\); **(f)** Amplitude-frequency curve of \(\lambda=1\). In Figure 10, it can be found that: (a) The two peaks in the frequency domain are the excitation frequency and the natural structural frequency of the structure without control. When the excitation frequency is smaller than the natural structural frequency, the first peak frequency is closed to the excitation frequency, and the second peak frequency is closed to the natural structural frequency. When the excitation frequency is greater than the natural structural frequency, the first peak frequency is closed to the natural structural frequency, and the second peak frequency is closed to the excitation frequency. (b) In the ARID controlled case, there is only one peak in the frequency domain. The peak frequency is closed to the excitation frequency. This result indicates that the ARID system completely suppresses the structural response at the natural structural frequency. Furthermore, it can be found that the structural spectral energy is significantly reduced at the excitation frequency. It can be inferred that the ARID system consumes the natural structural frequency energy as well as the external excitation energy. Furthermore, it can be found from Figure 10a that the ARID system has good control effect even though the swing angle is very small. It can be verified that the ARID system has better robustness and effectiveness than the TRID system. Figure 12 shows the peak swing angle curves of structures with ARID control and without control. The peak swing angle of structures with ARID control is smaller. There is a good agreement between the experimental results and numerical analysis results. It can be proved that the ARID system can reduce the maximum response of the structure. Moreover, when the external excitation is close to the structural natural frequency, the peak swing angle is larger. In this case, the peak swing angle of structures with ARID control is much smaller. It can be proved that the control system can effectively reduce the structural response under the most unfavorable excitation conditions. Figure 11: Frequency domain analysis diagram of the experiment and numerical analysis. Figure 13 shows that the control effect of the ARID system is close to the peak value when the excitation frequency is close to the structure natural frequency. It is proved that the ARID system has control effects under different excitations.