## 2 Sandwich-Type ATVA with ER Materials Embedded
### Experimental Validations  
Figure 9a presents the schematic diagram of the experimental setup for measuring the dynamic properties of the plate structure with the ERF embedded ATVA. The plate was clamped with the aluminum alloy fixture located on a cast iron platform and the impulse technique was employed in the measurement. The input excitation was provided by an impact hammer (PCB 084A17) and the induced vibration was measured by a non-contacting eddy-current displacement probe (Keyence AH-416). Both input and output signals were processed by a dynamic spectrum analyzer (Novian-N94) and the corresponding frequency response was obtained. To validate the simulation results, there are 36 points (as shown in Figure 9b) located at the structure for the experiments to obtain its dynamic properties. The eddy-current displacement probe is located at the 26 th point and the impact hammer hits the other 35 points to obtain the frequency responses. According to the experimental results, the mode shapes of the first three modes are obtained as shown in Figure 10. Comparing the mode shapes of simulation results (Figure 7) with the experimental outcome (Figure 10), we found that the experimental data were consistent with simulation results. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**W (mm)** & **1 st Mode Variation (Hz)** & **2 nd Mode Variation (Hz)** & **3 rd Mode Variation (Hz)** \\ \hline
20 & 1.362 & 1.811 & 10.069 \\
22 & 1.331 & 1.724 & 10.756 \\
24 & 1.406 & 1.939 & 14.912 \\
26 & 1.378 & 1.862 & 16.391 \\
28 & 1.392 & 1.825 & 17.613 \\
30 & 1.374 & 1.86 & 18.352 \\
32 & 1.357 & 1.963 & 18.790 \\
34 & 1.399 & 1.941 & 18.980 \\
36 & 1.361 & 2.001 & 19.157 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Frequency shifts at the vibration models of this structure equipped with the ERF embedded ATVA (with the width from 20 to 36 mm) for the electric field changed from 0 to 2 kV/mm. Figure 8: Simulated frequency responses of the plate structure with the ERF embedded ATVA (\(\
u=36\)) as different electric fields are applied. Moreover, the experimental data (in Figure 10) can help us to determine the suitable points for the following case studies, because the displacement probe and the stimulating input should not be located at vibration nodes to improve the precision of the frequency response. Figure 11 presents the experimental setup to measure the dynamic properties of the structure with different external electrical fields. For measuring the vibration mode of the structure, an electromagnetic shaker is used to stimulate the structure as shown in Figure 11. During measurement, a random excitation signal was generated by the dynamic signal analyzer and further amplified by the power amplifier to drive the shaker. One eddy-current displacement probe was used to measure the input and the other one was used to measure the output displacement with the largest amplitude at each vibration mode. Tables 4-6 show the experimental results for the first three modes of this structure as different external electric fields (0 kV/mm-2 kV/mm) were applied. Based on the experimental data in Table 4, the damping ratios of the ATVA can be obtained. According to the experimental results in Table 4, the first mode's frequency is changed from 11.625 to 13.375 Hz when the external electric field varies from 0 to 2 kV/mm; the variation of the frequency is 15.05% and the variation of the amplitude is almost 37.01% (from 16.1 dB to 10.14 dB). In Table 5, the second mode's frequency is changed from 18.375 to 18.5 Hz when the external electric field varies from 0 to 2 kV/mm; the variation of the frequency is only 0.68%. Because the amplitude at E = 0 kV/mm is 17.87 dB and the amplitude at E = 1 kV/mm is 12.42 dB, the maximal variation of the amplitude is almost 30.49% for the second mode. In Table 6, the third-mode frequency is changed from 77 to 78.625 Hz when the external electric field varies from 0 to 2 (kV/mm); the variation of the frequency is only 2.1%.