# Vibration Isolation of a Surveillance System Equipped in a Drone with Mode Decoupling
## 4 Results and Suggestions
### Design Enhancement of Vibration Isolator for a Camera System Deployed in a Drone
System parameters were identified using the coupled three-DOF model shown in Equation (25) to verify whether this configuration could separate the first natural frequency in each direction while taking the natural frequency position as low as possible. The predicted transmissibility in each direction is shown as blue-dotted lines in Figure 9; this corresponds well with the measurements. From the measurement and prediction, the rigid body mode shape could be estimated as shown in Figure 10. The mode shape caused by the double mount on the side close to the drone body in the initial design was modified toward to the double mount on the side close to the gimbal, and the position of the coupled modes in the horizontal directions was separated, as shown in Figure 9. In addition, in moving the mounts toward the camera gimbal as much as possible, the unwanted vibration amplification of more than 10 Hz observed in the isolation frequency range of Figures 3 and 6 was significantly reduced. Specifically, the R of the fore-after, side-by-side, and vertical directions were 0.95, 0.82, 0.97, respectively. Therefore, this model was used to predict responses with the initial velocity, \(V_{\text{X0}}\), of 1 m/s in the fore-after direction. All assumptions excluding the stiffness change in the natural frequency location redesign were the same; the results are shown in Figure 11. Following the design optimization purpose, the first natural frequency of the side-by-side direction was approximately the same, but it had only one peak (Figure 11). Moreover, the first natural frequency of the fore-after and vertical directions shifted to higher frequency regions compared to the side-by-side direction, suggesting that the natural frequency of each direction was decoupled. This is also shown in the responses in the time domain (Figure 11a). The responses attenuated continuously over a period in all directions, and no coupling effect was seen. It was again proven from the prediction results with the coupled model that the peak value in the time domain decreased. Moreover, the settling time also decreased in all directions for the same condition. Additionally, it can be seen that even in the frequency \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \(f_{N}\) (Hz)System Type & \multicolumn{2}{c}{**Fore-After Direction**} & \multicolumn{2}{c}{**Side-by-Side Direction**} & \multicolumn{2}{c}{**Vertical Direction**} \\ \cline{2-10}  & **No** & **Initial** & **Optimal** & **No** & **Initial** & **Optimal** & **No** & **Initial** & **Optimal** \\ \hline
1 st & 2.5 & 2.5 & 2.5 & 2.75 & 2.75 & 2.75 & 1.0 & 1.0 & 1.0 \\
2 nd & 6.25 & 7.5 & 10 & 9.25 & 7.75 & 7.5 & 8.0 & 7.0 & 8.5 \\ (rigid body mode) & & & & & & & & & \\
3 rd & 56.25 & - & - & 30.0 & - & - & 22.5 & - & - \\
4 th & 70.25 & & & 35.75 & & & 25.5 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of natural frequencies of the initial and optimal designs. Figure 9: Comparison of transmissibility before and after the mount design modification in (**a**) fore-after, (**b**) side-by-side, and (**c**) vertical directions. domain, vibration levels in the range with the highest peak or two simultaneously observed peaks decreased via mode separation. Finally, the transmissibility of the drone was measured under the operating condition of the take-off motor without the blades. It was compared with the RMS and ratio between a payload and base in the operational frequencies in the range of 30-85 Hz (Table 4). This comparison was aimed to quantitatively examine the level of vibration reduction with the proposed design suggestion. The comparison exemplified two factors. First, introducing the vibration isolator decreased the transmissibility in all directions. Specifically, the surveillance system showed a significant amplification in the fore-after and side-by-side directions when the vibration isolator was not installed in the drone. Second, introducing a jelly damper with the proposed configuration decreased transmissibility in all directions.