# 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  
The direction of the design optimization can be considered to change the location of the vibration isolators or replace the vibration isolator with various stiffnesses. This study attempts to replace vibration isolators to minimize design change and improve isolation performances. The vibration mode of each direction should be different from decoupling the first natural frequencies in the horizontal directions. However, both modes were translational in the initial design owing to the symmetric configuration of vibration isolators and the lowest stiffness of the DJI damper. Moreover, the stiffness of the vibration isolators on the gimbal side (a red box in Figure 8) should be lower than that of the drone side (a yellow box in Figure 8) to solve this problem. Therefore, the black DJI vibration isolator was removed from the drone body, and two jelly dampers were connected in a \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Item** & **Value** & **Item** & **Value** & **Item** & **Value** & **Item** & **Value** \\ \hline
**m** & **3.4 kg** & & & & & \\ \hline \(k_{x}\) & \(7.55\times 10^{3}\) N/m & \(c_{x}\) & 15.94 Ns/m & \(k_{xy}\) & \(0.78\times 10^{3}\) N/m & \(c_{xy}\) & 1.08 Ns/m \\ \(k_{y}\) & \(8.06\times 10^{3}\) N/m & \(c_{y}\) & 5.71 Ns/m & \(k_{yz}\) & \(0.75\times 10^{3}\) N/m & \(c_{yz}\) & 2.15 Ns/m \\ \(k_{z}\) & \(6.96\times 10^{3}\) N/m & \(c_{z}\) & 37.25 Ns/m & \(k_{xz}\) & \(0.73\times 10^{3}\) N/m & \(c_{xz}\) & 2.66 Ns/m \\ \hline \end{tabular}
\end{table} 
Table 2: Estimated parameters for a three-degree-of-freedom (DOF) coupled model. Figure 7: Simulation results of the coupled three-DOF mathematical model in (**a**) the time domain and (**b**) in the frequency domain. series for the surveillance system (yellow and red boxes in Figure 8). This configuration had the main stiffness element on the surveillance side, owing to the softest equivalent stiffness of two jelly dampers in a serial connection. Moreover, a mode of the first natural frequency of the fore-after direction was changed from a translational to a rotational (a purple arrow in Figure 8) because the surveillance system was hung at one point in this direction based on the proposed configuration. On the contrary, a vibration mode of the side-by-side direction was still translational (an azure arrow in Figure 8) because the surveillance system was hung at two points in this direction, implying that a different mode of each direction results in different natural frequencies of each direction. Furthermore, removing the black DJI vibration isolator increased the equivalent stiffness in the vertical direction, resulting in an increase in the natural frequency in the respective direction. In summary, the natural frequency in the side-by-side direction changed minimally owing to the same mode shape compared to an initial design. On the contrary, the first natural frequencies of the fore-after direction significantly changed because the first mode changed from a translation to a rotational mode. The first natural frequency in the vertical direction may also shift to a higher frequency than the initial design owing to an increase in the equivalent stiffness. This configuration aims to maintain constant stiffness in the side-by-side direction. However, stiffness of the fore-after and vertical directions increases, which decouples the natural frequency of all directions. The transmissibility was measured to validate the proposed suggestion (Figure 9). The position of natural frequency (\(f_{N}\)) was derived from the suggested design and not from the initial design (Table 3). The natural frequencies of the optimal design were 10, 7.5, and 8.5 Hz for each direction; this means that it was separated by more than 1 Hz for each direction and, therefore, coupling effects were reduced compared to the initial design. Figure 8: Optimal design of vibration isolators.