# Structural Optimization Design of Spaceborne Microwave Probe Antenna
## 4 Size Optimization of the Planar Antenna Reinforcement Structure
### Comparison Between the Size-Optimized and Original Structures  
The modal analysis of the optimized structure and the original structure is performed separately, and the first five orders of modal frequency values and vibration shapes are  
Figure 11: Display of the Moment of Inertia Value with Iteration Times.  
Figure 12: Final form of reinforcement.  
extracted and compared. The results of the comparison of the frequency values of each order are shown in Table 3.  
As shown in Figure 13 below, the left column shows the first- to fifth-order vibration patterns of the original structure, and the right column shows the first- through to fifth-order vibration patterns of the new structure. The red area represents the vibrating region of the structure, while the blue area represents the non-vibrating region of the structure.  
Figure 13: (**a**) The first five orders of vibration of the original structure; (**b**) The first five orders of vibration of the new structure.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Modal Order**} & \multicolumn{2}{c}{**Original Structure**} & **Optimized Structure** & **Improvement** \\  & **Frequency Value (Hz)** & **Frequency Value (Hz)** & **Ratio** \\ \hline
1 & 243.2 & 266.1 & 9.42\% \\
2 & 258.2 & 277.0 & 7.28\% \\
3 & 318.6 & 362.1 & 13.65\% \\
4 & 533.3 & 396.7 & \(-\)25.61\% \\
5 & 236.3 & 107.1 & \(-\)24.09\% \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison of modal frequency values between the original structure and the optimized structure of planar antenna reinforcements.  
Comparing the first- to fifth-order vibration patterns of the original structure and the new structure, it can be concluded that the first three orders are mainly the vibration of the front side of the rotating shaft, and the dynamic stiffness of the new structure in the front side of the rotating shaft is better than that of the original structure, so the frequency of the new structure is higher than that of the original structure in the first three orders. From the fourth order onwards, the higher-order vibration patterns are all at the edges. The ribs of the original structure are mainly distributed at the edges with a wider range, and the ribs of the new structure are all concentrated at the rotation axis.  
The dynamic stiffness of the new structure after topology optimization is higher than that of the original structure, with less rotational inertia and less mass of reinforcement. The key here is that optimizing the placement of reinforcement close to the rotational axis, rather than spreading it out along the edges, reduces unnecessary mass while maintaining or improving performance. This design change enhances the overall structural efficiency, which is critical for reducing torque disturbances and improving the satellite's dynamic behavior. The reinforcement of the new structure is distributed near the center of the rotating axis, and the reinforcement form of the original structure that surrounds the antenna along the plane is not the optimal layout.