## 5 Structural Analysis of the Full Model of Deployable Reflector Antenna
Transient analysis is conducted to evaluate the displacement at the end of the tip shown in Figure 9b. The acceleration input function is shown in Figure 9c determined by the Bang-Bang profile [20]. The satellite moves in the (+) direction for 0.5 s, the (\(-\)) direction for 1.5 s, and then stops for 0.5 s after moving in the (\(-\)) direction. As shown in Figure 9e, vibration reduction in the deployed antenna assembly with the stacking sequence of Case 2.2 is faster than that of the stacking sequence of Case 2.1. The displacement for dynamic behavior is calculated using Equation (2), andthe damping ratio for dynamic behavior is inversely proportional to mass and stiffness, as shown in Equation (3). Case 2.2 has a higher damping ratio compared to Case 2.1, as the mass reduction ratio is higher than the stiffness increase ratio, resulting in a decrease in the RMS value for dynamic behavior. The RMS value for the z-direction displacement at the moment of satellite attitude stabilization is \(1.90\times 10^{-4}\) m for the Case 2.1 model with a high-density core and \(1.34\times 10^{-4}\) m for the Case 2.2 model with a low-density core, indicating that the model with a low-density core has an about 25% better damping performance in terms of RMS displacement criteria. By applying a petal with high damping performance, the time required to stabilize the vibration occurring after high dynamics can be shortened, and additional image acquisition time and shooting frequency can be secured, thus improving the performance of the satellite. \[\ddot{u}+2\zeta\omega_{0}\dot{u}+\omega_{0}^{2}u=0, \tag{2}\]  
\[\zeta=\frac{c}{\sqrt{mk}}, \tag{3}\]  
where \(\omega_{0}\), \(\zeta\), \(c\), \(m\), and \(k\) mean the fundamental natural frequency, damping ratio, mass, and stiffness, respectively. Also, \(\ddot{u}\), \(\dot{u}\), and \(u\) mean the acceleration, velocity, and displacement of this system. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline  & & & **Maximum Stress (Unit: MPa)** & & & **MOS** & \\ \hline \multirow{4}{*}{Case} & \multirow{2}{*}{Laminate} & \(\sigma_{1,tensile}\) & 56.7 & \(\sigma_{1,comp}\) & \(-39.92\) & \(\sigma_{1,tensile}\) & 2.47 & \(\sigma_{1,comp}\) & 0.52 \\  & & stress & \(\sigma_{2,tensile}\) & 37.85 & \(\sigma_{2,comp}\) & \(-33.29\) & \(\sigma_{2,tensile}\) & 4.19 & \(\sigma_{2,comp}\) & 0.82 \\  & & \(\sigma_{shear}\) & 1.54 & & & \(\sigma_{shear}\) & 6.31 & & \\ \cline{1-1}  & & Longitudinal direction & & & & & & \\
2.1 & Core & (L-dir.) & & 0.13 & & L-dir. & & 76.5 \\  & & stress & Width direction & & & & & \\  & & (W-dir.) & & 0.08 & & W-dir. & & 4.71 \\  & & Thickness-dir. & & 0.01 & & Thickness-dir. & & 0.013 \\ \hline \end{tabular}
\end{table} 
Table 6: Quasi-static analysis and margin of safety (MOS) for the antenna model with high- (Case 2.1) and low-density honeycomb cores. Figure 8: (**a–c**) Result of quasi-static analysis for the antenna model in the deployed condition with a low-density core (Case 2.2). The structural analysis results of the antenna assembly are summarized in Table 6. Regardless of the honeycomb core type, all the cases satisfy the weight requirement (110 kg or less). However, in the case of the antenna assembly consisting of low-density core material (Case 2.2), the total weight of the antenna assembly decreased by approximately 5.7% compared to the high-density core material (Case 2.1). Although the low-density core used in this study has mechanical properties approximately 50% lower than the high-density core, the application of a low-density honeycomb core has better stiffness-to-mass performance than the high-density honeycomb core. Furthermore, as the weight of the structure decreased, the load applied to the structure by gravity decreased, and the dynamic characteristics improved, resulting in improved structural performance for static loads, thermal loads, and dynamic loads.