## 4 Structural Analysis of Unit Structure of Deployable Reflector Antenna
The results of the structural-thermal coupled analysis show that the maximum stress of the high-density model is higher than that of the low-density model; the unit structure with the low-density honeycomb core of Case 2.2 is reasonable from the viewpoint of thermal deformation. Dynamic stiffness is one of the most important design requirements for a satellite payload such as the antenna. The satellite is subjected to various dynamic loads like  
Figure 5: Structural–thermal coupled analysis of the unit structure in the deployable reflector antenna; temperature distribution of the main reflector calculated from (**a**) orbital thermal analysis for the worst hot case; (**b**) thermal input of temperature distribution of the unit structure determined by the orbital thermal analysis; stress distribution generated by the thermal gradient of unit structure models for (**c**) high-density and (**d**) low-density honeycomb cores. acoustic and vibration. In order to prevent the resonance between the primary payload and satellite body, the mode frequency of the primary payload should be sufficiently different from the satellite main body. Thus, all the payloads have a design requirement for dynamic stiffness. Because the configuration of the antenna developed in this paper is an axisymmetric shape of 24 main reflectors, dynamic stiffness of the unit structure can represent the entire structure of the antenna. The modal analysis of the unit structure in the DR-A is implemented to evaluate the dynamic stiffness for the high- and low-density honeycomb core of Cases 2.1 and 2.2. As shown in Figure 6a,d, modal analyses are implemented for the stowed and deployed conditions. Figure 6b,c,e,f show that the first and second mode frequencies of the unit structure with the stacking sequence of Case 2.2 are higher than those of Case 2.1 for the stowed and deployed conditions, and the low-density honeycomb core of Case 2.2 is reasonable from the viewpoint of the dynamic stiffness. The analysis results of the structural analyses conducted in this study are summarized in Table 5. It was confirmed that Case 2.2 had a weight reduction of approximately 8.8% compared to Case 2.1. Results of the modal analysis results show that all the mode frequencies for the deployed condition satisfy the design requirement for the dynamic stiffness of above 3 Hz (Figure 7). From a thermal and gravitational environment, the performance of the main reflector with low-density cores in Case 2.2 was relatively high than that of the high-density core. \begin{table}
\begin{tabular}{l c c} \hline \hline
**Unit Structure of Main Reflector** & **2.1; High-Density HC** & **2.2; Low-Density HC** \\ \hline Mass (kg) & 2.725 & 2.487 \\ Mode analysis & 1 st mode (Hz) & 93.42 & 97.94 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Results of structural analysis for unit structure in main reflector with respect to the type of honeycomb core (HC). Figure 6: Modal analysis of the unit structure in the deployable reflector antenna for the stacking sequence of Cases 2.1 and 2.2; (**a**) triple clamped configuration; (**b**) 1 st and (**c**) 2 nd mode frequencies and shapes under the stowed condition; (**d**) single clamped configuration; (**e**) 1 st and (**f**) 2 nd mode frequencies and shapes under the deployed condition. Figure 7: Mode frequencies and shapes of the deployable reflector antenna assembly under stowed and deployed condition with the high- and low-density cores; finite element configuration under (**a**) stowed and (**b**) deployed conditions; mode frequencies and shapes of (**b**) 1 st mode with the stowed condition, 1 st mode with the (**c**) stowed and (**d**) deployed conditions, 2 nd mode with (**e**) the stowed condition and (**f**) the deployed condition.