## 6 Conclusions  
In this paper, the Petal-type Deployable Solid-surface Reflector was researched from a perspective of its structural dynamic properties. The Cable Replacement Method was utilized to equivalently simulate the nonlinear structural stiffness of the revolute joint for numerical analyses. The FEMs of this reflector structure were established on the basis of ANSYS and verified by the theoretical analysis and dynamic test of actual prototype model. The natural frequencies and mode shapes of deployed reflector were computed to study the influence of drag spring design parameters as stiffness, pre-tensioned force, and distance of two adjacent linkage butts. The results were concluded as following. (1) The existence of drag springs radically changes the structural style for this reflector to largely improve the natural frequencies. It brings about the multi-petal vibration mode to narrow down the frequency domain. (2) The function of drag spring stiffness is mainly to develop the structure integrity and narrow down the frequency domain. The function of pre-tensioned force is to totally improve the structure stiffness by extra stress stiffness. (3) The distance between two adjacent linkage butts also decides the rigidity of drag springs, and the linkage butts should be set on the boundary of the petal for model design. (4) By means of setting up drag springs with these parameters, the dynamic properties of reflector structure can be improved to enhance the structural stiffness for natural frequencies and narrow down the frequency domain, which is effectively helpful in vibration isolation measures for reflector accuracy development. The drag springs between two adjacent petals can essentially improve the dynamic performance of reflector structure in deployed state. This conclusion can be a useful technical system for future engineering applications of the PDSR antenna. In summary, the CRM has been verified to effectively simulate the dynamic property of the structure with revolute joints. The simulation of the revolute joint locked by the torsion spring and rotation limiter can be modeled by the cable element to reflect the sudden change of the stiffness on clockwise and counterclockwise rotation. Thus, it is accurate to reflect the rotation DOF and define its stiffness for the revolute joint. Another advantage is that this method can be widely applied in the numerical simulations of deployable structures based on its efficiency. However, this method should be further explored by theoretical method to develop the accuracy for the stiffness definition of the real \begin{table}
\begin{tabular}{c c c c} \hline
**Frequency** & **Model 1** & **Model 15** & **Model 16** \\
**Order** & **L = 40 mm** & **L = 80 mm** & **L = 150 mm** \\ \hline
1 & 0.7847 & 0.7521 & 0.6500 \\
2 & 0.8301 & 0.7803 & 0.6639 \\
3 & 0.8533 & 0.7943 & 0.6779 \\
4 & 0.8819 & 0.8085 & 0.6785 \\
5 & 0.9268 & 0.8354 & 0.6929 \\
6 & 0.9858 & 0.8819 & 0.7287 \\
7 & 1.0077 & 0.8980 & 0.7588 \\
8 & 1.0359 & 0.9093 & 0.7827 \\
9 & 1.0896 & 0.9507 & 0.7845 \\
10 & 1.1364 & 1.0373 & 0.8706 \\ \hline \end{tabular}
\end{table} 
Table 8: Natural frequencies (Hz) of Mode 1, 15, and 16.  
revolute joint. Future works will focus on theoretical research of structure dynamics with revolute joints and deeply experimental studies on this reflector model and the CRM. Conceptualization, H.H. ; methodology, H.H. ; investigation, Q.C. and L.Z. ; model analysis, Q.C. ; test, L.Z. and Q.C. ; validation, H.H. ; writing--original draft preparation, Q.C. and H.H. ; writing--review and editing, H.H. All authors have read and agreed to the published version of the manuscript. This research is supported by the National Natural Science Foundation of China (Grant No. 11902253) and the Fundamental Research Funds for the Central Universities of China. The authors are grateful for this support. The authors declare that there is no conflict of interest.