# Dynamics Modelling and Simulation for Deployment Characteristics of Mesh Reflector Antennas
## 4 Dynamics Simulation of Truss Antenna  
In this section, dynamic simulation of the deployable truss antenna is performed numerically. It is noted that the bending curvatures in Equation (13) are less dominant than the axial strain in cable dynamics. Therefore, the bending deformation of the cable element is neglected in the dynamic simulation. Additionally, in order to obtain the initial configuration with a shrinking process of the truss, a small elastic modulus for the cable is adopted to enhance the simulation efficiency with an integration step as large as possible. The cable net is discretized with 1650 cable elements and Table 1 lists the parameters used in the numerical simulation. Figure 6 presents the deployment configuration associated with different deployed moment, in which an asynchronous deployment along the anticlockwise direction is clearly observed. The diameter of the truss is deployed from an initial 8 to 30 m for the final configuration. It should be noted that due to the complicated property of the initial configuration, the fully deployed configuration of the truss antenna using the ANCF cable element is established firstly. Then, under the action of identical driving velocity of the parallelogram mechanisms, the initial configuration of the antenna is obtained by shrinking the fully deployed configuration to a shrinkable quasi-static configuration [27]. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Value** & **Parameters** & **Value** \\ \hline Length of horizontal rods & 1 m & Truss cell number & 12 \\ Length of vertical rods & 1.2 m & Density of rod & 2700 Kg/m\({}^{3}\) \\ Diameter of rod & 0.025 m & Elastic modulus of rod & 75 Gpa \\ Diameter of cable net & 0.005 m & Cable density & 1430 Kg/m\({}^{3}\) \\ Number of cable elements & 1650 & Cable elastic modulus & 12 Mpa \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters used in simulation. The variation of the relative distance of the diagonal rods is illustrated in Figure 7. It can be seen that the deviation between different cells increases with the deployment of truss. In the initial deployed phase, each cell deploys synchronously with the action of the torque of the torsional spring. The driving force from a motor acts when the torque of the torsional spring is worked out, which leads to an asynchronous deployment caused by the attenuation of driving force. Figure 8 presents the variation of the deployment angle, which implies the phenomenon of asynchronous deployment as well. As a point of attention, the truss cell 12 reaches the final lock place more slowly than other truss cells, which indicates that the driving force acting on the diagonal  
Figure 6: Deployment configuration. (**a**) \(t=0.2\) s, (**b**) \(t=1.2\) s, (**c**) \(t=3.1\) s (**d**) \(t=4.1\) s.  
Figure 7: Relative distance of the diagonal rod. rod of cell 12 is affected by attenuation intensely. The fact that asynchronous deployment is caused by the attenuation of the driving forces can also be found in the literature [27], which indicates the effectiveness of the established dynamic model of the deployable antenna system. Furthermore, for a presentative point, the tensions of both the cable net and the tensile cable are obtained by the average value of element tensions, respectively. Figure 9 exhibits the time history response of the mean tension of the tensile cable; a rapid augment in tension from 1 to 6 N appears around the moment \(t=2\) s, when the antenna is deployed to the final configuration. Additionally, clear oscillation can be observed during the whole deployment. Variation of the mean tension of the cable net is displayed in Figure 10. Different from the amplitude of tension of the tensile cable in Figure 10, the tension of the cable net increases to 25 N and with a more intense oscillation. It is noted that the behavior of the rapid increase in amplitude of the cable tension in the phase of post-deployment is in line with the conclusions in the literature [29]. Figure 8: Deployment angle.