# Parallel Load-Bearing and Damping System Design and Test for Satellite Vibration Suppression
## 7 Experiment Results  
After designing the vibration isolation system, frequency response experiments were conducted to verify the effectiveness of the system. By adding dampers, the damping state PAF was manufactured as shown in Figure 14. The bottom of the PAF was connected to a vibration machine as in the original state, to simulate the vibrations transmitted from the rocket. The testing frequency range and amplitude were 5-100 Hz and 1 m/s\({}^{2}\). respectively. There were four measuring points that were used to obtain the acceleration characteristics and the vibration transfer properties. The acceleration measuring points were distributed at the four points where the satellite is connected with the PAF. Two measuring points are marked in Figure 14, while the other two were at the back of the equipment and are invisible in the figure. The results were averaged over the four measuring points.  
Figure 12: Final supports structure: (**a**) upper support; (**b**) lower support.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{2}{c}{**Object**} & \multicolumn{5}{c}{**Weight**} \\ \hline \multicolumn{2}{c}{**Constraint**} & \multicolumn{5}{c}{**Stress \textless{} 160 MPa**} \\ \hline \multirow{2}{*}{**Variables**} & **Lower Bound** & **Upper Bound** & **Original** & **Result** & **Rounded Value** \\ \hline \multirow{2}{*}{Upper support} & Base thickness/mm & \(1\) & \(20\) & \(10\) & \(15.36\) & \(15\) \\ \cline{2-6}  & Lugs thickness/mm & \(1\) & \(20\) & \(10\) & \(7\) & \(8\) \\ \hline \multirow{2}{*}{Lower support} & Base thickness/mm & \(1\) & \(20\) & \(10\) & \(15.42\) & \(15.5\) \\ \hline \hline \end{tabular}
\end{table}
Table 5: Sizing optimization model and results.  
Figure 13: Three-dimensional model: (**a**) one set of dampers; (**b**) PAF with the damping system.  
The frequency response analysis results of the damping state and the original state are shown in Figure 15. The results show that (1) the axial transmissibility of the damping state has obvious attenuation at the first two peaks compared with the original state; (2) the lateral transmissibility has obvious attenuation at the first peak; (3) at other frequency ranges, the transmissibility of the damping state is almost the same as the original.  
To make a better comparison between the damping state and the original state, Table 6 is shown below. The frequency deviation and attenuation percent are reductions of the damping state over the original state. All values in the table are rounded. From the table, it can be seen that the transmissibility of the axial acceleration peak decreased by 35.9%, and the transmissibility of the lateral (y) and lateral (z) acceleration peaks decreased by 34.6% and 12.5%, respectively. The fundamental frequency deviation was less than 5%. This indicates that the transverse and longitudinal stiffnesses were basically unchanged, ensuring the stability of the attitude control system and the safety of the dynamic clearance of the fairing.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Original State**} & \multicolumn{2}{c}{**Damping State**} & \multicolumn{2}{c}{**Frequency**} & \multicolumn{1}{c}{**Attenuation**} \\  & **Frequency/Hz** & **Acceleration** & **Frequency/Hz** & **Acceleration** & **Deviation** & **Percent** \\ \hline Axial (X) & 28.33 & 14.05 & 27.28 & 9.00 & 3.7\% & 35.9\% \\ Lateral (Y) & 7.5 & 3.1 & 7.2 & 2.0 & 3.5\% & 34.6\% \\ Lateral (Z) & 7.5 & 2.4 & 7.2 & 2.1 & 4.4\% & 12.5\% \\ \hline \hline \end{tabular}
\end{table}
Table 6: Comparison of peak frequency and acceleration transmissibility between the original state and damping state.  
Figure 14: Damping state PAF and the damper.  
Figure 15: Frequency response analysis results: (**a**) axial-X; (**b**) lateral-Y.