## 3 Design Validation Test  
To verify the effectiveness of the proposed WSVI design under a launch vibration environment, i.e., performance of launch load reduction and structure safety of the WSVI, sine and random vibration tests were performed at the qualification level. Low Level  
Figure 3: Static Load Test Results ((**a**) Lateral Direction, (**b**) Axial Direction). \begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**Case**} & \multicolumn{2}{c}{**Equivalent Damping Ratio (\(\zeta_{eq}\))**} & \multicolumn{2}{c}{**Equivalent Stiffness (\(k_{eq}\), N/mm)**} \\ \cline{2-5}  & **Axial** & **Lateral** & **Axial** & **Lateral** \\  & **(z-Axis)** & **(x- and \(y\)-Axes)** & **(z-Axis)** & **(x- and \(y\)-Axes)** \\ \hline
1 & 0.095 & 0.044 & 219.5 & 175.8 \\ \hline
2 & 0.087 & 0.032 & 386.6 & 325.4 \\ \hline \end{tabular}
\end{table} 
Table 3: Static Load Test Results of the Proposed WSVI. Sine Sweep (LLSS) tests were performed before and after the vibration test to confirm the characteristic variations of the WSVI. Figure 4 shows an example of the launch vibration test setup for the WSVI condition on the \(z\)-axis. In the test setup, to achieve a 28 Hz cut-off frequency for a 40 kg class satellite, four WSVIs with the Case (1) design were integrated with a mass simulating dummy satellite. The dummy satellite was configured as a flat plate-type to implement the design concept of a small synthetic aperture radar (SAR) technology experimental project (S-STEP) satellite [21]. The S-STEP satellite is an 80 kg class small SAR-satellite that provides a high resolution 1 m stripmap image. It was designed with a flat plate-type structure for mechanical design simplicity and high dimensional stability in orbit. In the test, the rigid mounted condition was also exposed to the vibration test for comparison with the WSVI. The vibration input from the vibration shaker was obtained from the reference accelerometer. The vibration responses for each axis of the WSVI were obtained from a three-axis accelerometer placed on the dummy satellite, as shown in Figure 4. The qualification levels of the sine and random vibration test specifications applied to the design verification of the WSVI are listed in Tables 4 and 5, and the axes of the test are shown in Figure 4.  
A modal analysis was performed to investigate the dynamic behavior of the dummy satellite combined with the WSVI. Figure 5 shows the results of the modal analysis. The first and second modes at 28 and 30 Hz, respectively, mainly represent the bending mode of the blade modules for the lateral direction in the \(x\)- and \(y\)-axes. The third mode at 34 Hz indicates the bending mode of the blade modules of the WSVI in the axial direction along the \(z\)-axis. The fourth mode at 40 Hz indicates the local bending mode of the center of the dummy satellite. These results were used to investigate the launch-vibration test results. Figure 6 shows the sine vibration test results for the WSVI during the \(x\)-, \(y\)-, and \(z\)-axis excitation. In the case of the \(x\)-axis vibration response, the highest acceleration of the dummy satellite with the WSVI was 4.7 g at 28 Hz, which corresponds to the bending mode of the SMA blade modules for the lateral direction of the WSVI along the \(x\)-axis. This value is almost similar to the estimated first eigenfrequency of 28 Hz from the modal analysis results shown in Figure 5. In addition, the second response was followed by approximately \begin{table}
\begin{tabular}{c c} \hline
**Item** & **Specification** \\ \hline Direction & \(x,y,z\) \\ \hline RMS Acceleration & 11.64 gms \\ \hline Duration & 2 min \\ \hline \multirow{6}{*}{Profile} & Frequency [Hz] & PSD [\(\mathrm{G}^{2}/\mathrm{Hz}\)] \\ \cline{2-3}  & 20 & 0.014 \\ \cline{2-3}  & 80 & 0.044 \\ \cline{2-3}  & 160 & 0.07 \\ \cline{2-3}  & 640 & 0.07 \\ \cline{2-3}  & 800 & 0.12 \\ \cline{2-3}  & 1150 & 0.12 \\ \cline{2-3}  & 1300 & 0.04 \\ \cline{2-3}  & 2000 & 0.04 \\ \hline \end{tabular}
\end{table} 
Table 5: Specification of the Random-vibration Test.