## 3 Design Validation Test
Figure 5: Modal Analysis Results ((**a**) 1 st Mode, (**b**) 2 nd Mode, (**c**) 3 rd Mode, and (**d**) 4 th Mode). 43 Hz, which was induced by the rotational mode of the SMA blade modules for the lateral direction of the WSVI along the \(z\)-axis. The \(y\)-axis response shows that the highest acceleration of 5.3 g was at 28 Hz. The overall tendency shows characteristics similar to the \(x\)-axis result, owing to the symmetric configuration of the test setup. The \(z\)-axis response shows the highest acceleration of 11.1 g at 35 Hz, which is similar to the estimated third eigenfrequency of 34 Hz. This response is higher than that of the \(x\)- and \(y\)-axes because of the coupling with the fourth mode of the structural elastic mode of 40 Hz for the test dummy structure. In addition, the second and third peak responses were followed at 72 and 98 Hz from the structural mode of the dummy satellite. From the sine-vibration test results, it can be seen that the highest acceleration response obtained from each of the \(x\)-, \(y\)-, and \(z\)-axes did not exceed the design load of 23 g, derived from the mass acceleration curve (MAC) [22]. This indicates that the WSVI is effective for attenuating sine vibration loads, as the design intends. Figure 7a,b show the representative random-vibration test results for the WSVI during the \(y\)- and \(z\)-axis excitation. To compare the vibration-reduction capabilities of the WSVI, the test results obtained from the rigid-mounted condition are also plotted in the Figure. The \(x\)-axis test result is not shown here, owing to the symmetrical configuration of the WSVI in the \(x\) and \(y\) planes, as mentioned in the sine-vibration test results. In the case of Figure 7a, the first eigenfrequency of the dummy satellite without the WSVI was observed at 975 Hz and a maximum acceleration of 23.8 g\({}_{\mathrm{rms}}\) was observed, with respect to the random test input of 11.64 g\({}_{\mathrm{rms}}\). However, the maximum acceleration was significantly decreased to 2.0 g\({}_{\mathrm{rms}}\) by applying the WSVI, and the random-vibration response was reduced by a factor of 11.9, comparing with the rigidly mounted condition. The maximum acceleration response along the \(z\)-axis without the WSVI was 114.8 g\({}_{\mathrm{rms}}\) at 260 Hz. This response is higher than that of the \(y\)-axis because the structural elastic modes of the dummy satellite are dominant along the \(z\)-axis. However, the maximum acceleration of the dummy satellite  
Figure 6: Sine-Vibration Test Results for \(x\)-, \(y\)-, and \(z\)-axes. with the WSVI was also significantly reduced to 12.2, as shown in Figure 7b. This indicates that the output response is reduced by a factor of 9.4. Table 6 summarizes the first eigenfrequencies of the dummy satellite with the WSVI in each axis, obtained through the LLESS tests performed before and after each vibration test. LLSS tests were performed to validate the structural safety of the SMA multilayered  
Figure 7: Random-Vibration Test Results ((**a**) _y_-axis, (**b**) _z_-axis). blade modules by investigating the dynamic responses of the dummy satellite with the WSVI. The results show that the maximum first eigenfrequency shift was within 3.9% throughout the test event, which was within the 5% criterion of the vibration test [23]. This indicated that no mechanical failures of the WSVI were observed, e.g., the plastic deformation or delamination of the SMA multi-layered blades with viscous lamina. This is because the interlaminated surfaces with the double-sided adhesive are effective in resisting the shear force acting on the multilayered blade with energy-absorption effects. These launch-vibration test results indicate that the SMA multi-layered blade is effective for ensuring the structural safety of the WSVI itself and reducing the transmitted launch loads to the dummy satellite, as the design strategy intended.