## 2 WSVI Design Description
\begin{table}
\begin{tabular}{c c} \hline \hline
**Characteristic** & **Value** \\ \hline Martensite Finish Temperature (\(M_{f}\), \({}^{\circ}\)C) & \(-\)21 \\ \hline Martensite Start Temperature (\(M_{s}\), \({}^{\circ}\)C) & \(-\)12 \\ \hline Austenite Start Temperature (\(A_{s}\), \({}^{\circ}\)C) & \(-\)5 \\ \hline Austenite Finish Temperature (\(A_{f}\), \({}^{\circ}\)C) & 15 \\ \hline \multirow{2}{*}{Young’s Modulus (GPa)} & Martensite & 75 \\ \cline{2-3}  & Austenite & 80 \\ \hline Tensile Strength (MPa) & 1300 \\ \hline Elongation at Break (\%) & 45 \\ \hline Density (g/cm\({}^{3}\)) & 6.45 \\ \hline Poisson’s Ratio (\(\rho\)) & 0.33 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Material Properties of the Superelastic SMA. \begin{table}
\begin{tabular}{c c} \hline \hline
**Item** & **Specification** \\ \hline Type & Double-sided Acrylic Tape \\ \hline Thickness (mm) & 0.06 \\ \hline \multirow{3}{*}{Adhesion Strength to Steel (N/100 mm)} & 58 (20-min Dwell) \\  & 85 (72-h Dwell) \\  & 159 (Ultimate Bond) \\ \hline Outgassing (\%, TML/CVCM) & 0.93/0.01 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Specifications of Viscoelastic Adhesive Tape (3M966). basic characteristics. The translational displacements acting on the SMA blade modules in Cases (1) and (2) are \(\pm\)4 mm and \(\pm\)3 mm, respectively, with a velocity of 2 mm/min. The corresponding displacement ranges are the estimated maximum displacements derived from the launch vibration analysis. Figure 2: Example of the Static Load Test Setup for the Lateral Axis. analysis of the SMA blade for the axial direction also showed a 2.2 times greater maximum strain than that of the blade for the lateral direction. The test results also showed that the hysteresis area obtained from Case (2) was almost the same or slightly less than that of Case (1). Moreover, a nonlinear characteristic induced by the phase transformation of the superplastic SMA blade was not observed within the tested displacement range. On the contrary, the stiffness of the WSVI in the axial direction increased as the displacement increased. This phenomenon seems to be mainly related to the WSVI design because the stiffness in the longitudinal direction of the SMA blade becomes dominant in determining the stiffness of the WSVI as the displacement increases. Therefore, these results from the static load test of the WSVI indicated that the design strategy of applying multi-layered viscous lamina to the SMA blades is a much more dominant factor in enhancing the damping of the isolator than the inherent damping performance of superelastic SMA. In addition, the multilayered viscous lamina contributes to reducing the stress acting on the thin SMA blade, owing to the viscoelasticity of the adhesive tapes [17]. Furthermore, a previous study [12] reported that a superelastic SMA developed for high damping SMA gear showed higher fatigue durability than titanium under cyclic loadings. Therefore, SMA blades may be useful for launch-vibration isolator applications. Figure 3: _Cont._  
The estimated values of the equivalent damping \(\zeta_{eq}\) for each case are summarized in Table 3. The values of \(\zeta_{eq}\) in each direction were obtained by the following equivalent linearization method, in which the nonlinear stiffness and damping coefficients are translated into linear ones [20]. \[\zeta_{eq}(\alpha_{0})=\frac{\Delta E(\pi_{0})}{2\pi a_{0}2^{k}{}_{eq}} \tag{1}\]  
where, \(k_{eq}\) is estimated from the linear-curve fitting of the overall slope of the load-displacement curve. \(\Delta E\) is the area of the closed loop of the hysteresis curve and \(a_{0}\) is the amplitude of the displacement.