## 3 Optimization and Matching Design of Rubber-Based SMA Suspension Systems
### Structural Parameter Matching Design of Rubber-Based SMA Composite Vibration Dampers  
The response surface analysis on rubber-based SMA composite shock absorbers was conducted based on the optimization results in Section 3.2. The structural parameters, displacement amplitude, and loading rate as shown in Table 1 were taken as design variables. The maximum dynamic reaction force was used as the output variable. Additionally, a stiffness output variable was created by dividing the maximum dynamic reaction force by the displacement amplitude. In this analysis, we utilized Workbench for parametric modeling, wherein the structural parameters were designated as design variables. Following the establishment of the parameter set module, we integrated a response surface optimization module to extend our investigation. In the CCD experimental design, the five structural parameters D1, D2, D4, H, and d are taken as independent variables, represented by P1-P5; structural stiffness is used as the dependent variable, represented by P6 (stiffness = dynamic reaction force/displacement). For each variable factor, five levels are designed using the CCD method. The horizontal distribution of the CCD method is characterized by a dense center and scattered sides. For example, for the D1 variable design thickness factor P1, the five levels are 18 mm, 19.43 mm, 20 mm, 20.57 mm, and 22 mm, respectively. The middle three levels of 19.43 mm, 20 mm, and 20.57 mm are distributed closer, while the two levels of 18 mm and 22 mm on both sides are distributed farther. Compared with the orthogonal design experimental group, the experimental group designed by CCD method has a flexible data structure and higher prediction accuracy of response surface for each variable. For the five independent variables, a total of 27 combinations are given, represented as K1-K27 in P6, as shown in Table 10 below. Based on the above analysis, the CCD method can be used to flexibly design experimental groups for various structural parameters, thereby obtaining the required response surface. The resulting response surface, with the diameter and loading rate of the SMA metal module as independent variables and the \(z\)-axis stiffness of the rubber-based SMA composite damper as the dependent variable, is depicted in Figure 16. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Excitation Amplitude (mm)** & \
\begin{tabular}{c} **Suspended Z-Direction** \\ **Stiffness (Kzd N/mm)** \\ \end{tabular} &
\begin{tabular}{c} **Suspension Z-Direction** \\ **Damping (Czd N-s/mm)** \\ \end{tabular} \\ \hline
3 & 163 & 1.8021 \\
4 & 176 & 2.2096 \\
5 & 231 & 3.3452 \\
6 & 247 & 3.8624 \\
7 & 254 & 4.0245 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Optimization results of suspension stiffness and damping under different excitation amplitudes. Given that the experimental group designed using the CCD method can only determine the z-stiffness values of rubber-based SMA composite dampers for various design variables, it is necessary to export all data to calculate the response surface for each design variable with respect to the damping characteristics of the composite damper. We used Matlab to compute the z-direction damping of the rubber-based SMA composite damper from the exported data.