## 3 Optimization and Matching Design of Rubber-Based SMA Suspension Systems
### Structural Parameter Matching Design of Rubber-Based SMA Composite Vibration Dampers
Figure 19: Comparison of optimized stiffness and damping with target stiffness and damping under different loading rates: (**a**) stiffness; (**b**) damping. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Loading Rate (mm/s)** & **Stiffness (N/mm)** & **Damping (N-s/mm)** \\ \hline
120 & 148 & 1.6543 \\
240 & 178 & 2.2648 \\
360 & 225 & 3.3054 \\
480 & 249 & 3.9321 \\
600 & 256 & 4.1349 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Stiffness and damping of rubber-based SMA suspension optimized under different loading rates. The stiffness and damping values derived from the structurally optimized rubber-based SMA composite shock absorber were employed to update the multi-body dynamic model of the cab's rubber-based SMA suspension. Various harmonic excitations at different loading rates were applied for loading and unloading analyses. A comparative evaluation was then conducted to assess the vibration reduction performance of the suspension system before and after optimization. Comparative Analysis of Vibration Reduction Performance Optimization of Rubber-Based SMA Suspension System  
The optimized cab suspension system was subjected to harmonic excitation at loading rates of 120 mm/s, 240 mm/s, 360 mm/s, 480 mm/s, and 600 mm/s--corresponding to excitation frequencies of 10 Hz, 20 Hz, 30 Hz, 40 Hz, and 50 Hz, respectively--with a constant amplitude of 3 mm. The performance of the optimized system was then compared to that of the pre-optimized system. As illustrative examples, Figures 20 and 21 display the response curves for the \(z\)-axis acceleration of the seat under excitation signals with loading rates of 120 mm/s and 600 mm/s, respectively, before and after optimization. As illustrated in the figures above, the z-direction acceleration response of the seat shows improvement under harmonic excitation at both a small loading rate of 120 mm/s and a large loading rate of 600 mm/s. A comparative analysis of the root mean square  
Figure 21: Comparison of \(z\)-axis acceleration response of seats with a loading rate of 600 mm/s before and after optimization. Figure 20: Comparison of \(z\)-axis acceleration response of seats with a loading rate of 120 mm/s before and after optimization. (RMS) values of acceleration before and after optimization for each loading rate is presented in Table 13.  
According to Table 13, it can be observed that the structural design and optimization of rubber-based SMA composite shock absorbers effectively control the z-direction acceleration response of seats across different loading rates. The root mean square (RMS) reduction in acceleration is more pronounced at lower loading rates. Specifically, at a low loading rate, the RMS value of seat \(z\)-axis acceleration decreases by 39.79%, whereas at a high loading rate, it decreases by 10.04%. This discrepancy arises because, for harmonic excitations with high loading rates, it is crucial to ensure a certain level of vibration attenuation speed to enhance comfort and allow the cab to achieve stability quickly. Consequently, the adjustment range for suspension stiffness and damping becomes limited, reducing the potential for optimizing the acceleration response.