## 2 Analysis of Stiffness and Damping Characteristics of Rubber-Based SMA Composite Dampers
Concurrently, the overall structural stiffness of the composite damper also progressively increases throughout the martensitic transformation process. This behavior is attributed to the fact that, with unchanged structural parameters, an increase in the outer rubber thickness reduces the maximum strain experienced by the rubber damping element under a constant displacement amplitude, consequently decreasing the transmitted stress. Therefore, a larger displacement is required to accumulate sufficient stress in the shape memory alloy (SMA) metal module to induce martensitic phase transformation, thereby increasing the displacement corresponding to the stiffness turning point. Moreover, as the thickness of the outer rubber components increases, their intrinsic stiffness is similarly enhanced. This enhancement, in turn, augments the overall stiffness of the composite vibration damper structure, impacting the stiffness during the martensitic transformation process. At the end of the unloading stage, the force-displacement curve of the composite damper's overall structure tends to approach the hysteresis loop characteristic of the rubber material. An increase in the proportion of rubber material also raises the residual stress within the overall structure. To quantify these effects, the stiffness, damping, and energy dissipation of composite dampers with varying thicknesses of outer rubber damping components were calculated and are provided in Table 3. Additionally, the parameter variations concerning the changes in outer rubber damping component thickness are depicted in Figure 5.  
As illustrated in Figure 5, with the increasing thickness of the outer rubber damping element, both the stiffness and damping of the composite damper exhibit a gradual increase. However, the magnitude of this increment is relatively modest. This phenomenon can be attributed to the fact that the stiffness and damping characteristics of rubber-based SMA composite shock absorbers are predominantly influenced by the SMA metal module. Con  
Figure 4: Force-displacement curves during loading and unloading process corresponding to different thicknesses of outer rubber damping layers. sequently, the changes in stiffness and damping resulting from variations in the thickness of the rubber shock absorbers remain comparatively minor. Effect of SMA Composite Shock Absorber Width on the Stiffness and Damping Characteristics of Composite Shock Absorbers  
To study the effect of SMA composite damper width on the stiffness and damping characteristics of the damper while keeping other structural parameters unchanged, rubber-based SMA composite dampers with widths of 45 mm, 50 mm, 55 mm, 60 mm, and 65 mm were selected and subjected to harmonic excitation with an amplitude of 3 mm and a loading rate of 75 mm/s. The force-displacement curves corresponding to different composite damper widths are shown in Figure 6.  
As illustrated in Figure 6, the stiffness of the shock absorber increases progressively with its width throughout the loading process, while the displacement corresponding to the stiffness turning point remains unchanged. This phenomenon can be explained by the fact that increasing the width of the shock absorber effectively increases the number of shock absorbers. Under a given displacement excitation load [36], this results in a greater dynamic reaction force, thereby enhancing overall stiffness. However, because the combination characteristics of rubber and SMA remain unchanged, the interaction between the rubber damping components and the SMA metal modules also remains constant, thus keeping the displacement corresponding to the stiffness turning point unchanged.