# The Performance Study of a Novel Vertical Variable Stiffness Disc Spring Seismic Isolation Bearing
## 4 Test Results and Discussion
### Results and Analysis of the Cyclic Load Test  
To more intuitively analyze the influence of the preloading displacement and loading amplitude, the state of the bearing under preloading displacement is defined as the initial state, and the corresponding load value is zero. Figure 9 presents the hysteresis curves of the bearing under different loading amplitudes at the same preloading displacements (16 mm, 23 mm, and 30 mm). As observed, for a given preloading displacement, the upper and lower ends of the same hysteresis curve exhibit asymmetry, with the upper end appearing fuller than the lower end. This is primarily attributed to frictional damping forces. During loading, as pressure increases, frictional damping forces rise, resulting in a more pronounced hysteresis loop. Conversely, during unloading, the reduction in bearing pressure leads to a decrease in the frictional damping forces, causing the hysteresis loop to become narrower. Additionally, at the same preloading displacement, increasing the loading amplitude enhances the asymmetry of the hysteresis curve while reducing its fullness. When the preloading displacement is 16 mm or 23 mm, the hysteresis curve of the bearing exhibits a bilinear characteristic. However, at a preloading displacement of 30 mm, the shape of the hysteresis curve changes significantly, with a noticeable increase in the vertical stiffness. This occurs because, in the isolation phase, both the upper and lower disc spring groups function together, resulting in lower vertical stiffness. Upon entering the protection phase, the upper disc spring group ceases to contribute, leading to an increase in vertical stiffness. Additionally, as the preloading displacement increases, the hysteresis curve becomes more pronounced. This is attributed to the greater vertical deformation and load on the disc springs at higher preloading displacements, which in turn increases the Coulomb friction force, thereby enhancing the energy dissipation capacity of the bearing. The energy dissipation capacity of the bearing is evaluated by calculating the enclosed area of the hysteresis loop, as shown in Figure 10. Figure 10a illustrates that, at a constant preloading displacement, the energy dissipation of the bearing increases with the loading amplitude. Specifically, when the preloading displacement is 23 mm, the energy dissipation rises from 45.68 kN-mm to 458.38 kN-mm as the loading amplitude increases. Furthermore, a comparison of the slope of the curves under different preloading displacements reveals that at 16 mm, the slope is 57.48 kN-mm/mm, whereas at 23 mm, it increases to 82.54 kN-mm/mm. This indicates that as the loading amplitude increases, the influence of preloading displacement on energy dissipation becomes more pronounced. As shown in Figure 10b, at a loading amplitude of 2 mm, the energy dissipation values are 80.95 kN-mm, 112.67 kN-mm, and 174.22 kN-mm for different preloading displacements. When the loading amplitude increases to 4 mm, the corresponding energy dissipation values rise to 203.64 kN-mm, 262.88 kN-mm, and 515.68 kN-mm. These results demonstrate a positive correlation between the preloading displacement and energy dissipation capacity at a given loading amplitude. Equivalent stiffness and equivalent damping ratio are the fundamental characteristics used to assess the seismic isolation capability of a bearing. Among them, the equivalent