# 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
Figure 11b reveals that the equivalent stiffness of the bearing increases with an increasing preloading displacement. For instance, with a loading amplitude of 4 mm, the stiffness values are 14.02 kN/mm, 15.89 kN/mm, and 27.42 kN/mm, respectively. Moreover, when the preloading displacement is 30 mm, the equivalent stiffness is significantly higher compared to when the preloading displacement is 16 mm or 23 mm. This is because, at preloading  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{ \begin{tabular}{c} **Preloading Displacement** \\ **with Loading Amplitude** \\ **(mm)** \\ \end{tabular}  } & \multicolumn{2}{c}{**Ke (kN/mm)**} & \multicolumn{2}{c}{**F\({}_{\text{max}}\) (kN)**} & \multicolumn{2}{c}{**F\({}_{\text{min}}\) (kN)**} \\ \cline{2-10}  & **Theo. V.** & **Expt. V.** & **Rel Err. ** & **Theo. V.** & **Expt. V.** & **Rel Err  
displacements of 16 mm and 23 mm, both the upper and lower spring sets work together, resulting in lower vertical stiffness. In contrast, at a preloading displacement of 30 mm, the upper spring set is close to its limit state, while the lower spring set continues to operate, thereby increasing the vertical stiffness. Figure 12 and Table 6 compare the equivalent damping ratios of the bearings under different preloading displacements and loading amplitudes. The results show that the equivalent damping ratio ranges from 11.12% to 23.96%. As seen in Figure 12a, when the preloading displacement is 16 mm or 23 mm, the equivalent damping ratio decreases with an increasing loading amplitude. This phenomenon is attributed to the reduction in the fullness of the hysteresis loop as the loading amplitude increases, leading to a lower equivalent damping ratio. When the preloading displacement is 30 mm, the equivalent damping ratio first increases and then decreases with an increasing loading amplitude. This is due to significant changes in the bearing's stiffness during this stage, which affects the equivalent damping ratio. Figure 12b shows that, for the same loading amplitude, the equivalent damping ratio is generally higher when the preloading displacement is 23 mm compared to 16 mm. This indicates that, during the isolation phase, the equivalent damping ratio increases with the preloading displacement. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Preloading Displacement (mm)**} & \multicolumn{4}{c}{**Loading Amplitude (mm)**} \\ \cline{2-5}  & 1 & **2** & **4** & **6** \\ \hline
16 & 20.88 & 17.57 & 14.31 & 11.12 \\
23 & 23.96 & 21.63 & 16.35 & 14.36 \\
30 & 15.52 & 18.75 & 18.53 & 14.83 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Experimental results of equivalent damping ratios of the VVSDSI bearing under different preloading displacements and different loading amplitudes. Figure 11: Equivalent stiffnesses of the VVSDSI bearing under different preloading displacements and loading amplitudes. (**a**) Different preloading displacements: (**b**) different loading amplitudes. Performance Comparison Between VVSDSI Seismic Isolation Bearings and Traditional Disc Spring Seismic Isolation Bearings  
In order to further study the mechanical properties of the VVSDSI bearing, this paper compares the working performance of the proposed seismic isolation bearing (VVSDSI) and the conventional disc spring seismic isolation bearing (CSDVI) [22] during loading. By normalizing the force-displacement curve, the performance difference between the two bearings can be analyzed more intuitively. As shown in Figure 13, the curve of the CSDVI bearing approximates a single-stiffness curve. The force-displacement relationship exhibits a linear growth trend with increasing displacement, reflecting the fixed stiffness response characteristic of traditional disc spring seismic isolation bearings. In contrast, the VVSDSI bearing demonstrates a bilinear stiffness characteristic with two distinct phases.