# The Performance Study of a Novel Vertical Variable Stiffness Disc Spring Seismic Isolation Bearing
## 1 Introduction  
Structural isolation technology reduces seismic energy input into the upper structure by establishing an isolation layer to prolong the natural vibration period of structures, thereby minimizing earthquake-induced damage to buildings. It serves as an effective means of enhancing structural seismic resistance [1, 2, 3]. Through investigations of destructive seismic events, such as the 1986 Kalamata Earthquake [4], 1994 Northridge Earthquake [5], 1999 Taiwan Chi-Chi Earthquake [6, 7], and 2013 Lushan Earthquake [8], researchers have observed that the energy from vertical ground motion in seismic fault zones can sometimes exceed that of horizontal motion, leading to numerous column failures and structural damage. Consequently, scholars have conducted various explorations and proposed the concept of three-dimensional (3D) isolation [9, 10, 11] to effectively mitigate structural damage caused by vertical seismic actions. To investigate the effects of three-dimensional seismic isolation on structures, [PERSON] et al. [12; 13] conducted experimental studies on a three-dimensional isolation system composed of laminated lead rubber bearings (LRBS) and vertical ring spring bearings (RSBs) connected in series. They further analyzed the vibration isolation performance of this system under three-dimensional ground motions using a six-story structure. [PERSON] et al. [14] developed a novel air spring-friction pendulum system (FPS) combining horizontal FPS isolators with vertical air spring isolators and evaluated its seismic isolation effectiveness for truss structures under different earthquake excitations. [PERSON] et al. [15] proposed a bilinear liquid spring (BLS)-magnetorheological fluid damper (CMRD) system for vertical vibration isolation, experimentally investigating its mechanical behavior. [PERSON] et al. [16; 17] performed experimental studies on the vertical isolation performance of a new multi-dimensional earthquake isolation and mitigation device (MEIMD), demonstrating its excellent seismic isolation capabilities. Laminated disc springs have garnered widespread attention from researchers due to their simple structure, controllable stiffness, and strong energy-dissipation capacity through friction, leading to their application in vertical seismic isolation devices for building structures [18; 19; 20]. [PERSON] et al. [21] combined lead-core rubber bearings with disc springs to create a three-dimensional multi-functional seismic isolation bearing installed at building foundations. They investigated the isolation effectiveness through a time-history analysis. [PERSON] et al. [22] conducted theoretical and experimental analyses to study the mechanical properties of composite disc spring vibration isolators (CDSVIs). [PERSON] et al. [23] performed shaking table tests using different seismic waves on 1:2 scale fixed-base models and DSB vertical seismic isolation models, demonstrating that disc spring bearings can effectively reduce the impact of vertical seismic forces on superstructures. Currently, three-dimensional isolation systems combining disc springs with rubber have been proven as an effective three-dimensional seismic isolation method [24; 25], being applied in structures, such as bridges and nuclear power plants [26]. However, traditional disc spring isolation bearings face challenges in simultaneously meeting the requirements of seismic isolation performance under minor earthquakes and controlling mechanical responses and deformations during major earthquakes due to their constant stiffness characteristics. Variable stiffness isolation technology has attracted significant attention due to its ability to adapt to seismic excitations of different intensities. However, current research predominantly focuses on horizontal stiffness adjustments, while exploration into the active control of vertical stiffness remains in its nascent stage. To address low-frequency vibration isolation for critical equipment, [PERSON] et al.