## 5 Conclusions  
Improving the isolation effect and displacement response of the isolation layer of long-period isolated structures is an urgent problem to be studied and solved at present. In this paper, a negative-stiffness device was proposed and analyzed theoretically, its mechanical model was established, and the seismic response of its isolation structure system was  
Figure 27: Hysteretic curves of viscous dampers under different earthquake waves at a peak of 0.6 g. (**a**) Hysteresis loops under EL seismic wave at peak of 0.6 g. (**b**) Hysteresis loops under PAS seismic wave at peak of 0.6 g. (**c**) Hysteresis loops under SBA seismic wave at peak of 0.6 g. (**d**) Hysteresis loops under REN1 seismic wave at peak of 0.6 g. (**e**) Hysteresis loops under REN2 seismic wave at peak of 0.6 g.  
analyzed and studied. The seismic responses of the LRB, NSD, and DNSD models were compared. The main conclusions are as follows:  
1. A negative-stiffness device composed of preloaded Belleville spring, guide sleeve, one-way roller, track surface, and viscous damper was proposed. The device uses a preloaded Belleville spring and track surface to provide a restoring force consistent with the direction of displacement, so as to realize the negative-stiffness effect. Additional damping enhances the energy dissipation capacity of the device and controls the displacement of the isolation layer, so as to reduce the displacement response of the isolation layer and the ground motion response of the superstructure at the same time. 2. The mechanical model of the negative-stiffness device was established, and the influence of various parameters on the mechanical model of the negative-stiffness device was analyzed. 3. The time history analysis results show that, under all working conditions, the acceleration response of NSD relative to LRB decreases by 3.17% on average, and the displacement response of the isolation layer increases by 5.50%. Under all working conditions, the acceleration response of DNSD relative to LRB decreases by 13.73% on average, and the displacement response of the isolation layer decreases by 10.89% on average. Under all working conditions, the isolation effect of NSD and DNSD is superior to that of LRB model, and the greater the peak value of input seismic wave, the more obvious the isolation effect is. It does not only realize the effective isolation of long-period structures but also improves the disadvantages of the previous negative-stiffness devices, such as their complex structure and residual deformation. Under the action of load, the device has good deformation capacity and can maintain stable small stiffness change, thus further ensuring the stability and reliability of the combined use of isolation bearings. 4. In this paper, the track surface function was studied only as the cosine function, but in fact, there are countless kinds of track surface functions that meet the boundary conditions in theory. How to adjust the track surface function to make the isolation performance better is still a problem that needs to be solved by a lot of research. At the same time, the track surface can be made into a functional surface in both \(x\) and \(y\) directions, so that the building has good seismic isolation performance in different directions. 5. In the future, the negative-stiffness model device will be designed and manufactured, and the mechanical model of the device will be obtained through the static mechanical performance test, which is compared with the theoretical analysis results; and the dynamic test research of the negative-stiffness isolation device and isolation system will be further carried out. Conceptualization, Y.Y. ; methodology, G.K. and Y.Y. ; software, G.K. and Z.W. ; formal analysis, G.K.; resources, Y.Y. ; data curation, G.K. and Z.W. ; writing--original draft preparation, G.K.; writing--review and editing, G.K., Z.W. and Y.Y. ; supervision, Y.Y. ; project administration, Y.Y. All authors have read and agreed to the published version of the manuscript.