# Dynamic Behavior of a Simple Rolling Seismic Isolator with a Position Restoring Device
## 4 Conclusions  
Mathematical modeling and numerical analysis were carried out to analyze the rolling bearing seismic isolation system equipped with PRD, and the results of the analysis of the equipment with and without PRD were compared. The following conclusions were obtained. 1. The PRD is an effective device to control the deviation of the original position and stop position after disturbance of the seismic isolation system, and to return quickly to the home position. Further, it is expected to solve the disadvantages of a general rolling type seismic isolation system. 2. The frequency response characteristics of the seismic isolation system equipped with PRD show that the relative displacement of the upper and lower parts and the magnitude of the response rise sharply at a specific frequency, depending on the magnitude of the spring-mass ratio and the amplitude of the excitation. It can be seen that the resonance can be avoided by controlling the design parameters because the jump frequency at which the response amplitude increases sharply is proportional to the stiffness to mass ratio \(\sqrt{k/M}\) and inversely proportional to the excitation amplitude \(U\). 3. The response characteristics of the rolling-type seismic system have been determined. It was found that the harmonic characteristics at the excitation frequency of an integral multiple of the resonant frequency appear, and that they can be controlled by the damping value. Figure 12: Responses of the system to earthquake excitation in case of \(k/M=0\) and \(\zeta_{r}=0.3\). \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **El Centro Earthquake** & **Isolator with PRD** & **Isolator without PRD** \\ \hline
**Maximum Relative** & & & \\
**Displacement** & & & \\
**Maximum Absolute** & & & \\
**Acceleration** & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Maximum values of seismic responses. When the El Centro earthquake excitation is applied, the PRD has good vibration damping effects, which reduce the maximum acceleration. Further, the relative displacement response is small, so the stroke of the seismic table can be designed to be small. From the above, we can conclude that the PRD system can improve the performance of the isolation device for restoring the original position and resonance avoidance. In addition, the rolling type seismic isolation system could investigate the nonlinear characteristics, which is the phenomenon of spikes at specific frequencies and of harmonics. This phenomenon can be controlled by the ratio of mass to stiffness and the damping coefficient. Therefore, the PRD system also can be designed to quickly converge and restore its original position and to avoid resonance phenomena. Additionally, we suggest that the PRD system could be a useful device for improving the performance of the seismic isolation system. In the future a theoretical study of harmonics will be carried out. All authors discussed and agreed on the idea and had equal scientific contribution and contributed to the writing. [PERSON] contributed to the establishment of the equation of motion, the numerical programing and simulation, analysis of results, composition, and organization. [PERSON]-[PERSON] contributed to the partially numerical analysis, discussion, and analysis of results, and reviewed and improved the manuscript. All authors have read and approved the final manuscript. This research was carried out without external funding. The authors  
* [PERSON] and [PERSON] (2013) [PERSON]; [PERSON] Introducing Orthogonal Roller Pairs as an effective isolating system for low rise buildings. In _Seismic Control. System_; WIT Press: London, UK, 2013; pp. 65-76. * [PERSON] and [PERSON] (2018) [PERSON]; [PERSON]; [PERSON] An equivalent method for optimization of particle tuned mass damper based on experimental parametric study. _J. Sound Vib._**2018**, _419_, 571-584. [CrossRef]
* [PERSON] et al.