# Dynamic Behavior of a Simple Rolling Seismic Isolator with a Position Restoring Device
## 1 Introduction  
The damage caused by earthquakes has been steadily increasing. In recent years, the scale of the damage has been increasing rapidly as the industry has advanced [1]. Also, to cope with the threats from earthquakes, various types of seismic isolation systems have been introduced and actively studied [2; 3]. Isolation systems use a basic separator to reduce the response of the structure caused by the ground vibrations of the earthquake. There are various types of seismic isolation systems, such as sliding bearings, rubber bearings, and rolling bearing isolation systems [4; 5]. In recent years, many methods of vibration protection have been developed, including energy dispersion, vibration control, and base isolation [6; 7; 8]. In addition, studies on anti-vibration rubber bearings (HDRB) have been continuously carried out to increase the damping force of materials, and their probabilistic reliability has been studied [9; 10; 11; 12; 13]. Initial research on the rolling bearing seismic isolation system (RIS) was carried out by [PERSON] and [PERSON] in 1993 [14; 15]. Their model consists of a flat plate and cylindrical rolling bearings, and is widely used because of its protective effect from earthquakes [16; 17]. To overcome the disadvantages of recentering, [PERSON] [18] constructed an RIS with cylindrical rollers between two V-shaped rolling surfaces, and applied them to a bridge structure. Research on RIS using spherical rollers instead of cylindrical rollers has also been conducted and used for light loads [19].  
Although RIS has excellent seismic performance, there is a problem in that the seismic table moves easily in the horizontal direction, even in the case of weak earthquakes or small vibrations around the RIS as well as further issues regarding resonance. In addition, there is a disadvantage that the return to the initial position is delayed or does not occur even after the earthquake due to insufficient restoring force. To overcome the limitations of traditional friction pendulum insulators, [PERSON] developed a variable curvature pendulum isolator and variable friction pendulum isolator and studied the effect of this isolating system [20; 21; 22]. Variable frequency pendulum isolators (VFPIs) and variable curvature friction pendulum systems (VCFPS) have also been proposed by [PERSON] and [PERSON] and [PERSON] et al. [23; 24]. The products development of new isolation systems is based on step-by-step procedures for theoretical design, manufacturing, and performance verification. The design of manufacturing and performance verification is to improve mechanical properties such as material selection and heat treatment to maintain durability. The rollers and plates that make up the core components in this system are made of materials with high strength, high hardness, and wear resistance. Studies on fatigue, fracture, and reliability have been conducted by analytical and experimental methods, and were performed by [PERSON], [PERSON], etc. [12; 25; 26; 27; 28].  
The purpose of this study is to develop the theoretical basis for analyzing seismic characteristics of PRD for the shape design of a new isolation system that combines PRD and RIS in order to improve performance in the design stage. The purpose of the isolation system is as follows.  
1. Performance that returns the object to the initial position after the earthquake
2. Improvement of damping, which is a disadvantage of the RIS system.
3. Suppression of movement during weak earthquakes.
4. Control of resonance generation in the RIS system.  
For this study, theoretical governing equations for the isolation system, the RIS with a PRS, are derived, and nonlinear problems are analyzed using a fourth and fifth order Runge-Kutta method. In addition, the behavior was examined with respect to the movement of the structure, convergence time, occurrence of resonance, and nonlinearity, according to various parameters such as the spring constant, magnitude of seismic input, etc.