## 1 Introduction  
There is an increasing demand for the protection of equipment from damage caused by vibrations and earthquakes in the environment [1]. In recent years, the scale of the damage and incidents resulting from earthquakes and vibrations have been increasing, not only for buildings, but also for industrial equipment. Therefore, various seismic isolation systems have been introduced and actively studied to deal with threats from earthquakes and vibrations [2, 3]. The isolation system incorporates basic mechanical devices to reduce the structural response owing to the shaking and vibration of earthquakes and similar events. Various types of mechanical isolation systems are available, such as sliding bearings, rubber bearings, spring-damper rolling bearings, and ball bearing isolation systems [4, 5, 6]. In recent years, numerous vibration isolation methods have been developed with a combination of technologies, including energy dissipation, vibration control, and base insulation [7, 8, 9]. Initial research on the rolling bearing seismic isolation system (RIS) was carried out by [PERSON] and [PERSON] in 1993 [10, 11]. Their model consists of a flat plate and cylindrical rolling bearings and is used extensively owing to its protective effect against earthquakes [12, 13]. To overcome the disadvantages of re-centering, [PERSON] [14] constructed an RIS with cylindrical rollers between two V-shaped rolling surfaces and applied these to a bridge structure. Although the RIS exhibits excellent seismic performance, the problem is that the seismic table moves easily in the horizontal direction, even in the case of weak earthquakes or small vibrations around the RIS, in addition to issues regarding resonance. Moreover, no vibration insulation exists in the vertical direction, and when vibration occurs in the horizontal direction, the phenomenon of vertical vibration amplification occurs, as a result of the geometric structure of the isolator. To overcome the limitations of traditional friction pendulum insulators, [PERSON] developed a variable curvature pendulum isolator and variable friction pendulum isolator and studied the effects of this isolating system [15; 16; 17]. [PERSON] and [PERSON] [18] published a study on systems with the addition of concave and springs to solve convergence problems. [PERSON] presented a numerical simulation and a comparison of the effects of four sliding isolators with variable curvature insulators [19]. Research on RIS using spherical balls instead of cylindrical rollers has also been conducted and applied to light loads [20; 21; 22; 23]. Furthermore, variable frequency pendulum isolators and variable curvature friction pendulum systems have been proposed by [PERSON] and [PERSON], and [PERSON] et al. [24; 25]. However, these studies did not address the problem of insulation against vertical vibration. Therefore, studies using springs and dampers for horizontal vibration control have also been conducted. Representative energy dissipation methods include the use of dampers and rubber, and numerous studies have been published in this area [26; 27; 28]. A representative study was conducted on the anti-vibration rubber bearing as a method for vibration control by means of damping. Such investigations have been carried out continually to increase the damping force of materials, and their probabilistic reliability has been studied [29; 30; 31; 32; 33; 34]. However, problems are encountered with the durability and natural aging of rubber materials for high loads [35]. Therefore, it is necessary to study isolators that can simultaneously insulate horizontal and vertical vibration for earthquakes and excitations. [PERSON] et al. [36; 37; 38] published a related study on a vertical spring-viscous damper-concave Coulomb friction isolation system. However, this method was structurally simplified and optimized by the relation of force for the one-degree-of-freedom motion of the superstructure.