## 1 Introduction  
Earthquakes are considered to be the most dangerous and unexpected loads causing much damage to civil engineering structures in a wide variety of ways [1; 2; 3; 4; 5]. Different ideas regarding earthquake reinforcement design were significantly advanced in order to improve structural behavior during ground motions. This is especially important in the case of fire stations, hospitals, and other buildings, in order to secure their functionality after the seismic event. Therefore, traditional designs are replaced with modern schemes and new solutions are proposed. From this point of view, the possibility of employing techniques to control structural vibrations is one of the proper directions to be taken. Energy attenuating systems, different types of dampers as well as base isolation devices can be used for such purposes to prevent buildings from possible damages by reducing the structural response during earthquakes [1; 6; 7; 8; 9]. Seismic isolation is a method capable of reducing the accelerations and relative displacements of a building by separating it from the horizontal components of the earth movements and creating a system with a predominant frequency much smaller than earthquake frequencies [10; 11; 12]. In the base-isolated buildings, the period and attenuation of the first natural mode of the structure is mainly dependent on the isolation system characteristics [13; 14]. If the isolation devices are designed properly, the relative displacements between the stories are relatively low and the seismic behavior of the structure is mainly dominated by the first natural vibration mode [15]. Different approaches have been applied in the past, including rollers, sand layers, elastomeric bearings, etc., to attain the idea of base isolation [15]. For example, [PERSON] and [PERSON] [16] studied the seismic response of 31 isolated models with different periods and attenuation ratios by static methods and time history dynamic analysis. The study considered the proposed formula of SEAOC/UBC (Structural Engineers Association of California/Uniform Building Code) with the bi-linear hysteric model of an isolation system for the case of hard and medium rocky soils. [PERSON] et al. [17] evaluated the regulations of SEAOC/UBC considering the superstructure of the base-isolated structure to be elastic. [PERSON] [18] conducted extensive investigations on base-isolated structures. [PERSON] et al. [19] studied the vibrational base isolation system with controllable stiffness. [PERSON] et al. [20; 21; 22] investigated the seismic response of base-isolated structures equipped with polymeric bearings. Most recently, a number of researchers focused their studies on a better description of the responses of base-isolated structures. [PERSON] and [PERSON] [23] assessed the behavior of base-isolated steel structures subjected to far-field earthquakes using the probabilistic risk-based performance approach. Moreover, [PERSON] et al. [24] investigated changes in stiffness of the base-isolated layer and the superstructure of the high-rise seismic isolated building with respect to different levels of seismic excitation amplitude. Furthermore, [PERSON] et al. [25] proposed the simplified method of modal evaluation of base-isolated high-rise structures considering the soil-structure interaction effects. Tuned mass dampers (TMDs) are also often employed as one of the most effective passive control approaches in the case of high-rise buildings [1; 7; 26]. The method is characterized by the use of relatively small mass-spring-dashpot systems calibrated to be in resonance with a particular mode of structural vibration. TMDs are usually installed on the roofs of buildings. They are effective in reducing wind-induced vibrations as well as vibrations induced by the activity of occupants. The application of TMDs for the seismic protection of buildings is also often considered. TMDs are capable of significantly reducing the dynamic response of linear structures without any need for external power sources or sophisticated hardware.