## 3 Magnetorheological Dampers for Structural Buildings
### Application of MR Dampers in Building Structures
The variability in the study was more stringent for the semi-active system for all ground motions used and indicated a more robust control system [165]. [PERSON] compared the seismic application of MR dampers in two buildings of different sizes under optimal parameters. His study investigated the efficacy of a damping device with semi-active systems in optimizing the responses of two structures that are located close to each other and connected to MR dampers under seismic loading. The challenge of this study was to effectively enhance the control strategy for MR dampers in two separate structures (Figure 5) [166]. Depending on the requirements, the control force and the number of damping devices were calculated and analyzed using MathWorks(r) Simulink, a MATLAB-based graphical programming environment. The linear-quadratic regulator (LQR) algorithm and linear-quadratic-Gaussian (LQG) control were used to achieve the desired control force while the law of truncated voltage was used to synthesize the voltage that was used. As a result, it was possible to control the displacement response of the MR dampers at lower stresses for shorter buildings. Improvements in the performance of a damping device that is attached to two adjacent buildings were intended in order to design an optimal nonlinear hysteretic damping device. The stochastic response of the two adjacent buildings linked to a nonlinear damping device was efficient. The stochastic linearization method was used in the optimal design to avoid the need for multiple nonlinear time history analyses. The results showed that high-voltage applications were not needed as they were not effective for MR dampers. The proposed optimal design method achieved improved seismic performance that enhanced the productivity on the economic side [166]. [PERSON] et al. conducted an experimental study on a three-story steel structure and a bridge structure. The three-story model was tested with and without fluid viscous dampers (FVDs) installed at an approximately 35\({}^{\circ}\) angle on braces. Four dampers were installed on the first floor and six dampers were installed in pairs. Figure 6 shows the schematic design of the building structure used in this study. The bridge model was tested using 15 different isolated system configurations. Four FVDs, similar to those used in the three-story building, were added to the insulation system. The study found that the FVDs effectively reduced the seismic response of the tested structures [167; 168]. Figure 5: Schematic of an MR damper between two buildings [166]. [PERSON] et al. designed and applied a seismic enhancement procedure to an existing building using FVDs and discussed some of the critical issues of using FVDs for seismic enhancement. This study included models of analytic dampers in major earthquakes as well as the layout of the dampers. The case study investigated the application of FVDs to a 21-story hotel that had been built in 1991 (Figure 7). The hotel was structurally modified and seismically upgraded by placing 56 damping devices on six selected floors due to limited space. A damping ratio of 5.3% was used in all the damping devices. The study found that the FVDs were able to minimize damage to the interior decorations of the building above the sixth floor as well as significantly reduce earthquake responses on the upper floors. Apart from that, the application of the damping devices made it possible for the hotel to execute short-term and economical construction projects [169]. Figure 6: Model of the three-story building test structure [168]. Figure 7: Installation of a damper in a building structure: (**a**) Chevron-brace damper; (**b**) Diagonal-brace damper [169]. [PERSON] and [PERSON] investigated the efficacy and financial feasibility of using damping devices to improve the seismic performance of a 35-story steel building. Three different types of additional damping devices were also used to prevent the building from collapsing. One of the types of damping devices investigated was a FVD.