# Review of Magnetorheological Damping Systems on a Seismic Building

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## Abstract

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## Featured Application

**The discussion in this article could be used as a literature study on the application of semi-active damping to building structures in general and the application of MR dampers to building structures specifically related to earthquake damage mitigation.**

## Abstract

## 1. Introduction

## 2. Types of Dampers on Structural Buildings

#### 2.1. Friction Dampers

^{®}(SAP2000

^{®}) software was used in these cases to investigate samples from seismic zones in India. The skid load determination was adjusted to find the response of the frame without damping and the frame with a FD. The obtained results were then compared and the decrease in displacement and mean force were estimated [70,71].

^{®}FDs. They found that FDs in the steel frame increased the ductility and decreased the drift to less than 1%. However, the infill panels not only fulfilled their function during the imposition of drift but also increased the structural strength. Therefore, the use of infill panels in conjunction with FDs was found to reduce the number of dynamic structural responses as the infill panels dissipated the input energy of the earthquake by 4% to 10% depending on the thickness [80].

^{®}, was used to analyze the performance of friction absorbers in these asymmetrical structures. The study found a significant increase in seismic behavior, which demonstrated the efficacy of FDs as tools for seismic reinforcement in these buildings [83]. Chandra et al. used the Extended Three-Dimensional Analysis of Building Systems

^{®}(ETABS

^{®}) software to dynamically analyze the nonlinear dimension time history of a new structural system of FD frames in an 18-story apartment building. The critical 5% viscous damping value was assumed to be in the initial elastic stage in order to account for the presence of nonstructural components [84].

#### 2.2. Tuned Mass Dampers

#### 2.3. Viscous Dampers

## 3. Magnetorheological Dampers for Structural Buildings

#### 3.1. Magnetorheological Fluids

^{®}80 and TWEEN

^{®}80 emulsifiers are often used to improve the sedimentation stability [141], while organic acid and stearic acid are often used to increase the density of the carrier liquid [135] and stabilize the sedimentation [138].

#### 3.2. Application of MR Dampers in Building Structures

^{®}Shake Table II [163,164].

^{®}Shake Table II to experimentally and numerically compare the various control strategies. However, the study only yielded results when certain earthquake inputs, such as the El Centro earthquake, were used. In the numerical example, a three-storey structure was controlled using a MR damper on the first floor. The simulation showed that a clipped optimal control algorithm produced improvements in uncontrolled systems [163,164].

^{®}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].

## 4. Modeling and Control of MR Dampers for Structural Buildings

#### 4.1. Modeling of MR Dampers

#### 4.2. Semi-Active Controllers for MR Dampers

## 5. Future Research

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Tuned mass damper applications: (

**a**) 101-Taipei, Taipei—Taiwan; (

**b**) Aspire Tower, Doha—Qatar; (

**c**) Sanghai World Financial Center, Sanghai—China.

**Figure 3.**Building structure with a metal frame and an installation [163].

**Figure 4.**Segmentation of the 12-story building: (

**a**) Sketch of the 12-story building structure with ‘10 + 2’ and ‘8 + 4’ models; (

**b**) Schematic of isolated sections [165].

**Figure 5.**Schematic of an MR damper between two buildings [166].

**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].

**Figure 9.**Comparison between experimental data and the predicted damping force [165].

**Figure 10.**Control of restraining-cable-free vibrations: comparison between the proposed model and the Bingham model [179].

**Figure 11.**Comparison between predicted (black) and experimentally obtained (red) responses for the Gamota and Filisko model [180].

**Figure 12.**Block diagram of a passive system for a MR damper [181].

**Figure 13.**Block diagram of a semi-active controlled system for a MR damper [181].

Model | Equation | Figure |
---|---|---|

Bingham Model | $f={c}_{1}\dot{x}+{f}_{0}sgn\left(\dot{x}\right)$ where c _{1} and f_{0} are equal to the damping coefficient and the shear friction force, respectively; and sgn () is a function of the signum. The damping force is linearly dependent on the damper speed, while the friction force depends on the velocity [177,179]. | |

Gamota and Filisko Model | $\begin{array}{c}f={k}_{1}\left({x}_{2}-{x}_{1}\right)+{c}_{1}\left({\dot{x}}_{2}-{\dot{x}}_{1}\right)+{f}_{0}\\ ={c}_{0}{\dot{x}}_{1}+{f}_{c}sgn\left({\dot{x}}_{1}\right)+{f}_{0}\\ ={k}_{2}\left({x}_{3}-{x}_{2}\right)+{f}_{0}\end{array}\},\text{}\mathrm{if}\text{}\left|f\right|{f}_{c}$ $\begin{array}{c}f={k}_{1}\left({x}_{2}-{x}_{1}\right)+{c}_{1}{\dot{x}}_{2}+{f}_{0}\\ ={k}_{2}\left({x}_{3}-{x}_{2}\right)+{f}_{0}\end{array}\},\text{}\mathrm{if}\text{}\left|f\right|\text{}\le {f}_{c}$ where c _{0} is the damping coefficient of the Bingham model, and k_{1}, k_{2}, and c_{1} are the coefficients of stiffness and viscous damping, respectively, in relation to the linear solid material [179,180]. | |

Bouc-Wen Model | $f={c}_{1}\dot{y}+{k}_{1}\left(x-{x}_{0}\right)$ ${c}_{1}\dot{y}=\alpha z+{k}_{0}\left(x-y\right)+{c}_{0}\left(\dot{x}-\dot{y}\right)$ $\dot{z}=-\gamma \left|\dot{x}-\dot{y}\right|z{\left|z\right|}^{n-1}-\beta \left(\dot{x}-\dot{y}\right){\left|z\right|}^{n}+A\left(\dot{x}-\dot{y}\right)$ k _{1} represents the damper stiffness of the accumulator and c_{0} is the dashpot coefficient associated with viscous damping at higher velocities. A dashpot c_{1} was included in the model to produce the roll-off observed in the experimental data at a low velocity. k_{0} is the stiffness control at a higher velocity, and x_{0} is the initial displacement of the spring k_{1} in relation to the nominal damper force due to the battery [180]. | |

BingMax Model | $f\left(t\right)=k\text{}{{\displaystyle \int}}_{0}^{t}\mathrm{exp}\left(-\frac{t-\tau}{\lambda}\right)\dot{x}\left(\tau \right)d\tau +{f}_{y}sgn\left(\dot{x\left(t\right)}\right)$ where a = c/k is the quotient of the dashpot c and the spring k, and f _{y} is the friction force on the slider [180]. | |

LuGre Model | ${F}_{ss}\left(v\right)=g\left(v\right)sgn\left(v\right)+f\left(v\right)$ where g(v) is the Coulomb friction and the Stribeck effect, and f(v) represents viscous friction. |

No. | Author and Year | Controller | Finding |
---|---|---|---|

1 | Zafarani and Halabian (2020) [190] | Clipped optimal with LQG control | Control of the seismic inelastic torque response of multi-story buildings. |

2 | Mohebbi et. al. (2018) [191] | H2/LQG control | Modification of H2/LQG control to optimize the control system’s performance |

3 | Zizouni et. al. (2019) [192] | Neural network control | Efficacy of neural network control on a three-story small-scale structure using the Tōhoku 2011 and Boumerdès 2003 earthquake data. |

4 | Bozorgvar and Zahrai (2019) [193] | Adaptive Neuro-Fuzzy inference system | Neuro-fuzzy optimization adapted to genetic algorithms. |

5 | Li and Liang (2018) [194] | Sliding mode control Fuzzy system | Developed a sliding mode control method based on a fuzzy system. Fuzzy logic control mitigates the chattering phenomenon. |

6 | Cesar and Barros (2017) [195] | Adaptive Neuro-Fuzzy inference system | Verified the efficacy of neuro-fuzzy controllers in reducing the responses of building structures equipped with MR dampers. |

7 | Al-Fahdawi and Barroso (2021) [196] | Adaptive Neuro-Fuzzy inference system and Simple adaptive control | Reduction of the seismic response of three-dimensional combined buildings under two-way seismic excitation with adaptive neuro-fuzzy inference system control and simple adaptive control. |

8 | Mousavi (2020) [197] | Fuzzy logic controller | Use of wavelet networks and fuzzy logic controllers to copy the inverse dynamics of MR dampers and nonlinear isolators. |

9 | Ndemanou and Nbendjo (2018) [185] | Fuzzy logic controller | Fuzzy logic controls are better than traditional controls and algorithmic controls and are critical when optimizing the response of a structure to seismic loads. |

10 | Mehrkian et. al. (2017) [186] | Fuzzy logic controller | Improving a fuzzy control system with a smart multi-objective fuzzy–genetic controller produced controls that were more effective than others. |

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Lenggana, B.W.; Ubaidillah, U.; Imaduddin, F.; Choi, S.-B.; Purwana, Y.M.; Harjana, H. Review of Magnetorheological Damping Systems on a Seismic Building. *Appl. Sci.* **2021**, *11*, 9339.
https://doi.org/10.3390/app11199339

**AMA Style**

Lenggana BW, Ubaidillah U, Imaduddin F, Choi S-B, Purwana YM, Harjana H. Review of Magnetorheological Damping Systems on a Seismic Building. *Applied Sciences*. 2021; 11(19):9339.
https://doi.org/10.3390/app11199339

**Chicago/Turabian Style**

Lenggana, Bhre Wangsa, Ubaidillah Ubaidillah, Fitrian Imaduddin, Seung-Bok Choi, Yusep Muslih Purwana, and Harjana Harjana. 2021. "Review of Magnetorheological Damping Systems on a Seismic Building" *Applied Sciences* 11, no. 19: 9339.
https://doi.org/10.3390/app11199339