# Modeling the Response of Magnetorheological Fluid Dampers under Seismic Conditions
## 1 Introduction  
Advancements in nanotechnology have allowed for the fabrication of micrometer- and nanometer-sized magnetic-responsive particles, and when mixed with non-magnetic-responsive carrier fluids and at least one type of thiocarbamate and/or thiophosphrous additives, a type of smart fluid material is developed, known as the magnetorheological (MR) fluid [1]. Under the application of external magnetic fields, magnetic-responsive particles interact with each other through dipole moments to form chain-like structures along the direction of the applied magnetic field [2]. These chain structures contribute to resisting shear stress in the perpendicular direction to the magnetic field. Therefore, by varying the magnitude of external magnetic fields, MR fluids can exhibit a rapid, reversible, and tuneable transition between a liquid state (off-state) and a more viscous semisolid state (on-state) [3]. The initial development of MR fluid devices can be traced back to the late 1940s by [PERSON] [4]. Carbonyl iron particles obtained from the thermal decomposition of iron pentacarbonyl are the mostcommonly used magnetic-responsive particles in MR fluids due to their large saturation magnetization. Typical base fluids used in MR fluids include mineral and silicone oils, synthetic hydrocarbons, polyethers, polyesters, and water [5]. [PERSON] et al. [6] studied the influences of particle shape on the properties of MR fluids. Experimental results showed that the off-state viscosity of MR fluids containing only wires was substantially higher than MR fluids containing only spherical particles. The effects of particle size on the properties of MR fluids were examined in References [7; 8]. It was shown that larger magnetic-responsive particles had a larger yield stress compared to particles with smaller sizes. However, MR fluids with smaller particle sizes showed higher stability against sedimentation. [PERSON] et al. [7] explained these effects as the results of fluctuations of particle positions in the particle chain. Figure 1 shows the three basic modes of operations of MR fluid devices [9]. The valve mode, or the pressure-driven flow mode, is often observed in dampers, shock absorbers, and servo-valves [5]. The shear mode is often utilized in clutches and brakes. The squeeze mode has not been as thoroughly studied as the previous two operating modes but can be used as low amplitude vibration dampers [9]. Among these applications, MR fluid dampers have received the most extensive research interest. MR fluid dampers, first introduced in 1992 by [PERSON] and [PERSON] [10], utilize the controllable properties of MR fluids, including viscosity and shear stress, while only requiring a low power input. The peak power requirement in some commercially available dampers is less than 10 W, where the power from a small camera battery would allow for more than one hour of continuous operation [11; 12]. The schematic diagram of a typical MR fluid damper is shown in Figure 2.  
Compared to conventional dampers, the damping coefficient of MR fluid dampers can be continuously and quickly adjusted by modifying the strength of the applied external magnetic field. Hence, they can be effectively used as shock absorbers to increase passenger comfort and safety in  
Figure 1: Basic operational modes for MR fluid devices: (**a**) valve mode, (**b**) shear mode, and (**c**) squeeze mode. Figure 2: Schematic diagram of an MR fluid damper [13]. automobile ground vehicles [14; 15; 16; 17; 18], railway vehicles [19; 20; 21; 22; 23], and aircraft [24; 25; 26; 27]. They can also be built into various civil structures, such as buildings [28; 29; 30], bridges [31; 32], and piping systems [33], in order to minimize their responses to vibrations caused by strong winds and earthquakes. Studies on these systems were reviewed by [PERSON] et al. [34], [PERSON] and [PERSON] [35], and [PERSON] et al. [36].