## 2 Materials and Methods
### Properties of Self-Decoupling MR Dampers  
The previously engineered and manufactured self-decoupling MR damper with a standard MRF includes two piston types [36]: a primary piston and an auxiliary piston. Figure 3a illustrates that these pistons were linked by a decoupling mechanism (disk spring), which significantly affected the damping performance. At large displacements, the damper's maximum output was roughly double that at minimal displacements, thus providing a sufficient safety margin. The coil within the damper can produce magnetic fields that either align with or oppose the permanent magnets, allowing for fine modulation of the damping force magnitude as needed. Variations in the input current of the excitation coil, ranging from \(-2\) A to 2 A, provide distinct magnetic induction intensities at the working gap, as depicted in Figure 3b. It is apparent that when the current is positive, the magnetic induction intensity at the operational gap escalates with the augmentation of current. Nevertheless, when the current increases, the enhancement in magnetic induction intensity near the operational gap decreases. This effect is ascribed to the nonlinearity of the material's magnetic permeability and its similarity to the saturation magnetic induction strength. Conversely, when the current is negative, the magnetic induction intensity at the operational gap diminishes as the current magnitude increases. Consequently, it is evident that the permanent magnet and the excitation coil interact synergistically, facilitating bidirectional modulation of the damping force of the main piston while maintaining the damper's output force during power failure. Moreover, in civil engineering structures exposed to seismic and wind-induced vibrations, the duration of MR damper operation is significantly shorter than the intervals of inactivity. A significant disadvantage of these dampers is the sedimentation of solid-phase particles in the MRF during extended static positioning, which undermines the stability of the MRF. The inclusion of permanent magnets in the self-decoupling MR damper alleviates this problem by diminishing particle sedimentation, therefore improving their operational stability.  
The dynamic characteristics of the self-decoupling MR damper filled with the prepared HP-MRFs were obtained using the servo dynamic testing machine (SDS-300), as seen in Figure 3c. The experiment utilized a sine wave input excitation curve and employed a displacement control approach. The test parameters were as follows: a large displacement of 60 mm at a frequency of 0.1 Hz and a small displacement of 5 mm at frequencies of 0.1 Hz, 1.0 Hz, and 2.5 Hz. For each test condition, current excitations of \(-2.0\) A, \(-1.0\) A, \(0\) A, \(1.0\) A, and \(2.0\) A were employed.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sample** & **CIP Gradation** & **Sample** & **CIP Gradation** \\ \hline HP-MRF-1 & 100\% not milled & HP-MRF-7 & 100\% milled for 60 h \\ HP-MRF-2 & 100\% milled for 6 h & HP-MRF-8 & 100\% milled for 72 h \\ HP-MRF-3 & 100\% milled for 12 h & HP-MRF-9 & 90\% not milled + \\  & & & 10\% milled for 12 h \\ HP-MRF-4 & 100\% milled for 24 h & HP-MRF-10 & 90\% not milled + \\  & & & 10\% milled for 24 h \\ HP-MRF-5 & 100\% milled for 36 h & HP-MRF-11 & 90\% not milled + \\  & & & 10\% milled for 60 h \\ HP-MRF-6 & 100\% milled for 48 h & HP-MRF-12 & 92\% not milled + \\  & & & 8\% milled for 24 h \\ \hline \hline \end{tabular}
\end{table}
Table 1: Composition of HP-MRF samples with different CIP gradations.