## 3 Results and Discussion
### Dynamical Mechanical Properties of the Self-Decoupling MR Damper  
In this study, based on the maximum shear yield strength, HP-MRF-10 was chosen as the filler for the self-decoupling MR damper. The dynamic characteristic curve of the self-decoupling MR damper is illustrated in Figure 7, with the input current range spanning from \(-\)2.0 A to 2.0 A. This figure illustrates that the damping force of the damper rises as the input current increases and diminishes as the current decreases across all working conditions. When the displacement is limited to 5 mm, meaning that the amplitude of the self-decoupling MR damper remains within 5 mm of the maximum compression of the disk spring, only the main piston operates independently. The dynamic characteristic curve of the damper is illustrated in Figure 7a-c. At an applied frequency of 0.1 Hz, the output force of the damper can be adjusted within a range of 77.9 kN to 260.2 kN, using the damping force at the equilibrium position as a reference point. The adjustability factor for the damping force is roughly 3.34. At an applied frequency of 1.0 Hz, the output force of the damper can be adjusted within a range of 107.8 kN to 276.6 kN, with the damping force being adjustable by a factor of approximately 2.57. At an applied frequency of 2.5 Hz, the output force of the damper can be adjusted within a range of 112.8 kN to 281.5 kN, with the damping force being adjustable by a factor of approximately 2.50. Figure 6: The relationship between shear stress and magnetic flux density of double-graded HP-MRFs. (**a**) The influence of different particle sizes of sub-micron CIPs in double-graded HP-MRFs; (**b**) the influence of different particle contents of sub-micron CIPs in double-graded HP-MRFs. In scenarios where there is a large displacement of 60 mm, specifically when the amplitude of the self-decoupling MR damper surpasses the maximum compression of the disk spring by 5 mm, the main piston and the auxiliary piston operate in a coordinated manner. Figure 7d illustrates the dynamic characteristic curve of the damper. The output force can be adjusted within a range of 262.8 kN to 300 kN under large displacement conditions, while the damping force can be adjusted to approximately 1.14. The force-displacement hysteresis curves directly indicate the energy storage and consumption of the self-decoupling MR damper. To quantitatively elucidate the damping performance of the self-decoupling MR damper, performance parameters including equivalent stiffness (\(K_{\text{h}}\)), post-yield stiffness (\(K_{\text{d}}\)), yield force (\(Q_{\text{d}}\)), and equivalent damping ratio (\(h_{\text{eq}}\)) can be derived from the dynamic hysteretic curves. Figure 8 illustrates the schematic diagram of performance parameters, with \(Q\) denoting shear behavior and \(D\) indicating displacement. Figure 7: The force-displacement characteristics of the self-decoupling MR damper with current input of \(-2.0\) A, \(-1.0\) A, \(0\) A, \(1.0\) A, and \(2.0\) A at (**a**) a small displacement of 5 mm and applied frequency of 0.1 Hz; (**b**) a small displacement of 5 mm and applied frequency of 1.0 Hz; (**c**) a small displacement of 5 mm and applied frequency of 2.5 Hz; (**d**) a large displacement of 60 mm and applied frequency of 0.1 Hz.