# Modeling the Response of Magnetorheological Fluid Dampers under Seismic Conditions
## 4 Results and Discussion
### Sinusoidal Pressure Profile  
The model was shown to simulate the expected characteristics of MR fluid dampers in the constant pressure case. The response of the system to a variable sinusoidal pressure inlet condition with a peak-to-peak amplitude of 500 Pa was tested with magnetic field strengths of \(B\) = 0 T, 0.5 T, 1.0 T, and 1.5 T applied to the annular orifice. This was to simulate the response of the MR fluid damper when used in civil structures to dampen the vibration induced from strong wind conditions.  
In Figure 10a-d, between locations 1 to 5, there was a large pressure variation, and between locations 4 to 6, there was a much smaller pressure variation across all cases, indicating that the fluid velocity was damped after the annular orifice. The largest pressure drops once the flow has developed across locations 5 and 4 at \(t\) = 1.32 s were 88.46 Pa, 131.99 Pa, 228.45 Pa, and 320.01 Pa for the \(B\) = 0 T, 0.5 T, 1.0 T, and 1.5 T cases, respectively. As expected, the magnetized cases had a much higher pressure drop across the annular orifice than the unmagnetized case. When the magnetic field strength was increased across the cases, the pressure drop across the annular orifice could be  
Figure 9: Velocity distribution along length of the channel with various magnitudes of externally applied magnetic fields.  
seen to almost linearly increase with the peak-to-peak pressure differences across locations 3 and 4, increasing as the field strength was increased, as illustrated in Figure 11.  
Meanwhile, in the constant pressure case, the pressure drop tapered off as the field strength was increased toward the saturation point of the particles; this could not be seen in the sinusoidal case. In the sinusoidal case, there was a constant increase as the magnetic field strength was increased from \(B=1.0\) T to 1.5 T. While this seems to suggest that the saturation field strength was not being approached, at \(B=1.5\) T, there should be asymptotic behavior. However, this did not occur in the sinusoidal case as the velocity of the fluid through the annular orifice was lower than in the constant pressure case. This was evident in the significantly lower pressure drops for the sinusoidal case shown in Figure 11, despite the theoretical mean inlet pressure of the two conditions being the same, and in the vertical shift of the inlet pressures profile. Although the inlet pressure profile was set to \(500+250\sin(\omega t)\), which should create a mean pressure identical to the constant pressure case, because of the resistance due to the magnetic field, the actual mean inlet pressure achieved was 434.54 Pa for the sinusoidal case. This lower mean pressure meant that the fluid velocity in the annular orifice did not approach the requisite velocity required for the current channeled through the fluid to result in saturation. This indicates that if the frequency of the wave was decreased, the pressure drop of the damper under sinusoidal loading would approach the values in the constant pressure case. Actual wind loading conditions would have a much lower frequency than the inlet condition used in the model and this accounted for the poorer performance of the damper when loaded with a sinusoidal profile. In general, it appears that the damper was more effective at damping lower frequency profiles as these allowed the flow in the annular orifice to fully develop. Regardless, the damper still achieved significant damping and the model was shown to capture the relevant characteristics of MR fluid dampers.  
Figure 10: _Cont._  
Figure 10: Change in static pressure at various measurement locations with respect to time under a sinusoidal inlet pressure profile and an externally applied magnetic field of: (**a**) \(B\) = 0 T, (**b**) \(B\) = 0.5 T, (**c**) \(B\) = 1 T, and (**d**) \(B\) = 1.5 T.