## 5 Experimental Validation and Parameters Identification
### Active Dynamics Test in Fluid-Filled State and Parameters Identification  
As shown in Table 1, the input of the active dynamics in the fluid-filled state is the actuator current \(I\), and the outputs are the engine-side force \(F_{1}\) and chassis-side force \(F_{5}\). The frequency and amplitude of the resonance peak, the 4 th horizontal segment and the 5 th horizontal segment can be obtained. In contrast to the passive dynamics test, the active dynamics test does not need to be excited and measured by the MTS elastomer test system. The tests were performed and measured by Siemens Simecnter Testlab with the corresponding equipment. The active mount was assembled on the MTS test system, which maintains the boundary conditions consistent with the passive dynamics test.  
Moreover, improvements in the modalities of fixtures were achieved through structure optimization and material selection. The effective bandwidth of the FRFs on the upper side reached 400 Hz. Even in the non-fluid state, the effective bandwidth of the FRFs on the  
Figure 4: Experimental validation of passive dynamics **in mid- and low-frequency bands.** (**a**) experimental setup, **(b**) dynamic stiffness in-phase. _Key_: the numbers 1–4 correspond to the excitation amplitudes of \(Y_{1}\) = 0.4 mm, 0.6 mm, 0.8 mm, and 1.0 mm, respectively; \(R\) is the fixed point in dynamic stiffness in-phase.  
Figure 5: Experimental validation of passive dynamics **in mid- and high-frequency bands.** Dynamic stiffness in-phase and the 1 st and 3 rd horizontal segments; _Key_: numbers 1 and 2 correspond to the excitation amplitudes of \(Y_{1}\) = 0.05 mm and 0.10 mm; numbers 3 and 4 correspond to \(Y_{1}\) = 0.05 mm and 0.10 mm for the main rubber spring of the AHM-IT-DM-OCA.  
upper side reached 1000 Hz. The active dynamics in the filled fluid are shown in Figure 6, and it is clear that there is a 4 th horizontal segment before the mover resonance peak. Unfortunately, the 5 th horizontal segment did not appear owing to the distortion by the fixture modality on the lower side, which is also indicated by a red text box as a warning.  
The distinct features, \(f_{\rm p,1}\) and \(A_{\rm p,1}\), can be obtained from the test results. The 4 th horizontal segment \(F_{i,\infty,4}\) is slightly concave and is induced by the mover modal. The lowest point is closest to the 4 th horizontal segment; therefore, the minimum value \(A_{\rm min}\) was chosen as the estimate of \(F_{i,\infty,4}\). Thus, coupling parameter \(A_{3}K_{3}\) can be identified by \(F_{i,\infty,4}\) according to Equation (19). Subsequently, \(\xi_{3}\) and \(f_{\rm n3}\) can be identified by \(F_{i,\infty,4}\) and \(A_{\rm p,1}\) successively according to Equation (21). The detailed procedure and results are presented in 3.1-3.6 of the Table 1.  
The natural frequency of the actuator mover in the fluid-filled state is \(f_{\rm n3}\) = 246.68 Hz, which is higher than that of the fluid channel (\(f_{\rm n2}\) = 14.00 Hz) identified by passive dynamics. Therefore, it is reasonable to divide the frequency into three frequency bands, based on these two natural frequencies. The mover resonance band of the FRF \(|F_{5}/1|\) is easily affected by the modals of the fixture at the lower side. Therefore, it is not recommended to use the tested \(|F_{5}/1|\) for parameter identification in the high-frequency band.