## 5 Experimental Validation and Parameters Identification
### Active Dynamics Test in Non-Fluid State and Parameters Identification  
As shown in Table 1, the input of the active dynamics in the non-fluid state is the actuator current \(I\), and the outputs are the mover acceleration \(\ddot{Y}_{3}\) and chassis-side force \(F_{5}\). Distinct features such as the frequency and amplitude of the resonance peak, the 6 th horizontal segment and the 7 th horizontal segment can be obtained. The test was designed to decouple parameters \(K_{\rm ul}\) and \(A_{3}K_{3}\), and the test equipment was the same as that used in Section 5.2. The tests were performed under boundary conditions with the main rubber spring removed. For the measurement of the mover acceleration \(\ddot{Y}_{3}\), the accelerometer was attached to the mover; thus, its mass effect had to be considered for the identification of key parameters. Accordingly, tests with three different added masses were performed to verify the consistency and stability of the mass identification results. The result for the actuator mover mass identified directly was the parameter with added mass, defined as \(m_{3,\rm{nof,mad}}\). Subsequently, the parameter \(m_{3,\rm{nof}}\) can be calculated by subtracting the added mass. The FRF curves measured with three different added masses are shown in Figure 7. The added masses were 8.90 g, 38.97 g and 93.03 g. Figure 7a,b shows the FRFs of \(\left|\dot{Y}_{3}/I\right|\) and \(|F_{5}/1|\), which clearly show the mover resonance peaks, 6 th horizontal segment \(\ddot{Y}_{i,\infty,6}\), and 7 th horizontal segment \(F_{i,\infty,7}\). This indicates that the two FRFs for the same added mass have the same peak frequency \(f_{\rm p,3,not,mad}\), which is consistent with the analysis using  
Figure 6: Experimental validation of active FRFs **in the fluid-filled state**. _Key:_ Measured FRF \(|F_{1}/1|\) (—); measured FRF \(|F_{5}/1|\) (-). Equation (25). For the distinct features of the 6 th horizontal segment shown in Figure 7a, the mover acceleration FRFs converged to a different horizontal segment influenced by different added masses according to Equation (23). For the distinct features of the 7 th horizontal segment shown in Figure 7b, the test results of the chassis-side force FRFs changed with the added mass, which should theoretically converge to the same horizontal segment \(k_{\text{M}}\), according to Equation (25). The FRFs increased owing to the influence of the fixture modalities at 550 Hz on the lower side. As the added mass increased, the 7 th horizontal segment decreased and gradually approached parameter \(k_{\text{M}}\). When the added mass \(m_{\text{ad}}=93.03\) g, the minimum value in the concave section was \(A_{\text{min},5,\text{nof},\text{mad}}=14.59\) N\(\cdot\)A\({}^{-1}\), which was already very close to the true value of \(k_{\text{M}}=14\) N\(\cdot\)A\({}^{-1}\). Based on the distinct features of \(\left|\tilde{Y}_{3}/I\right|\), which are more suitable for identification than \(\left|F_{5}/I\right|\), the parameter \(m_{3,\text{nof},\text{mad}}\) can be obtained, which can then be used to identify the linear stiffness \(k_{3}\) and viscous damping \(c_{3,\text{nof}}\) of the decoupler membrane. Subsequently, the net mover mass \(m_{3,\text{nof}}\) can be obtained by subtracting the added mass, so that the natural frequency \(f_{n3,\text{nof}}\) and the damping ratio \(\xi_{3,\text{nof}}\) of the mover system can be obtained. The detailed procedure is listed in 4.1-4.12 of the Table A1. Based on all parameters identified by distinct features, the following key parameters can be identified: the equivalent piston area \(A_{3}\) and bulk stiffness \(K_{3}\) of the decoupler membrane; bulk stiffness \(K_{1}\) of the main rubber spring; total mass \(m_{3}\) of the mover including the attached fluid in the fluid-filled state; and total viscous damping \(c_{3}\).