## 5 Experimental Validation and Parameters Identification
### Passive Dynamics Test and Parameters Identification  
As shown in Table 1, the input of the passive dynamics is the engine-side displacement \(Y_{1}\), and the output is the engine-side force \(F_{1}\) and chassis-side force \(F_{5}\). The distinct features were the fixed point and the 1 st, 2 nd and 3 rd horizontal segments according to the theoretical results. The experiment was designed and performed based on the MTS elastomer test system. It should be noted that the drive-point dynamics test was not supported and could not be measured. Therefore, the distinct features of the 2 nd horizontal segment test results are not discussed. The experimental setup and passive dynamics of cross-point dynamics are shown in Figure 4. The specific fixtures shown in Figure 4a were needed for the tests; thus, the dynamics tested contained the modal of fixtures in the high-frequency band. Figure 4b shows the features of the amplitude dependence, and the fixed-point \(R\) in the dynamic stiffness in-phase agrees well with the analysis. The cross-point passive dynamics in the mid-and high-frequency bands were measured at 2-400 Hz, as shown in Figure 5. The figure shows the 1 st horizontal segment \(k^{\prime}_{\infty,1}\) and the 3 rd horizontal segment \(k^{\prime}_{\infty,3}\). However, the 3 rd horizontal segment was distorted by the fixture modalities; therefore, it was marked by a red text box as a warning. It is difficult to obtain accurate and reliable cross-point dynamics in higher frequency bands because the test generally requires a complex and bulky fixture system, as shown in Figure 4a. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Dynamics**} & \multirow{2}{*}{**Input**} & \multirow{2}{*}{**Output**} & \multirow{2}{*}{\(f_{\text{aa}}\)} & \multirow{2}{*}{\(f_{\text{aa}}\)} & \multirow{2}{*}{\(f_{\text{aa}}\)} & \multirow{2}{*}{\(f_{\text{aa}}\)} & \multirow{2}{*}{\(f_{\text{aa}}\)} & **Distinct Features** & & **Key Parameters** \\  & & & & & & & & & **Identification** \\ \hline \multirow{2}{*}{**Passive dynamics**} & Engine-side & \multirow{2}{*}{\begin{tabular}{c} Engine-side \\ displacement \(Y_{1}\) \\ force \(F_{5}\) \\ force \(F_{1}\) \\ force \(F_{1}\) \\ force \(F_{5}\) \\ \end{tabular} } & \multirow{2}{*}{\(f_{\text{R}}\)} & \multirow{2}{*}{1 st : \(k_{1}+A_{1}^{2}K_{\text{A}1}\)} & \multirow{2}{*}{/} & \multirow{2}{*}{2 nd : \(k_{1}+A_{1}^{2}K_{\text{A}1}\)} & \multirow{2}{*}{\(A_{1}\)} \\  & & & & & & & \(K_{\text{ul}}\) \\ \hline \multirow{2}{*}{**Active dynamics**} & Actuator & \multirow{2}{*}{\begin{tabular}{c} Engine-side \\ force \(F_{1}\) \\ current \(l\) \\ force \(F_{5}\) \\ \end{tabular} } & \multirow{2}{*}{/} & \multirow{2}{*}{4 th : \(G_{\text{BM}}\)} & \multirow{2}{*}{\(f_{\text{pA}}\)} & \multirow{2}{*}{0} & \multirow{2}{*}{\(A_{3}K_{3}\)} \\  & & & & & & & \\ \hline \multirow{2}{*}{**Active dynamics**} & Actuator & \multirow{2}{*}{\
\begin{tabular}{c} Linear acceleration \\ \(\text{Chassis-side}\) \\ force \(F_{5}\) \\ \end{tabular} } & \multirow{2}{*}{/} & \multirow{2}{*}{/} & \multirow{2}{*}{\(f_{\text{p},3,\text{nof}}\)} & \multirow{2}{*}{6 th : \(k_{\text{M}}/\text{m}_{\text{s},\text{nof}}\)} & \multirow{2}{*}{\(K_{1},A_{2},K_{3}\)} \\  & & & & & & & \\ \hline \multirow{2}{*}{**Active dynamics** (non-fluid)} & Actuator & \multirow{2}{*}{
\begin{tabular}{c} Linear acceleration \\ \(\text{Chassis-side}\) \\ force \(F_{5}\) \\ \end{tabular} } & \multirow{2}{*}{/} & \multirow{2}{*}{/} & \multirow{2}{*}{\(f_{\text{p},3,\text{nof}}\)} & \multirow{2}{*}{7 th : \(k_{\text{M}}\)} & \multirow{2}{*}{\(m_{\text{s},\text{c}}\)} \\  & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Dynamics and distinct features of AHM-IT-DM-OCA. Therefore, the bulk stiffness \(K_{\rm ul}\) of the upper fluid chamber and the equivalent piston area \(A_{1}\) of the main rubber spring, can be identified based on the fixed point \(R\) and the 1 st horizontal segment \(k^{\prime}_{\infty,1}\) by passive dynamics in the mid- and low-frequency bands according to Equation (11).