## 3 Design of a New Semiactive HEM Tuning Only the Damping without MR/ER Fluid  
Although there are some differences between the HEM and TMD systems, the expression of the drive point stiffness \(k_{\rm D}^{\rm TMD}(s)\) for the TMD system is similar to the drive point stiffness \(k_{\rm D}(s)\) and transfer dynamic stiffness \(k_{\rm T}(s)\) for the HEM. Experts can consider the key frequency points of the dynamic stiffness spectrum, such as the notch frequency, and experts can also refer to the design experience of the TMD system. The equivalent parameters \(k_{\rm r}\), \(b_{\rm r}\), \(M_{\rm ie}\), \(b_{\rm ie}\), and \(k_{\rm ie}\) of the TMD system are derived by the changeable lumped parameters (\(k_{\rm r}\), \(b_{\rm r}\), \(A_{\rm p}\), \(L_{\rm i}\), \(A_{\rm i}\), \(P\), \(\mu\), and \(C_{1}\)) and the invariable parameter fluid density \(\rho\) of the HEM:  
\[k_{\rm r}|_{\rm TMD}=k_{\rm r}|_{\rm HEM}, \tag{23}\]  
\[b_{\rm r}|_{\rm TMD}=b_{\rm r}|_{\rm HEM}, \tag{24}\]  
\[M_{\rm ie}|^{\rm TMD}=\rho A_{\rm p}^{2}\left(\frac{L_{\rm i}}{A_{\rm i}} \right)|^{\rm HEM}, \tag{25}\]  
\[b_{\rm ie}|^{\rm TMD}=A_{\rm p}^{2}\mu\left(\frac{L_{\rm i}}{A_{\rm i}^{4}}P^ {4}\right)|^{\rm HEM}, \tag{26}\]  
\[k_{\rm ie}|^{\rm TMD}=A_{\rm p}^{2}\frac{1}{C_{1}}|^{\rm HEM}. \tag{27}\]  
From Equations (23)-(27), tuning one parameter of the HEM may change more than one parameter of the TMD, changing one parameter of the TMD may occur by tuning more than one parameter of the HEM. From the viewpoint of the TMD, the clear goal is to adjust each parameter with a proper value when designing a passive HEM. However, with the semiactive HEM, it is also not difficult to determine which parameter or parameters are adjusted. For example, [PERSON] [12] tunes only \(k_{\rm r}\) with the aid of shape memory alloys; [PERSON] [14] tunes both \(M_{\rm ie}\) and \(b_{\rm ie}\) by tuning the area of the inertia track; [PERSON] [2] tunes both \(M_{\rm ie}\) and \(b_{\rm ie}\) by tuning both the inertia track length \(L_{\rm i}\) and the cross-section area \(A_{\rm i}\); [PERSON] [17] tunes \(b_{\rm ie}\) with the aid of ER fluid; [PERSON] [19] tunes \(b_{\rm ie}\) with the aid of MR fluid, etc. To tune only the \(b_{\rm ie}\) of the TMD system like an MR/ER semiactive HEM, this paper proposes a new semiactive HEM by tuning both the cross-section area \(A_{\rm i}\) and the inertia track length \(L_{\rm i}\) simultaneously with the aid of a screw thread between the moving plate and the lower block. This newly designed semiactive HEM can continuously adjust the damping of the inertia track without other lumped parameters. It can function like an MR/ER HEM but is less expensive and has a wider adjustability range. The detail of the proposed semiactive HEM in a 2D cutaway view is shown in Figure 3a, and a 3D cutaway view is shown in Figure 3b. When assembling it, the metal inserter, rubber main, and inner ferrule are bonded together. Secondly, the inertia track comprises an upper block, an inlet baffle, a moving plate, a lower block, an outlet baffle, and a rotating plate. From Figure 3c, there is a threaded connection between the lower block and the moving plate, allowing the moving plate to rotate and move in an axial direction relative to the lower block, enabling control of both the length and cross-sectional area of the inertia track simultaneously. The upper and lower blocks are fixed to the inner ferrule. The rotating plate is embedded between the inner ferrule and the lower block through a slide groove to ensure the synchronized rotation of the rotating plate and the outlet baffle. A fluid medium is injected, and the rubber below is used to seal the fluid. A protector is fixed to protect the inner components. The engine connects with the mount through a metal inserter, a protector is used to connect the chassis, and then this HEM can function as a vibration isolator. Figure 3d shows the location of the outlet on the lower block at the right of the block.