# Shunt Damping Vibration Control Technology: A Review
## 4 Active Shunt
This voltage is passed through an additional power amplifier and input to terminals of the electromagnet in the physical system [107]. Figure 9b presents a prototype of the shunt. Using the synthetic shunt impedance shown in Figure 9a, [PERSON] et al. [52] proposed a capacitor-matching-inductance method and a negative resistive capacitor-matching-inductance method. In the work, \(Z_{s}\) was replaced by the transfer function \(R_{t}+1/sC_{t}\), and the electrical governing equation of the EMSD system is  
\[V_{e}=\left(\frac{1}{sC_{t}}+R_{t}+R_{e}+L_{e}\right)I \tag{27}\]  
where the transfer function \(R_{t}+1/sC_{t}\) of the analog impedance was implemented using the dSPACE system. Therefore, \(R_{t}\) and \(C_{t}\) can be adjusted conveniently. If \(R_{t}\) is negative, the analog shunt impedance will produce negative resistance. Using this shunt, [PERSON] et al. [53] designed a negative resistance shunted electromagnetic isolator by replacing \(Z_{s}\) with \(R_{s}\). Fully theoretical modeling and experimental investigation of a single degree of freedom system have been carried out. It was found that negative resistance shunted electromagnetic damping has both electromagnetic damping \(C_{\textit{EMSD}}\) and electromagnetic stiffness \(K_{\textit{EMSD}}\)[107]. The two coefficients are  
\[ \begin{split} C_{\textit{EMSD}}&=-\frac{C_{m}C_{e}( R_{e}+R_{s})}{\left(R_{e}+R_{s}\right)^{2}+L_{e}^{2}\omega^{2}}\\ K_{\textit{EMSD}}&=-\frac{C_{m}C_{e}L_{e}}{\left(R_ {e}+R_{s}\right)^{2}+L_{e}^{2}\omega^{2}}\end{split}  \tag{28}\]  
\(R_{s}\) cancels the inherent resistance of the coils \(R_{e}\), and as a result \(C_{\textit{EMSD}}\) will increase, which make it feasible to suppress the vibration. Furthermore, the natural frequency will shift toward a higher value with the increase of \(K_{\textit{EMSD}}\). Herein, the vibration of the beam [55] and plate [108] were also discussed. The results pointed out that the negative resistance shunt is capable of isolating multimode vibrations. Figure 9: **(a)** Schematic of a synthetic shunt impedance converter; **(b)** photograph, reproduced with permission from [53], IOP Publishing, 2012. In order to reduce the electromagnetic shunt stiffness \(K_{\text{EMSD}}\) brought by the negative resistance, [PERSON] et al. [PERSON] et al. (2016) proposed negative inductance negative resistance shunted electromagnetic damping. The negative inductance cancels the inherent inductance of the coil, and the impedance of the circuit consisting of the coils and shunt will be a pure resistance. Then, the current of the closed circuit will be frequency independent as the inductance of the shunt and the coil are equal to each other. The experimental result demonstrated that this negative inductance negative resistance shunt attenuated the multimodal vibration of the plate. Moreover, the electromagnetic shunt stiffness decreased when negative inductance was used. Furthermore, the negative resistance shunt can generate a relative broadband damping effect. [PERSON] et al. [PERSON] et al. (2016); [PERSON] et al. (2016) applied the negative impedance shunt to an electromagnetic absorber and discussed the multimodal vibration absorption of this shunt. The experimental results implied that the first three mode vibrations can be reduced by 15.11, 16.08, and 11.45 dB using negative resistance (NR) absorber, and 20.57, 21.75, and 15.33 dB amplitude reductions were achieved using negative inductance negative resistance (NINR) absorber. Both the two shunts are capable of suppressing multimode vibration efficiently. The negative inductance negative resistance shunt has a better absorption effectiveness at high frequency than the pure negative resistance shunt. It also demonstrated that the negative impedance is less sensitive to the frequency shift than resonant shunts. Furthermore, [PERSON] et al. [PERSON] et al. (2016) presented the basic designs of the magnetostrictive actuator connected to the negative inductance shunt. The shunt is implemented using the NIC that can be found in Figure 8a.