# Shunt Damping Vibration Control Technology: A Review
## 3 Passive Shunt
### Single Modal Vibration Control  
In 1979, [PERSON] [27] carried out a preliminary experimental demonstration of the feasibility of using external electronic circuits to damp mechanical vibrations in optical systems. If the shunt is a simple resistor, the piezoelectric device will act similarly to viscoelastic damping treatment. [PERSON] and [PERSON] [29] discussed two shunting circuits: the case of a resistor alone (shown in Figure 4a) and that of a resistor and inductor (in Figure 4b). The resistive shunt is a one-order electrical circuit nd the energy is dissipated at the resistor in form of heat. Therefore, the shunt is equivalent to an extremely light viscoelastic damping treatment that offers very little mechanical damping [67]. The piezoelectric transducer shunted with a resistor and an inductor [29] or the electromagnetic transducer shunted with a resistor and a capacitor [31] are the two-order circuit that can generate an electrical resonance. If the resonance of the electrical circuit is equal to that of the mechanical system, the circuit will be in resonance and a considerable control force will be generated to resist the vibration of the mechanical system. Then vibration is controlled. In principle, the two-order shunt is like a vibration absorber. Then fixed point theory can be used to optimize the parameters of the shunt. [PERSON] et al. [68] used the electrical impedance model to tune the RL circuit. The optimal resistance of series shunt was obtained [69], which is \(R_{opt}=\omega_{s}L_{e};\omega_{s}=\sqrt{(2 kL_{e}+\phi^{2})/2 mL_{e}}\), where \(m\), \(k\), and \(\phi\) are the mass, stiffness, and the electromechanical coupling coefficient of the electromagnetic transducer, respectively. As to the piezoelectric transducer, [PERSON] et al. [70] studied RL shunted piezoelectric transducer and optimized the parameters. The optimal inductance and resistance are  
\[L_{opt}=\frac{1}{G+C_{p}\omega_{n}} \tag{14}\] \[R_{opt}=2L\omega_{n}\sqrt{\frac{3 LG}{8(1-0.5 LG)}}\]  
where \(G\) is a modal constant. [PERSON] et al. [71] proposed an exact closed-form solution to the \(H_{\infty}\) optimization of the piezoelectric material shunted with inductive-resistive circuits. This solution imposes exactly two equal peaks in the receptance function that are associated with the smallest possible vibration amplitude of the host structure. The single mode vibration control using a two-order shunt can generate an antiresonance effect to reduce the vibration of the host structure, and it has been successfully employed to reduce an HDD disk-spindle system [72; 73], see Figure 5. The results showed that a RL shunt circuit can reduce the target mode vibration by 60%. [PERSON] and [PERSON] [74] established a passive smart beam using a shaped piezoelectric transducer and an RL circuit. The previous studies on the single mode shunt focused on the design and optimization of the circuit, such as the parallel shunt, series shunt, and series-parallel shunt. [PERSON] [75] proposed the parallel RL shunt circuit shown in Figure 4c, the similar shunt can be found in [76; 77; 78]. [PERSON] and [PERSON] [79] utilized the R-L shunt to construct a modal piezoelectric transducer to control vibrations of a truss-cored sandwich panel. The series and parallel resonant shunts can obtain similar vibration control performance, but the parallel one is less sensitive to the optimal resistance. Figure 4d is an RL-C parallel shunt circuit [47]. [PERSON] et al. [80] studied vibration suppression of a hard disk driver actuator arm by using serial RL and parallel R-L shunts. Al these results showed that a good one mode vibration can be achieved using the resonant shunt. Figure 4: Single mode shunts, (**a**) resistive, (**b**) series, (**c**) parallel, and (**d**) RL-C parallel. [PERSON] et al. [81] derived governing equations according to the equilibrium of force principle and used an equivalent mechanical model of a piezoelectric transducer. Series RL circuit (see Figure 4b) and parallel LR circuit (see Figure 4c) are used.