# A Review on Vibration Control Using Piezoelectric Shunt Circuits
## 2 Types, Applications, and Recent Advances of Piezoelectric Shunt Circuits
### Quadratic and Cubic Nonlinear Shunt Circuits  
The introduction of quadratic and cubic nonlinear electrical components in piezoelectric shunt circuits has demonstrated great potential for improving vibration suppression capabilities. Unlike linear elements, which provide damping across a narrow frequency range, quadratic and cubic nonlinearities allow for a more flexible and adaptable response to  
Figure 7: Time domain plots of the displacement [86]. changing vibration intensities and frequencies. The first introduction of quadratic and cubic nonlinear electrical elements into piezoelectric shunt circuits was performed by [PERSON] and [PERSON] [87]. The proposed model can expand the bandwidth of a piezoelectric absorber, but it also generates undesired nonlinear phenomena, including quasiperiodic and chaotic motions. [PERSON] and [PERSON] [88] investigated the impacts of a nonlinear piezoelectric tuned vibration absorber based on the similarity principle that is intended to reduce the vibrations of a nonlinear primary system. This principle, which particularly requires that the order of the absorber's nonlinearity equal that of the main system, guarantees that the absorber's dynamic behavior mirrors that of the primary system. These properties work together to transfer energy efficiently, which improves vibration attenuation. [PERSON] et al. [89] presented the first fully passive nonlinear piezoelectric tuned vibration absorber (NTTVA). In contrast to traditional systems, which depended on synthetic inductors and external power, the NPTVA implemented closed magnetic circuits in ferrite material to reach the high inductance values required for low-frequency vibration mitigation. Furthermore, the NPTVA could effectively attenuate vibrations in nonlinear structures by adopting the nonlinear similarity principle. This work was improved in [PERSON] et al. [90] to account for mitigating multiple modes. Also, the principle of similarity was applied to create synthetic impedance for nonlinear applications by utilizing a digital signal processor in [91; 92; 93]. One sort of nonlinear absorber that can accomplish targeted energy transfer without depending on linear stiffness or damping mechanisms is known as a nonlinear energy sink (NES). Consequently, an NES can be tuned to match any natural frequency of the fundamental structure because its natural frequency is theoretically zero. This property makes it possible to effectively suppress the resonance of the primary structure across a broad frequency range, [PERSON] et al. [94]. The idea of NES has developed further throughout time. More researchers considered modern NES designs as nonlinear shunt circuits that use nonlinear electrical components to increase the absorber's effective damping frequency range and responsiveness to resonant frequencies [95; 96]. [PERSON] et al. [97] demonstrated a piezoelectric-based nonlinear energy sink for wideband vibration attenuation that has been experimentally verified. Utilizing operational amplifiers, the study presented a novel shunt circuit that combines a negative capacitance with a cubic nonlinear capacitance. The one-way transfer of energy from the structure to the NES is improved by the cubic nonlinearity, while the negative capacitance eliminates the piezoelectric material's internal capacitance. Another NES shunt circuit utilizing a cubic voltage source was proposed in [98; 99]. In linear vibration, modes can be excited independently, leaving the other modes inactive; however, this is not necessarily the case in nonlinear systems. Internal resonances take place when two modes of a nonlinear system are mutually synchronized [100], which means that their frequencies are of a simple integer ratio. This condition can be utilized to result in a unique interaction between these modes, known as the saturation phenomenon, which was first demonstrated by [PERSON] et al. [101].