# New Optimal Design of Multimode Shunt-Damping Circuits for Enhanced Vibration Control
## 1 Introduction
The idea was to introduced _current-flowing LC_ shunts into each parallel branch of the multimode shunt circuit in order to adequately isolate branches from one another at each resonance frequency of the host structure. The \"current-flowing\" shunt method is simpler to implement and requires fewer electrical components. The method was validated experimentally on piezoelectric beam and plate structures. Another piezoelectric multimode shunt-damping structure was introduced in [16]. The _series-parallel_ impedance structure was proposed as a method for reducing inductive component values. Compared to most earlier circuit designs, the proposed shunt circuit uses less components and contains smaller inductors. The series-parallel impedance structure produces less damping than previous multimode shunt approaches [13, 17], particularly at higher frequencies. A modified current-blocking circuit [16] was applied in [18] to control several vibration modes of a composite piezoelectric beam structure. In order to analyze the electromechanical behavior of the structure with piezoelectric materials, a 3D finite-element model was introduced by using \(p\)-version FEM. The optimal shunt electrical components for the piezoelectric shunt-damping system were determined using the particle swarm optimization (PSO) technique, taking into account the inherent mechanical damping. The structural damping performance of the optimal shunt-damping system was demonstrated numerically and experimentally. Recently, [PERSON] et al. [19] presented tuning rules for piezoelectric shunts, aiming to mitigate multiple structural resonances. Starting from a specification procedure of the shunt characteristics proposed in [20], the electrical parameters were derived for shunt topologies proposed in the literature that use a single piezoelectric transducer. Effective vibration mitigation of multiple structural modes was demonstrated numerically and experimentally on a piezoelectric beam. Table 1 presents a classification of the various methods for passive piezoelectric shunt damping discussed above. From this table, it can be observed that only one study concerning multimode vibration control used the PSO algorithm for optimization, and most of them used methods other than the current-flowing circuit. All of the resistant shunt circuits introduced thus far consist of passive components, i.e., resistors, inductors and capacitors in various configuration layouts. Extending the mechanisms of single-mode shunt damping, each branch in multimode shunt circuits is tuned to a specific frequency. In most multimode shunt-damping methods that use a single piezoelectric transducer, the capacitors' values are chosen arbitrarily, and the inductive components are obtained using the resonance frequency formula (closed-form tuning solutions). The remaining resistor damping components are either determined experimentally by a trial-and-error method [10, 22] or by an optimization approach [4, 12, 17, 18]. The arbitrary selection of capacitance values can have a negative impact on a shunt-damping system. The suitable choice of the capacitance values is crucial since large capacitance values worsen electromechanical coupling, while small capacitances create a requirement for larger inductance values in the shunt circuit. In addition, due to the electrical interaction of the different shunt branches of the multimode shunt-damping circuit, closed-form solutions for resonant shunt branches are subject to significant approximations, resulting in sub-optimal designs. Thus, further fine tuning for electric shunt parameters needs to be performed via an optimization procedure. On the other hand, the predictive model considered for the design of the compound system (base structure with piezoelectric elements connected to shunt circuits) may be extremely important. More efficient description of the dynamics of these systems and more accurate calculation of their resonant frequencies are very crucial for shunt-damping performance.