Modal analysis of finite-size piezoelectric metamaterial plates

Abstract

Two-dimensional electromechanical metamaterials composed of thin plates with local piezoelectric resonators can display extreme vibration attenuation characteristics at desired frequencies. The typical bandgap analyses in the literature use the assumption of wave propagation in an infinite elastic structure and do not consider the modal characteristics of the structure. However, for practical implementation and design of finite-size electromechanical metamaterials, modal behaviour of the host structure and piezoelectric elements must be coupled with the dynamics of shunt circuits. To this end, we present a system-level modal analysis framework for finite-size thin plates with a segregated array of piezo-patches connected to resonant shunt circuits. The developed model takes into account the spatially discontinuous flexural rigidity of the metamaterial plate due to discrete placement of piezoelectric resonators on the substrate. Using the developed framework, we show that the electrical quality factor of resonators is critical for transitioning from broadband shunt damping to bandgap formation in piezoelectric plate metamaterials. This enables on-demand tailoring of effective dynamic stiffness of metamaterial plates for the targeted task. Lastly, for a fixed number of discrete resonators, we demonstrate the effect of physical gap size between resonators on the bandgap creation. Overall, the modelling frameworks in this study can be used for predicting the dynamics of piezoelectric plate-type metamaterials for applications in waveguiding, attenuation, filtering, and energy harvesting.

Advances in Tunable Bandgaps of Piezoelectric Phononic Crystals

“…Sugino et al [41] proposed a theoretical framework for piezoelectric PCs with double piezoelectric patches, which can generally divide these structures into multiple electrodes of any shape and study the effect of electrode shape on the response of the plate. For topology optimization and other vibration control applications, Aghakhani et al [60] proposed a 2D piezoelectric composite plate theoretical model to analyze the influence of different pasting methods and circuit parameters on the propagation of curved waves in the frequency domain. In addition to those studies, researchers have focused on the binding of piezoelectric PCs to mechanical metamaterials to couple the mechanical and electromechanical LR and expand the bandgap.…”

Smart piezoelectric phononic crystals and metamaterials:State-of-the-art review and outlook

“…Aghakhani 等人 [104] 也提出了一个二维压电复合板理论模型， 用于在频域内分析压电片不同的粘贴方 式、电路参数对于弯曲波传播的影响。Lian 等人 [105] 则将电压作为未知量改进了传统的平面波展开 法，并用改进的平面波展开法计算了不同的分流电路对于弯曲波传播的影响。 在实际工程应用中，结构的减振降噪非常重要。而二维压电复合板的研究结果可以直接应用于 实际的工程结构中。例如 Mokrani 等人 [106] 利用压电片降低了鼓风机叶片的振动。Dai 等人 [107] ，Shu 等人 [108] ，Liu 等人 [109] 则将压电片以环状贴在圆形板上，并研究了不同分流电路对于弯曲波在其中 传播的影响。Ouisse 等人 [110] 将压电片贴在金字塔蜂窝点阵夹芯结构中提高了其隔振降噪的性能。 Koutsianitis 等人 [111] 利用遗传算法以最宽带隙为优化目标，优化了拉胀结构中最佳的压电片分布位 置。Wu 等人 [112] 通过将压电复合梁呈十字型相连接，并用谱元法求解了弯曲波的传输谱以及频域相 应。Xiao 等人 [96] 将压电片贴在碳钎维增强聚合物上，研究了负电容电路和材料参数对于弯曲波传 播的影响，如图 5(c)所示。结果表明，负电容值的增加会使带隙变宽。Chen 等人 [113] 将压电片贴在 蜂窝晶格夹芯板上，以便提高夹芯板的减振性能。 除了外接电路的调控方式之外，也可通过主动控制的措施对二维复合压电声子晶体/超材料实 施调控。Li 等人 [94]…”

Modal analysis and demonstration of metastructure combining local resonators and an autonomous synchronized switch damping circuit

“…Unlike the aforementioned metastructure having a mechanical resonator, the metastructure having an electromechanical resonator uses piezo elements located periodically and a shunt circuit. Aghakhani et al 24 developed a system-level analytic methodology for a plate-type piezo metastructure connecting to a resistive-inductive shunt circuit. Sugino et al 25 proposed a methodology to achieve a wide bandgap by merging the bandgaps created by mechanical and electromechanical resonators.…”

“…Given that piezo ceramics/stacks are costly, a large metastructure throughout which many of piezo ceramics/stacks are deployed 24−28 may be impractical. This study considers a metastructure having mechanical resonators because of the cost-effectiveness and ease of design of such resonators.…”