Modal analysis of finite-size piezoelectric metamaterial plates

Amirreza Aghakhani,Mehmet Murat Gozum,Ipek Basdogan

doi:10.1088/1361-6463/abb5d5

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.

Highlights

IntroductionAnalogous to an array of purely mechanical resonators, an array of piezoelectric elements connected to resonant shunt circuits (e.g. resistive and inductive elements) can be integrated to flexible substrates to display low-frequency bandgap for vibration/noise attenuation
Two-dimensional electromechanical metamaterials made from a thin plate with an array of piezoelectric elements connected to resonant shunt circuits can display bandgap for vibration reduction in aerospace, marine, and automotive applications
We developed a modal analysis framework for thin plates with an array of piezopatches shunted to resonating circuits for investigating the bandgap formation

Summary

Introduction

Analogous to an array of purely mechanical resonators, an array of piezoelectric elements connected to resonant shunt circuits (e.g. resistive and inductive elements) can be integrated to flexible substrates to display low-frequency bandgap for vibration/noise attenuation. Sugino et al presented a distributed-parameter model and modal analysis of a locally resonant one-dimensional (1D) electromechanical metastructure, where a finite-size bimorph piezoelectric beam with many segmented electrodes connected to inductive circuits was used for the bandgap formation [25]. Later, they extended their model to two-dimensional (2D) bimorph piezoelectric plate metamaterial with multiple electrodes [27]. The effects of physical segmentation of resonators on the host structure are presented

Modal analysis of a piezoelectric metamaterial plate

Locally resonant bandgap formation

Transition from broadband shunt damping to bandgap formation

Discrete local resonators

Conclusion