Resonator-Based Piezoelectric Metastructures: Efficient Bandgap Estimation and Parametric Analysis

Abstract

Abstract The integration of piezoelectric elements as resonators inside a periodic structure for vibration suppression and energy harvesting (at low frequencies) was experimentally demonstrated recently. In particular, employing a square array of free-standing piezoelectric cantilevers attached to a primary structural frame. The configuration could be understood as a periodic cell that contains a series of cantilevered Piezoelectric Energy Harvesters (PEHs). This work aims to implement a finite element model of a piezoelectric periodic structure capable of presenting vibration suppression and energy harvesting and use it to study the influence of the model parameters on the generated bandgaps. Different frame geometries with cantilever piezoelectric beams are studied. Through these geometrical arrangements, it is found that the domain of the wave vectors that must be evaluated in the Floquet-Bloch periodic condition to identify bandgaps can be restricted to only 5 wave vectors contained in the first Brillouin zone. This issue can be exploited to generate a large decrease in computational resources when optimizing this configuration. The work also presents a parametric analysis to identify the model parameters’ influence on the bandgap’s location and size. The parametric analysis also reveals the need to incorporate uncertainty quantification in the design and optimization process, simultaneously offering comprehensive information about the continuity of the bandgap in relation to the model parameters.