Parametric study of piezoelectric-based resonators in metamaterials design for bandgap generation and energy harvesting

Abstract

Within the spectrum of metamaterials, periodic structures are widely studied since they can present bandgaps, which correspond to frequency ranges in which mechanical waves are completely suppressed. Recently, some authors have added piezoelectrics to the periodic structures with the aim of incorporating energy harvesting properties. This work is motivated by the 2D configuration used by Li et al., in which the properties of vibration suppression and energy harvesting are combined. The objective of this work is to implement a finite element model of a periodic structure that is capable of presenting vibration suppression and energy harvesting, and use it to see the influence of the parameters on the bandgaps and the relationship between energy harvesting and bandgaps. Specifically, an electromechanically coupled finite element model of Bernoulli beams is developed to model periodic structures, which are composed of square unit cells with free-standing cantilevers featuring piezoelectric properties being attached to the primary structural frame. Through these models, it is found that the domain of the wave vectors that must be evaluated in the Floquet Bloch periodic condition to identify bandgaps generated by local resonators can be restricted to only 5 wave vectors of the first Brillouin zone, which can generate a large decrease in computational resources when optimizing this type of configuration. Based on this result, a parametric analysis is performed to identify the influence of the model parameters on the location and size of the bandgap. The parametric analysis is complemented by a simultaneous variation of parameters, which shows the benefits of the quantification of uncertainties and some recommendations if you want to develop an optimization of the bandgap due to local resonances in this type of structures. Finally, voltage frequency response functions (FRF) for finite panels are presented, which deliver consistent results with what was studied at the unit cell level, and allows us to see the relationship between energy harvesting and vibration suppression.