Investigation of geometrical properties of single-phase local resonators in the formation of bandgaps in three-dimensional elastic metamaterials

Abstract

Elastic metamaterials – man-made resonant structures exhibiting unusual functionalities – have shown promising results for controlling structural vibration, specially at a low frequency regime. Such functionalities rely on the presence of resonant bandgaps, which consists of a frequency band where waves cannot propagate in response to the out-of-phase motion of the local resonators. Usually, the contrast between the properties of different material phases in such resonators results on the resonant effect, however, the manufacturing of such multi-phase structures is challenging and can be a high-cost process. This work proposes a parametric investigation of an elastic metamaterial constituted by single-phase local resonators. The bandgap formation in such structure depends on the geometrical properties of the resonators, instead of the material parameters. This analysis allows us to understand which geometrical features are sensitive to the position of the resonant bandgaps and its width. Designing such single-phase resonators provides an alternative to manufacture low-cost structures for engineering application.