Elastic wave control in reticulated plates using Schwarz primitive cells

Abstract

In this work, the Schwarz primitive unit cell is used as the building block of different types of metastructures for steering and focusing elastic vibrations. The emergence of a Bragg-type bandgap when constructing a two-dimensional plate from such unit cells is experimentally validated. It is demonstrated that increasing both mass and porosity of the Schwarz primitive leads to a decrease in the frequency of the out-of-plane propagating wave targeted in this study. By arranging these modified Schwarz primitive unit cells in constant and graded layouts, two-dimensional plates with an embedded metabarrier and a metalens are numerically designed. The metabarrier protects an interior area of the plate from the propagating waves on a wide frequency band (approx. 1.4-3.4 kHz). Equally, the refractive index profile necessary for gradient index lenses is obtained via a progressive variation of the added mass or, alternatively, the porosity of the unit cell over a rectangular area. For the first time, bending of the out-of-plane mode towards the focusing point is practically validated in a challenging mesoscale experiment requiring the assembly of different three-dimensional printed sections of the plate. The increased porosity design is advantageous not only in terms of overall lightweight, but also towards additive manufacturing as it requires less material.