  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.
