Fig. 1: Considered metamaterial platform supporting beyond-nearest-neighbor interactions along two orthogonal directions. | Communications Materials

Fig. 1: Considered metamaterial platform supporting beyond-nearest-neighbor interactions along two orthogonal directions.

From: Nonlocal interaction engineering of 2D roton-like dispersion relations in acoustic and mechanical metamaterials

Fig. 1

a Scheme of a single unit cell for \(N=3\). b 2D square lattice with lattice constant \(a\) built from this unit cell. The colors are for illustration only. The colored regions form a channel system that is bounded by rigid walls (not shown for clarity). The cuboid compartments (yellow) are connected to their four immediate neighbors along the \(x\)- and \(y\)-direction by tubes (yellow) with radius \({r}_{1}\). They are further connected to their \(N\)th nearest neighbors by tubes (blue) with radius \({r}_{N}\). The tubes along the \(x\)-direction (\(y\)-direction) are located above (below) the \({xy}\)-plane spanned by the yellow tubes. c gallery of unit cells for \(N=4\) to \(N=8\) as indicated. For our calculations, we use the following fixed geometrical parameters: \({r}_{1}/a=0.03\), \({r}_{N}/a=0.05\), \(w/a=0.30,h/a=0.80,{h}_{0}/a=0.24,{h}_{N}/a=0.25,\) and \(d/a=0.86\). We choose \(a=10{{{{{\rm{cm}}}}}}\) for the metamaterials supporting airborne sound and \(a=100{{{{{\rm{\mu }}}}}}{{{{{\rm{m}}}}}}\) for the elastic metamaterials.

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