Bloch waves in a triangular lattice with tilted resonators: Applications to focussing

We consider a vibrating triangular mass-truss lattice whose unit cell contains a rigid resonator. The resonators are linked by trusses to the triangular lattice nodal points. We assume that the resonator is tilted, i.e. it is rigidly rotated with respect to the triangular lattice's unit cell by an angle üq. This geometric parameter controls a resonant mode in the spectrum for elastic Bloch waves and affects the dispersive properties of the lattice. We provide physical interpretations of these phenomena and discuss the dynamic implications on elastic Bloch waves. In addition, we describe a structured interface containing tilted resonators which exhibits focussing by negative refraction, as in a “flat elastic lens”.