Tight-binding model for torsional and compressional waves in high-quality coupled-resonator phononic metamaterials

A tight-binding theoretical model which describes the vibration properties of a new type of mechanical metamaterial, the coupled-resonator phononic metamaterial (CRPM), is developed. This metamaterial, composed of mechanical resonators coupled through finite phononic crystals, exhibits spectral properties analogue to those of crystalline atomic systems. The CRPMs obey a quantum tight-binding model when a normal mode frequency of the resonators lies within a bandgap of the finite phononic crystals. Analytical expressions for the dispersion relation and group velocity are obtained. The results suggest that almost any material described by the tight-binding model, of solid-state physics, can be emulated with CRPMs.

Automated summary

A theoretical model describing the vibration properties of a new mechanical metamaterial, the coupled-resonator phononic metamaterial (CRPM), was developed in this study. The CRPM, composed of mechanical resonators coupled through finite phononic crystals, exhibits spectral properties similar to those of crystalline atomic systems. The study found that CRPMs follow a quantum tight-binding model when a normal mode frequency of the resonators lies within a bandgap of the finite phononic crystals.