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

Abstract

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.

Keywords:

• Tight-binding model
• phononic crystal
• coupled-resonator phononic metamaterial
• mechanical waves
• Bragg reflection
• mechanical resonator

Acknowledgments

J. A. L.-T. would like to thank the SEP-SES for financial support through a postdoctoral fellowship at the CBI department of UAM-Azc.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by DGAPA-UNAM and CONACYT under projects PAPIIT-IN111021 and CB/284096, respectively. G. B. was supported by CONACYT under project CB2017-2018/AI-S-33920.