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.
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).