Negative refraction in a single-phase flexural metamaterial with hyperbolic dispersion

We analyze the band structure of a single-phase metamaterial involving low-frequency flexural resonances by combining asymptotic homogenization and Bloch-Floquet analysis. We provide the closed-form expression of the dispersion relation in the whole Brillouin zone. The dispersion relation involves two effective, frequency-dependent, mass densities associated with symmetric and antisymmetric flexural resonances of the beams at the microscopic scale. We demonstrate that our simple locally-resonant structure produces at low-frequency band-gaps and, in the hyperbolic regions of the dispersion diagram, negative refraction. Our findings are validated by direct numerical calculations.

Automated summary

In this study, we analyze the band structure of a single-phase metamaterial involving low-frequency flexural resonances by combining asymptotic homogenization and Bloch-Floquet analysis. We provide a closed-form expression of the dispersion relation in the whole Brillouin zone and demonstrate the existence of band-gaps and negative refraction in the hyperbolic regions of the dispersion diagram at low frequencies. Our findings are validated through direct numerical calculations.