Journal
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
Volume 170, Issue -, Pages -Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.jmps.2022.105126
Keywords
Negative refraction; Band-gap; Single-phase metamaterial; Flexural resonances; Hyperbolic and elliptic dispersion; Homogenization; Bloch-Floquet analysis
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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.
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.
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