Negative refraction in a single-phase flexural metamaterial with hyperbolic dispersion. (January 2023)

• Record Type: Journal Article
• Authors: Marigo, Jean-Jacques; Maurel, Agnès; Pham, Kim
• Is Part Of: Journal of the mechanics and physics of solids. Volume 170(2023)
• Publication Date: 2023-01
• Subjects: 00-01 -- 99-00; Negative refraction -- Band-gap -- Single-phase metamaterial -- Flexural resonances -- Hyperbolic and elliptic dispersion -- Homogenization -- Bloch–Floquet analysis; Mechanics, Applied -- Periodicals; Solids -- Periodicals; Mechanics -- Periodicals; Mécanique appliquée -- Périodiques; Solides -- Périodiques; Mechanics, Applied; Solids; Periodicals; 531.05
• DOI: 10.1016/j.jmps.2022.105126
• Languages: English
• ISSNs: 0022-5096

Abstract

Abstract: 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.