Spiral-Based Phononic Plates: From Wave Beaming to Topological Insulators

Abstract

Phononic crystals and metamaterials can sculpt elastic waves, controlling their dispersion using different mechanisms. These mechanisms are mostly Bragg scattering, local resonances, and inertial amplification, derived from ad hoc, often problem-specific geometries of the materials' building blocks. Here, we present a platform that ultilizes a lattice of spiraling unit cells to create phononic materials encompassing Bragg scattering, local resonances, and inertial amplification. We present two examples of phononic materials that can control waves with wavelengths much larger than the lattice's periodicity. (1) A wave beaming plate, which can beam waves at arbitrary angles, independent of the lattice vectors. We show that the beaming trajectory can be continuously tuned, by varying the driving frequency or the spirals' orientation. (2) A topological insulator plate, which derives its properties from a resonance-based Dirac cone below the Bragg limit of the structured lattice of spirals.

Enhancement of Deep-Subwavelength Band Gaps in Flat Spiral-Based Phononic Metamaterials Using the Trampoline Phenomena

“…The introduction of holes increases the band gap relative width to 23.79% with an increase of 322%. All the band gaps reported in figures 2 and 3 are in the deep-subwavelength frequency range(i.e., below the Bragg scattering limit) 24 , in comparison to the homogeneous plate properties. For the considered unit cells, the square lattice band gaps are lower in frequency than the hexagonal ones by approximately a factor of 5.…”

“…These resonancebased approaches enable metamaterials to retain properties that do not exist in conventional materials, like negative effective density or stiffness [21][22][23] . Recently, we presented a platform for realizing different phononic metamaterial physics based on Archimedean spirals spanning Bragg-scattering, local resonance and amplification of inertia utilizing simple variations of the spirals' geometrical parameters and symmetries 24 .…”

Experimental demonstration of topological waveguiding in elastic plates with local resonators

“…Recent studies in photonics [28] and acoustics [29] have proposed the use of resonating elements within a topological medium to lower the operating frequencies. In elastic systems, recent numerical investigations have provided novel solutions to these issues [26,30,31]. However, the experimental realization of topological manipulation of low-frequency elastic waves remains a formidable challenge to date.…”

Dark state, zero-index and topology in phononic metamaterials with negative mass and negative coupling

“…Additionally in 2011, Liu et al proposed an elastic model with double negative parameters by integrating a tri-chiral lattice with softly coated inclusions [25] and an other double negative systems constructed by chiral mass-spring unit [26]. Since then, a plenty of phononic metamaterials based on chiral and spiral structures are proposed [28][29][30].…”