Phononic crystals, periodic structures composed of a finite array of solid inclusions in a host medium, have shown to possess powerful, application-rich physical phenomena such as invisibility cloaking, negative refraction, and one-way sound propagation. More recently, researchers inspired by the presence of a Dirac cone in the band structure of graphene have used phononic crystals to study wave transportation phenomena near Bloch mode degeneracies to realize structures that mimic zero refractive index (ZRI) acoustic materials. Waves do not experience spatial phase changes in ZRI materials. Consequentially, the phase of the wave on input will be the same as the phase on exit of a ZRI phononic crystal. Researchers have used  ZRI phononic structures as acoustic lenses to produce plane waves given planar and non-planar field input.

 

The Bloch mode degeneracies required for these phenomena can be separated into two groups, symmetric and accidental. Symmetric degeneracies, as the name suggests, are due to the underlying symmetry of the lattice. For example, triangular and honeycomb lattices inherently possess degeneracies at the corners of the Brillouin zone. Degeneracies not produced by the system symmetry, such as degeneracies at the center of the Brillouin zones for square and triangular lattices, are referred to as accidental degeneracies. Using effective medium theory, these degeneracies form specific combinations of effective mass density and effective bulk modulus and can therefore be tuned with lattice parameters. While it is possible to achieve zero refractive index material at various points in the Brillouin zone for both symmetric and accidental degeneracies, these degeneracies only occur at individual frequencies. This is because the band structures of phononic crystals are highly dependent on lattice geometry and material properties. 

 

To address this issue, researchers are exploring adaptable structures that can produce Dirac points at tunable frequencies. While these structures are tunable to some degree, the tunable range was very limited  and  difficult to physically implement. Using a reconfigurable origami structure to modulate between different classes of phononic Bravais lattices, this research investigates the effects of phononic lattice perturbation to produce drastic changes in the frequency of useful accidental degeneracies. Specifically, a folded Miura-origami sheet was used as a base to create a phononic lattice that can transition from a hexagon to a square to a second hexagonal Bravais lattice. Ultimately, this research will explore the potential for useful degeneracies in both Bravais and non-Bravais transition lattices at and between the , M, K, and X points for denser frequencies of operation.


On the Modulation of Origami Phononic Structure for Adaptive Wave Transmission in Brillouin Zone

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Aerospace, Bioengineering, Applied Mechanics, Design Engineering Division, Advanced Energy Systems, Manufacturing Engineering Division, Noise Control and Acoustics, Nondestructive Evaluation, Diagnosis, and Prognosis (NDPD), Nuclear Engineering Division, Process Industries Division, Fluids Engineering, Heat Transfer, Materials, Microelectromechanical Systems, Safety Engineering and Risk Analysis, Computers & Information in Engineering


Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2020/volume/84478

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