Design and Robustness Evaluation of Valley Topological Elastic Wave Propagation in a Thin Plate with Phononic Structure

Abstract

Based on the concept of band topology in phonon dispersion, we designed a topological phononic crystal in a thin plate for developing an efficient elastic waveguide. Despite that various topological phononic structures have been actively proposed, a quantitative design strategy of the phononic band and its robustness assessment in an elastic regime are still missing, hampering the realization of topological acoustic devices. We adopted a snowflake-like structure for the crystal unit cell and determined the optimal structure that exhibited the topological phase transition of the planar phononic crystal by changing the unit cell structure. The bandgap width could be adjusted by varying the length of the snow-side branch, and a topological phase transition occurred in the unit cell structure with threefold rotational symmetry. Elastic waveguides based on edge modes appearing at interfaces between crystals with different band topologies were designed, and their transmission efficiencies were evaluated numerically and experimentally. The results demonstrate the robustness of the elastic wave propagation in thin plates. Moreover, we experimentally estimated the backscattering length, which measures the robustness of the topologically protected propagating states against structural inhomogeneities. The results quantitatively indicated that degradation of the immunization against the backscattering occurs predominantly at the corners in the waveguides, indicating that the edge mode observed is a relatively weak topological state.

Robust and Reconfigurable Waveguide Design in Valley-Topological Phononic Crystals

“…One of our proposed structural changes by translation of a rod array leaves a dimer array at the interface region, which may induce localized mode leading to less energy transfer in the reconfigurable waveguide. We have shown, however, that despite the presence of the localized mode the reconfigurable straight waveguide interface can accommodate wave transmission with the robustness as high as that in the valley topological phononic waveguide without the dimers [8]. Secondly, we also propose a reconfigurable phononic structure in a thin plate for topological elastic waveguide design.…”

Reconfigurable waveguide based on valley topological phononic crystals with local symmetry inversion via continuous translation

“…We examined the transmission analysis for a Z-shaped waveguide that involves two corners, in which a large portion of transmission loss can be attributed to the propagation path, to demonstrate that the robustness can also be preserved by the present scheme of reconfiguration. 39) We arranged 27 × 18 rectangular array of unit cells with C 3v symmetry with two differently oriented rod arrays, a =  30 and mm. The waveguide structure and the pressure field distribution for an incident acoustic wave at 400 kHz are shown in Fig.…”

Acoustic metasurfaces and topological phononics for acoustic/elastic device design

“…11(a). 61) A valley-shaped band structure can be varied by changing the length of the six legs of the snowflake (Δr). These snowflake-like unit cells have been adopted in a variety of studies for PnCs as simple but highly controllable structural units in designing phonon band structures.…”