Fig. 1: Type-II nodal rings induced by fluid-solid interaction.
From: Topological phononics arising from fluid-solid interactions
a Perspective and cross-sectional views of the 3D phononic crystal, formed with identical aluminum plates with circular through holes immersed in water. The phononic crystal belongs to the space group P4/mmm (No. 123). Inset: schematic of the first Brillouin zone (FBZ). The red dashed square indicates a single unit cell (z direction not shown). The in-plane lattice constant a0 = 3 mm, the diameter of holes d0 = 2 mm, the thickness of plates tm = 2 mm, the separation of plates tw = 2 mm, corresponding to out-of-plane lattice constant az = tm + tw = 4 mm. b Calculated band structure along high-symmetry directions in FBZ. The dots indicate the crossings of the 1st and 2nd bands, with different colors indicating different nodal rings. Inset: Enlarged view of the bands around Γ point, where the four bands are identified as flexural Lamb (FL) modes, waterborne guided (WG) modes, shear horizontal (SH) modes, and extensional Lamb (EL) modes, respectively. c Distribution of the nodal rings in the FBZ. The colors of the nodal rings the same as the corresponding dots in (b). d Spectral variations of the three nodal rings. e 3D band structures of the first two modes on specified cross sections of the FBZ. Nodal rings formed by their crossings are denoted.
