Quasilossless acoustic transmission in an arbitrary pathway of a network

Acoustic metamaterials have exhibited extraordinary potential for manipulating the propagation of sound waves. To date, it has been a challenge to control the propagation of a sound wave through arbitrary pathways in a network. Here, we design a symmetry-breaking, cross-shaped metamaterial comprising Helmholtz resonant cells and a square column. The square column is eccentrically arranged. The sound wave can be transmitted in a quasilossless manner through the channels along the eccentric direction with compressed spaces, which breaks through the general transmission phenomenon. This exotic propagation characteristic is verified by the band structure and the mode of the metamaterial. Two acoustic networks, including a $2\times 2$ network and an $8\times 8$ network, demonstrate the quasilossless propagation of the sound wave along various arbitrarily shaped pathways, which include a Great Wall shape, a stairway shape, and a serpentine shape, by reconfiguring the eccentric directions. This ability opens up a new method for routing sound waves and exhibits promising applications ranging from acoustic communication to energy transmission.

Figure 1

Schematic diagrams of the cross-shaped metamaterial. The white regions represent air, and the blue regions represent the metamaterial and the steel column. The black boundaries represent the contours of the structure. (a) The cross-shaped metamaterial with a centric square steel column; $l_0=45\mathrm{mm},d=25\mathrm{mm}$. (b) The cross-shaped metamaterial with an eccentric square column. The red arrows represent the eccentric direction, $l_e=48\mathrm{mm}$. (c) The unit cell is $a=20\mathrm{mm},b=1\mathrm{mm},c=1\mathrm{mm}$, and $t=1\mathrm{mm}$.

Figure 2

Transmission coefficients and sound pressure field distributions at 3995 Hz. The red arrow represents the eccentric direction. (a), (b) Transmission coefficients of the symmetrical cross-shaped tube without resonant unit cell and the symmetrical cross-shaped metamaterial. The sound wave is incident from the top channel. (c), (d) Transmission coefficients of the symmetry-breaking, cross-shaped tube without resonant unit cell and the symmetry-breaking, cross-shaped metamaterial. The sound wave is incident from the top channel. (e), (f) The sound wave is incident from the left channel. The sound pressure field distributions of six cases at 3995 Hz are plotted in (a)–(f).

Figure 3

Modes of the symmetry-breaking, cross-shaped metamaterial at 3989 Hz (a) and at 4021 Hz (b).

Figure 4

The band structures of the centric cross-shaped metamaterial (a) and the symmetry-breaking, cross-shaped metamaterial (b).

Figure 5

Sound pressure field distributions of a $2\times 2$ network at 3995 Hz. The red arrows represent the eccentric directions. The sound wave is incident from channel 1. (a) The export is channel 4. (b) The export is channel 6. (c) The export is channel 8. (d) The export is channel 2.

Figure 6

Sound pressure field distributions of an $8\times 8$ network at 3995 Hz. (a) The Great Wall-shaped pathway. (b) The stairway-shaped pathway. (c) The serpentine-shaped pathway.