Labyrinth acoustic metamaterials with fractal structure based on Hilbert curve

Acoustic metamaterials can break the law of mass and manipulate acoustic wave propagation with a deep subwavelength structure. We designed a labyrinthine acoustic metamaterial with ultra-high refractive index fractal structure based on the construction method of Hilbert curve, which is capable of acoustic wave control in the deep subwavelength range. Simulation by finite element software reveals that the band gap moves to lower frequencies as the fractal level increases. The transmission characteristics analysis shows that stable acoustic isolation performance can be obtained at the frequency points of monopole resonance (800 Hz) and dipole resonance (1520 Hz), and the isolation performance at this point shows strong stability to very small filling rates or small displacements. In addition, the designed second-order acoustic metamaterial can achieve sound cloaking and sound supertunneling.