Coiling up space acoustic metamaterial with Hilbert fractal in a subwavelength scale

Abstract

Acoustic metamaterials have exhibited wonderful engineering application prospects due to their excellent physical characteristics. Inspired by great successes of the self-similar fractal technique in the design of biomimetic materials, the Hilbert fractal structure is applied to the design of the subwavelength coiling up space acoustic metamaterial. Namely, the curl propagation channel of the sound wave is a Hilbert fractal curve. Thus, the propagation length of the sound wave is greatly multiplied, and the effective fluid particle in the acoustic metamaterial is ultraslow. The numerical results show that with the increase of the order of the Hilbert fractal curve, the lowest bandgap whose normalized frequency is much less than 1 gradually move the lower frequency range. Furthermore, with the increase of the order of the Hilbert fractal curve, the number and the total width of bandgaps gradually increase. Thus, the coiling up space acoustic metamaterial with Hilbert fractal can be used to design the subwavelength and multi-bandgaps acoustic filter.