Inspired by fractal photonic/phononic crystals, the self-similar fractal technique is applied to design acoustic metamaterial. By replacing the straight channel of coiling up space with a smaller coiling up space, a class of topological architectures with fractal coiling up space is developed. The significant effect of the fractal-inspired hierarchy on the band structure with fractal coiling up space is systematically investigated. Furthermore, sound wave propagation in the acoustic metamaterial with the fractal coiling up space is comprehensively highlighted. Our results show that the acoustic metamaterial with higher-order fractal coiling up space exhibits deep subwavelength bandgaps, in which the sound propagation will be well blocked. Thus, this work provides insights into the role of the fractal hierarchy in regulating the dynamic behavior of the acoustic metamaterial and provides opportunities for the design of a robust filtering device in a subwavelength scale.

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