Hilbert fractal acoustic metamaterials with negative mass density and bulk modulus on subwavelength scale

Abstract

Acoustic metamaterials (AMs) are artificially engineered composite materials, structured to have unconventional effective properties for flexibly manipulating the wave propagation, which can produce a broad range of applications such as sound cloaking and tunneling. In nature, bio-inspired fractal organization with multiple length scales has been found in various biological materials, which display enhanced dynamic properties. By introducing Hilbert curve channels, this work will design a class of topological architectures of Hilbert fractal acoustic metamaterials (HFAMs) with negative mass density and bulk modulus on subwavelength scale. In this paper, we will highlight the influences of the self-similar fractal configurations on multipole modes of HFAM. To further demonstrate multipole resonances, the pressure magnifications are assessed in the center region of HFAM with losses. Moreover, based on effective medium theory, we systematically calculate and investigate effective bulk modulus and mass density, as well as density-near-zero of HFAM, to demonstrate the negative properties and the zero-phase-difference effects of HFAMs. Numerical results show that HFAM can enable a number of applications, from sound blocking, quarter bending, sound cloaking to sound tunneling, and may further provide a possibility for the engineering guidances of the exotic properties on subwavelength scale. Keywords: Hilbert fractal acoustic metamaterials, Negative mass density, Negative bulk modulus, Sound blocking, Zero-phase-difference