Acoustic metamaterials are a class of artificially periodic structures with extraordinary elastic properties that cannot be easily found in naturally occurring materials and can be applied to regulate the sound propagation behavior. The fractal configuration can be widely found in the acoustic system, like characterizing the broadband or multi-band sound propagation. This work will engineer three-dimensional (3D) labyrinthine fractal acoustic metamaterials (LFAMs) to regulate the sound propagation on subwavelength scales. The dispersion relations of LFAMs are systematically analyzed by the Bloch theory and the finite element method (FEM). The multi-bands, acoustic modes, and isotropic properties characterize their acoustic wave properties in the low-frequency regime. The effective bulk modulus and mass density of the LFAMs are numerically calculated to explain the low-frequency bandgap behaviors in specific frequencies. The transmissions and pressure field distributions of 3D LFAMs have been used to measure the ability for sound suppression. Furthermore, when considering the thermo-viscous loss on the transmission properties, the high absorptions occur within the multi-band range for low-frequency sound. Hence, this research contributes to potential applications on 3D LFAMs for multi-bands blocking and/or absorption on deep-subwavelength scales.

中文翻译：

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具有低频多频带声音抑制功能的三维迷宫式分形声学超材料

声学超材料是一类具有非凡弹性特性的人工周期性结构，在天然材料中不易发现，可用于调节声音的传播行为。分形配置可以在声学系统中找到，就像表征宽带或多频带声音传播一样。这项工作将设计三维（3D）迷宫形分形声学超材料（LFAM），以调节亚波长范围内的声音传播。通过Bloch理论和有限元方法（FEM）系统地分析了LFAM的色散关系。多频带，声模和各向同性特性表征了低频状态下的声波特性。通过数值计算LFAM的有效体积模量和质量密度，以解释特定频率下的低频带隙行为。3D LFAM的透射率和压力场分布已用于测量声音抑制的能力。此外，当考虑到热粘性损失的传输特性时，在低频声音的多频带范围内会发生高吸收。因此，这项研究有助于3D LFAM在深亚波长尺度上进行多波段阻塞和/或吸收的潜在应用。当考虑热粘滞损耗对传输特性的影响时，在低频声音的多频带范围内会发生高吸收。因此，这项研究有助于3D LFAM在深亚波长尺度上进行多波段阻塞和/或吸收的潜在应用。当考虑热粘性损失对传输特性的影响时，在低频声音的多频带范围内会发生高吸收。因此，这项研究有助于3D LFAM在深亚波长尺度上进行多波段阻塞和/或吸收的潜在应用。