Drawing upon the advantages of lightweight nature and highly efficient energy harvesting capabilities, acoustic black holes (ABHs) serve as local resonator units with significant potential in constructing phononic plates. In this paper, we introduce a novel composite ABH structure made of different materials, and extends this composite concept to the infinite plate model. Analytical results reveal that the composite ABH exhibits a stronger local resonance effect and more localized trapped modes compared to traditional homogeneous types. By employing linear algebraic equation systems derived from boundary conditions and utilizing the closed-form solutions of the varying-thickness Kirchhoff plate, we compare the wave propagating behaviors of different ABH scatterers. Numerical results highlight that the enhanced trapped modes resulting from material inhomogeneity lead to more pronounced peaks in scattering energy. Moreover, we address the multiple scattering problem for composite ABH array in the infinite plate using the -matrix relationship between the scattering and exciting energy. Displacement spectra and wave field results demonstrate that the larger impedance mismatch and increased interaction caused by periodic composite ABHs in the plate result in more effective vibration isolation. Our discussion on array configurations concludes that the ABH square array, incorporating both rows and columns, produces a significant bandgap for flexural vibration, while also expanding the larger and more efficient vibration-attenuated region.

中文翻译：

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钢板中复合ABHs的散射和阻波特性


声学黑洞（ABH）利用轻质特性和高效能量收集能力的优势，作为局部谐振器单元，在构建声子板方面具有巨大潜力。在本文中，我们介绍了一种由不同材料制成的新型复合ABH结构，并将这种复合概念扩展到无限板模型。分析结果表明，与传统的均质类型相比，复合 ABH 表现出更强的局部共振效应和更多的局域捕获模式。通过采用从边界条件导出的线性代数方程组并利用变厚度基尔霍夫板的闭式解，我们比较了不同 ABH 散射体的波传播行为。数值结果强调，材料不均匀性导致的增强的捕获模式导致散射能量的峰值更加明显。此外，我们利用散射和激发能量之间的矩阵关系解决了无限板中复合ABH阵列的多重散射问题。位移谱和波场结果表明，板中周期性复合 ABH 导致更大的阻抗失配和增加的相互作用，从而实现更有效的隔振。我们对阵列配置的讨论得出的结论是，ABH 方形阵列结合了行和列，为弯曲振动产生了显着的带隙，同时还扩展了更大、更有效的振动衰减区域。