The acoustic scattering is theoretically studied in this paper for three-dimensional spherical cloak composed of unideal pentamode material, for which small shear rigidity is always inevitable for a real designed microstructure. A theoretical formulation is developed to efficiently evaluate the cloaking performance. The generic scattering feature of the cloak and the effects of material imperfectness and inner cloak boundary constraints are systematically examined. The preferable constraint type and the critical imperfectness parameter of the material are identified for possible broadband invisibility. In addition, a very practical lining shell scheme is proposed to tune the constraint strength on the inner boundary. By combining the theoretical model with optimization algorithm, it is further proved that the cloak can be reduced by several piecewise-uniform layers and optimized to achieve excellent invisibility in targeted frequency bands. The study will provide valuable guidance for the future microstructural design of cloaks.

中文翻译：

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非理想五模态材料球形球形披风的散射分析与优化

本文从理论上研究了由不理想的五峰材料构成的三维球形披风的声散射，对于实际设计的微结构而言，始终不可避免地需要较小的剪切刚度。开发了一种理论公式来有效评估隐身性能。系统地检查了披风的一般散射特征以及材料不完善性和披风内部边界约束的影响。确定了材料的最佳约束类型和关键不完美参数，以实现可能的宽带隐身效果。此外，提出了一种非常实用的衬壳方案来调整内部边界上的约束强度。通过将理论模型与优化算法结合起来，进一步证明，该斗篷可以减少多个分段均匀的层并进行优化，以在目标频带中实现出色的隐身性。该研究将为斗篷的未来微结构设计提供有价值的指导。