声学超材料等几何拓扑优化及弹性波调控

Acoustic metamaterials are a kind of artificially designed and manufactured composite structure，which can exhibit extraordinary physical properties in the subwavelength frequency range such as negative effective density and negative bulk modulus, and have broad application prospects in mechanical, civil and other fields. The specific physical properties of acoustic metamaterials and the effective manipulation of elastic waves can be achieved through the topology optimization of the microstructure. In topology optimization based on isogeometric analysis, the exactly geometric model is utilized to achieve the effective integration of design, analysis and optimization, which avoids the geometric discrete errors and complex data exchange in the finite element method. However, the theory of isogeometric topology optimization of acoustic metamaterials has not been established. Therefore, by using isogeometric analysis and trimming technique, this project aims to develop the isogeometric topology optimization theory of acoustic metamaterials. Material and structure of microstructures are optimized to reveal the influence of microstructure topology variation on band structure of acoustic metamaterials. Considering the viscoelastic effect, the internal relation between attenuation characteristics and directional bandgap in the multiphase acoustic metamaterials is exposed. The local resonant unit is introduced to analyze topology evolution of the connecting phase between resonant unit and matrix in the multiphase viscoelastic acoustic metamaterial microstructure, and to uncover the changing mechanism of effective physical properties and wave characteristics of acoustic metamaterials. So that the active manipulation of elastic wave propagation can be realized. This research provides significant theoretical basis and methodological guidance for design and application of acoustic metamaterials.

声学超材料是一种人工设计、制造的复合结构材料，在亚波长频段可具备负密度、负模量等超常物理属性，在机械、土木等领域有着广泛的应用前景。通过微结构的拓扑优化设计，声学超材料可实现特定的物理属性及有效的弹性波调控。基于等几何分析的拓扑优化，采用精确几何模型，做到设计、分析与优化的有效集成，避免有限元的几何离散误差和复杂数据交互。然而声学超材料的等几何拓扑优化理论尚未建立。因此，本项目拟采用等几何分析，结合裁剪技术，建立声学超材料等几何拓扑优化理论；优化微结构的材料组成和结构特征，揭示拓扑构型变化对声学超材料能带结构的影响机理；考虑粘弹性效应，明确多相声学超材料弹性波衰减特性与方向带隙的内在关联；引入局域共振单元，分析多相粘弹性声学超材料微结构共振单元与基体之间连接相的拓扑演变，阐释等效物理属性及波动特性的变化机理；进而实现弹性波传播的主动调控，为声学超材料的设计与应用提供重要的理论基础和方法指导

声学超材料是一种人工设计、制造的复合结构材料，在亚波长频段可具备负密度、负模量、负折射率等超常物理属性，在国防及民用工业的各个领域有着广泛的应用前景。通过对微结构的拓扑优化设计，声学超材料可获得特定的物理属性，进而实现对弹性波传播、衰减、带隙等特性的有效调控。本项目基于等几何分析理论，结合局部裁剪算法，实现了微结构复杂拓扑优化模型的精确、高效构建，发展了适用于声学超材料的能带显式分析方法，完善了声学超材料的等几何拓扑优化理论；通过优化微结构的材料组成和结构特征，研究了拓扑构型变化对声学超材料能带结构的影响规律，揭示了多相粘弹性声学超材料拓扑构型的演变、衰减特性与方向带隙的内在关联，实现了弹性波的定向传播与调控；提出了具有宽频负等效密度的局域共振型多相粘弹性声学超材料，阐释了微结构拓扑演变、局域共振特性、衰减系数对超材料物理属性、波动特性的影响机理，实现了声学超材料中弹性波传播的主动调控，为声学超材料的设计与应用提供了重要的理论基础和方法指导。