Chen Hongfang, Fu Yu, Ling Ling, Hu Yujin, Li Li
State Key Lab of Intelligent Manufacturing Equipment and Technology, School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China.
Materials (Basel). 2024 Jul 20;17(14):3591. doi: 10.3390/ma17143591.
Locally Resonant Acoustic Metamaterials (LRAMs) have significant application potential because they can form subwavelength band gaps. However, most current research does not involve obtaining LRAMs with specified band gaps, even though such LRAMs are significant for practical applications. To address this, we propose a parameterized level-set-based topology optimization method that can use multiple materials to design LRAMs that meet specified frequency constraints. In this method, a simplified band-gap calculation approach based on the homogenization framework is introduced, establishing a restricted subsystem and an unrestricted subsystem to determine band gaps without relying on the Brillouin zone. These subsystems are specifically tailored to model the phenomena involved in band gaps in LRAMs, facilitating the opening of band gaps during optimization. In the multi-material representation model used in this method, each material, except for the matrix material, is depicted using a similar combinatorial formulation of level-set functions. This model reduces direct conversion between materials other than the matrix material, thereby enhancing the band-gap optimization of LRAMs. Two problems are investigated to test the method's ability to use multiple materials to solve band-gap optimization problems with specified frequency constraints. The first involves maximizing the band-gap width while ensuring it encompasses a specified frequency range, and the second focuses on obtaining light LRAMs with a specified band gap. LRAMs with specified band gaps obtained in three-material or four-material numerical examples demonstrate the effectiveness of the proposed method. The method shows great promise for designing metamaterials to attenuate specified frequency spectra as required, such as mechanical vibrations or environmental noise.
局部共振声学超材料（LRAMs）具有显著的应用潜力，因为它们可以形成亚波长带隙。然而，目前大多数研究并未涉及获得具有特定带隙的LRAMs，尽管这种LRAMs在实际应用中具有重要意义。为了解决这个问题，我们提出了一种基于参数化水平集的拓扑优化方法，该方法可以使用多种材料来设计满足特定频率约束的LRAMs。在这种方法中，引入了一种基于均匀化框架的简化带隙计算方法，建立了一个受限子系统和一个非受限子系统，以在不依赖布里渊区的情况下确定带隙。这些子系统经过专门设计，用于对LRAMs中带隙所涉及的现象进行建模，便于在优化过程中打开带隙。在该方法使用的多材料表示模型中，除基体材料外，每种材料都使用类似的水平集函数组合公式进行描述。该模型减少了基体材料以外的材料之间的直接转换，从而增强了LRAMs的带隙优化。研究了两个问题，以测试该方法使用多种材料解决具有特定频率约束的带隙优化问题的能力。第一个问题是在确保带隙宽度涵盖指定频率范围的同时使其最大化，第二个问题是获得具有特定带隙的轻质LRAMs。在三材料或四材料数值示例中获得的具有特定带隙的LRAMs证明了所提方法的有效性。该方法在设计超材料以根据需要衰减特定频谱（如机械振动或环境噪声）方面显示出巨大的潜力。
