In this paper, dynamic effective parameters of mass-type and stiffness-type bilayer perforated thin-plate acoustic metamaterials (MBPM and SBPM) are investigated by simulations and experiments. Dynamic effective parameters are calculated by the retrieval method, and formation mechanisms of special effective parameters are analyzed by simulated fields. Divergent effective parameters are produced by anti-resonances of coupled perforations or coupled perforated thin-plates, zero effective parameters are produced by resonances of coupled perforated thin-plates. The impacts of perforation parameters on dynamic effective parameters for symmetric and asymmetric BPMs are systemically studied, the simulated and experimental results both show that variation trends of resonance and anti-resonance frequencies of mass-type bilayer perforated thin-plate acoustic metamaterial (MBPM) are different from stiffness-type bilayer perforated thin-plate acoustic metamaterial (SBPM), because perforations mainly change system mass in MBPM and system stiffness in SBPM, respectively. Dynamic effective parameters are bi-anisotropic in asymmetric BPM, and doubly negative effective parameters are achieved by coupled perforations when plan wave normal incident from the side with smaller perforation parameters. A modified retrieval method is proposed to calculate unified effective parameters for the asymmetric BPM, and the unified effective parameters equal to averaged effective parameters of two symmetric BPMs. This work systematically studies dynamic effective parameters of bilayer perforated structures, which has a great guiding significance in design of perforated acoustic devices.

中文翻译：

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双层穿孔薄板声学超材料动态有效参数研究

本文通过模拟和实验研究了质量型和刚度型双层穿孔薄板声学超材料（MBPM和SBPM）的动态有效参数。采用反演方法计算动态有效参数，通过模拟场分析特殊有效参数的形成机制。耦合穿孔或耦合穿孔薄板的反共振产生发散有效参数，耦合穿孔薄板的共振产生零有效参数。系统研究了射孔参数对对称和非对称BPM动态有效参数的影响，仿真和实验结果均表明，质量型双层穿孔薄板声超材料（MBPM）的共振频率和反共振频率变化趋势与刚度型双层穿孔薄板声超材料（SBPM）不同，因为穿孔主要改变 MBPM 中的系统质量和 SBPM 中的系统刚度，分别。非对称BPM动态有效参数是双各向异性的，当平面波法向从射孔参数较小的一侧入射时，通过耦合射孔实现双负有效参数。提出了一种改进的检索方法来计算非对称BPM的统一有效参数，统一有效参数等于两个对称BPM的平均有效参数。