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力-力偶型振子超材料梁带隙特性研究

A STUDY ON THE BAND GAP CHARACTERISTICS OF METAMATERIAL BEAMS WITH FORCE-MOMENT RESONATORS

  • 摘要: 弹性波超材料是一类由阵列化的人工微结构单元构筑的复合结构/材料, 具有传统材料所不具备的一些超常物理性质, 这些超常性质主要由微结构胞元(局域共振单元)决定. 针对弯曲波超材料梁, 根据局域共振单元与基体梁之间的作用力, 可以将其分为力型振子、力偶型振子、力-力偶型振子超材料梁. 目前多数研究聚焦于力型振子, 对力-力偶型振子超材料梁的带隙特性及其机理仍缺乏深入理解. 基于此, 本文以悬臂梁构造力-力偶型振子, 研究力-力偶型振子超材料梁的能带结构和带隙性质. 当梁型振子呈对称布置时, 可将其等效为解耦的力-力偶型振子, 并建立二者之间的具体参数关系, 通过其带边频率方程与相应的胞元固有频率分析阐述了解耦的力-力偶型振子超材料梁的带隙形成机理, 同时推导出局域共振带隙的近似预测公式. 对于非对称布置的梁型振子, 其表现为耦合的力-力偶型振子. 通过引入非对称因子, 系统研究了耦合效应对能带结构及带隙的影响, 并揭示了带隙转化与带隙耦合现象, 上述结论得到实验很好的验证. 本研究加深了对力-力偶型振子超材料的理解, 为超材料梁的优化设计与工程应用提供了理论指导.

     

    Abstract: Elastic wave metamaterials are a class of composite structures or materials composed of artificially designed microstructural units arranged in periodic arrays. These materials exhibit extraordinary physical properties not found in conventional materials, which are primarily determined by the microstructural resonators (local resonance units). For flexural wave metamaterial beams, the local resonance units can be classified into three types based on their interaction forces with the host beam: force-type resonators, moment-type resonators, and force-moment coupled resonators. Currently, most research focuses on force-type resonators, while the bandgap characteristics and underlying mechanisms of metamaterial beams with force-moment coupled resonators remain insufficiently understood. To address this gap, this study employs cantilever beams to construct force-moment coupled resonators and investigates their band structures and bandgap properties. When the beam-type resonators are symmetrically arranged, they can be equivalently treated as decoupled force-moment resonators. The specific parameter relationships between them are established, and the band gap formation mechanism of metamaterial beams with decoupled force-moment resonators is elucidated through their band-edge frequency equations and natural frequency analysis of the corresponding unit cell. An approximate prediction formula for the local resonance band gap generated by metamaterial beams with decoupled force-moment resonators is also derived. In contrast, asymmetrically arranged beam-type resonators exhibit coupled force-moment interactions. By introducing an asymmetry factor, this work systematically examines the influence of coupling effects on the band structure and bandgap properties, revealing phenomena such as bandgap transition and bandgap coupling. The above conclusions were validated through experimental verification. This research enhances the understanding of metamaterial beams with force-moment coupled resonators and provides theoretical guidance for the optimized design and engineering applications of metamaterial beams. The findings contribute to a deeper insight into the interplay between force and moment interactions in metamaterial beams, paving the way for advanced vibration and wave control in structural systems.

     

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