声学超材料板的弯曲波带隙与减振降噪特性

Flexural Wave Band Gaps and Vibration Attenuation Characteristics of Acoustic Metamaterial Plates

利用周期结构的波传播理论和有限元法相结合的方法计算了含双层柱状局域共振结构的声学超材料板的能带结构图,分析了晶格常数的变化对超材料板的带隙特性的影响。研究发现:晶格常数的变化会影响基板和柱体的振动耦合作用,对超材料板的带隙特性产生显著影响。通过对比不同算例,分别得到了限定或不限定局域共振结构附加质量比条件下,晶格常数对带隙的调控规律,研究表明选择适中的晶格常数,可以增大带隙的归一化宽度。此外还进一步仿真计算了超材料板在力激励下的振动与声辐射特性,结果表明在带隙频率范围内,超材料板具有良好的低频宽带减振降噪效果。论文研究为基于带隙理论的板类结构的低频宽带减振降噪设计提供了有益参考。

The energy band structure diagram of an acoustic metamaterial plate with a double cylindrical local resonance structure was calculated by the combination of finite element method and wave propagation theory of periodic structures. The influence of the lattice constant variation on the band gaps of the metamaterial plate was analyzed. It was found that the change of lattice constants can affect the vibration coupling between substrate and the cylinders, which have a significant influence on the band gaps. Then, through the comparison of results of different examples, the regulation of influence of lattice constants on the band gaps was obtained with or without considering the additional mass ratio of the local resonance structures. The study showed that selection of a moderate lattice constant can increase the normalized width of the band gaps. In addition, the vibration and acoustic radiation characteristics of the metamaterial plate under the force excitation were calculated. The results indicated that the metamaterial plate has a good performance on low frequency broadband vibration attenuation and noise reduction in the band gaps. The paper has also provided a useful reference for the design of low frequency broadband vibration and noise reduction based on bandgap theory.