Department of Mechanical Engineering, The University of British Columbia, 6250 Applied Science Lane, Vancouver, BC V6T1Z4 Canada.
J Acoust Soc Am. 2013 Sep;134(3):1950-9. doi: 10.1121/1.4817894.
Periodic composites such as acoustic metamaterials use local resonance phenomenon in designing low frequency sub-Bragg bandgaps. These bandgaps emerge from a resonant scattering interaction between a propagating wave and periodically arranged resonators. This paper develops a receptance coupling technique to combine the dynamics of the resonator with the unit cell dynamics of the background medium to analyze flexural wave transmission in a periodic structure, involving a single degree of freedom coupling between the medium and the resonator. Receptance techniques allow for a straightforward extension to higher dimensional systems with multiple degrees of freedom coupling and for easier experimental measurements. Closed-form expressions for the location and width of sub-Bragg bandgaps are obtained. Rigid body modes of the unit cell of the background medium are shown to set the bounding frequencies for local resonance bandgaps. Results from the receptance analysis compare well with Bloch wave analysis and experiments performed on a finite structural beam with periodic masses and resonators. Stronger coupling and inertia of the resonator increase the local resonance bandgap width. Two-fold periodicity widens the Bragg bandgap, narrowed by local resonators, thus expanding the design space and highlighting the advantages of hierarchical periodicity.
周期性复合材料（如声超材料）利用局部共振现象设计低频亚布拉格带隙。这些带隙源于传播波与周期性排列的谐振器之间的共振散射相互作用。本文开发了一种接受耦合技术，将谐振器的动力学与背景介质的单元胞动力学相结合，分析周期性结构中的弯曲波传输，涉及介质和谐振器之间的单自由度耦合。接受技术允许轻松扩展到具有多个自由度耦合的更高维系统，并且更便于进行实验测量。获得了亚布拉格带隙的位置和宽度的封闭形式表达式。显示背景介质单元胞的刚体模态为局部共振带隙的边界频率。接受分析的结果与 Bloch 波分析和在具有周期性质量和谐振器的有限结构梁上进行的实验吻合良好。谐振器的更强耦合和惯性增加了局部共振带隙的宽度。两倍周期性拓宽了由局部谐振器缩小的布拉格带隙，从而扩展了设计空间，并突出了分层周期性的优势。
