南京大学学报(自然科学版) ›› 2017, Vol. 53 ›› Issue (1): 69–.

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密度为零的零折射率声学超材料研究

蓝 君1,李义丰1,2*   

  • 出版日期:2017-01-19 发布日期:2017-01-19
  • 作者简介:1.南京工业大学计算机科学与技术学院,南京,211800;2.近代声学教育部重点实验室,南京大学声学研究所,南京,210093
  • 基金资助:
    基金项目:国家自然科学基金(61571222,11104142),江苏省六大人才高峰高层次人才项目,江苏省青蓝工程人才项目 收稿日期:2016-09-14 *通讯联系人,E­mail:lyffz4637@163.com

Research on zero density acoustic metamaterial with refractive index of zero

Lan Jun1,Li Yifeng1,2*   

  • Online:2017-01-19 Published:2017-01-19
  • About author:1.College of Computer Science and Technology,Nanjing Tech University,Nanjing,211800,China;2.Key Laboratory of Modern Acoustics,MOE,Institute of Acoustics,Nanjing University,Nanjing,210093,China

摘要: 以普通波导管内部嵌入弹性薄膜为基本单元结构,构造了零折射率声学超材料.研究表明,在频率为fm=453.64 Hz时能实现等效质量密度为零的零折射率超材料.在零折射率超材料两端接上截面积较大的普通波导管构造了复合零折射率超材料,利用声传输线理论和声阻抗匹配理论,分析了该复合超材料中能量传输和轴向声压分布情况.理论和仿真结果表明:尽管在零折射率超材料与普通波导管之间存在极大的几何不匹配,系统在输入声波频率为fm和Fabry­Pérot(FP)共振频率时能实现声波完全传输,且在频率fm处具有相位超耦合和传输增强等特性.除此之外,当改变复合超材料中零折射率超材料的长度D和弯曲角度θ时,发现其在频率为fm时所具有的特性不变,而FP共振频率的大小会随零折射率超材料长度的变化而改变.

Abstract: An acoustic metamaterial with a refractive index of zero(RIZ)is constructed by using an interspaced array of thin elastic membranes which located along a normal waveguide.Theoretical analyses exhibit that the RIZ metamaterial with only effective mass density being zero can be achieved at the characteristic frequency fm =453.64 Hz.A composite metamaterial system is designed,in which the acoustic RIZ metamaterial is placed in the middle and two large cross­section normal waveguide are connected on the both sides.With the uses of acoustic transmission line method and impedance match theory,the acoustic energy transmission and acoustic pressure distribution along axial direction of the system are discussed.Theoretical derivations and numerical simulations show that there are two kinds of characteristic frequencies,which are the special frequency fm and Fabry­Pérot(FP)resonant frequencies,respectively,and at these frequencies the acoustic wave can realize total transmission through the RIZ metamaterial,despite there is a strong geometrical mismatch at the connections between the RIZ metamaterial and the normal waveguides.Moreover,the properties of phase super coupling and transmission enhancement are achieved at the frequency fm in the system and these properties are independent of the length and bend degree of RIZ metamaterial.However,the FP resonant frequencies are changed with the variation of the RIZ metamaterial length.

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