Flexural wave band-gaps in phononic metamaterial beam with hybrid shunting circuits

Periodic arrays of hybrid-shunted piezoelectric patches are used to control the band-gaps of phononic metamaterial beams. Passive resistive-inductive(RL) shunting circuits can produce a narrow resonant band-gap(RG), and active negative capacitive(NC) shunting circuits can broaden the Bragg band-gaps(BGs). In this article, active NC shunting circuits and passive resonant RL shunting circuits are connected to the same piezoelectric patches in parallel, which are usually called hybrid shunting circuits, to control the location and the extent of the band-gaps. A super-wide coupled band-gap is generated when the coupling between RG and the BG occurs. The attenuation constant of the infinite periodic structure is predicted by the transfer matrix method, which is compared with the vibration transmittance of a finite periodic structure calculated by the finite element method. Numerical results show that the hybrid-shunting circuits can make the band-gaps wider by appropriately selecting the inductances, negative capacitances, and resistances.     

A chiral elastic metamaterial beam for broadband vibration suppression

One of the significant engineering applications of the elastic metamaterial (EMM) is for low-frequency vibration attenuation because of its unusual low-frequency bandgap behavior. However, the forbidden gap from many existing EMMs is usually of narrow bandwidth which limits their practical engineering applications. In this paper, a chiral-lattice-based EMM beam with multiple embedded local resonators is suggested to achieve broadband vibration suppression without sacrificing its load-bearing capacity. First, a theoretical beam modeling is suggested to investigate bandgap behavior of an EMM beam with multiple resonators. New passbands due to dynamic interaction between resonators are unpleasantly formed, which become a design barrier for completely broadband vibration suppression. Through vibration attenuation factor analysis of the resonator, an EMM beam with section-distributed resonators is proposed to enable broadband vibration attenuation function. Required unit number of the resonator in each section is quantitatively determined for complete vibration attenuation in a specific frequency range. Finally, the chiral-lattice-based EMM beam is fabricated, and experimental testing of the proposed structure is conducted to validate the design.     

Flexural wave suppression by an acoustic metamaterial plate

A new acoustic metamaterial plate is presented for the purpose of suppressing flexural wave propagation. The metamaterial unit cell is made of a plate with a lateral local resonance (LLR) substructure which consists of a four-link mechanism, two lateral resonators and a vertical spring. The substructure presents negative Young’s modulus property in certain frequency range. We show theoretically and numerically that two large low-frequency band gaps are obtained with different formation mechanisms. The first band gap is due to the elastic connection with the foundation while the second is induced by the lateral resonances. Besides, four-link mechanisms can transform the flexural wave into the longitudinal vibration which stimulates the lateral resonators to vibrate and to generate inertial forces for absorbing the energy and thus preventing the wave propagation. Frequency response function shows that damping from the vertical spring has little influence on the band gaps, although the damping can smooth the variation of frequency response (see the dotted line in Figs. 10 and 11). Increasing the damping of the lateral resonators may broaden the second band gap but deactivate its effect. This study provides guidance for flexibly tailoring the band characteristics of the metamaterial plate in noise and vibration controls.     

超材料谐振子间的电耦合谐振理论与实验研究

通过将两个金属开口环谐振器口对口地放置, 实现了超材料谐振子间的电耦合谐振. 对电耦合谐振的微波等效电路进行了理论分析和数值计算, 结果表明耦合后的超材料谐振子能产生两个谐振频率, 其中一个随耦合强度的增加逐渐向低频方向移动, 而另一个固定在单谐振子的谐振频率处不变. 微波透射谱的实验测试和电磁仿真结果表明, 两个谐振峰随耦合强度的增加分别向低频和高频方向移动. 分析表明: 低频谐振峰的位置主要是由超材料谐振子间的电耦合强度决定的; 高频谐振偏离单谐振子的谐振频率主要是由不可避免的磁耦合引起的, 而且在耦合间距越小时磁耦合影响越大. 提出的基于超材料谐振子间的电磁耦合实现的双频谐振及其可调性极大地增加了超材料的设计与应用空间.     

Analysis of underwater decoupling properties of a locally resonant acoustic metamaterial coating

This paper presents a semi-analytical solution for the vibration and sound radiation of a semi-infinite plate covered by a decoupling layer consisting of locally resonant acoustic metamaterial. Formulations are derived based on a combination use of effective medium theory and the theory of elasticity for the decoupling material. Theoretical results show good agreements between the method developed in this paper and the conventional finite element method(FEM), but the method of this paper is more efficient than FEM. Numerical results also show that system with acoustic metamaterial decoupling layer exhibits significant noise reduction performance at the local resonance frequency of the acoustic metamaterial, and such performance can be ascribed to the vibration suppression of the base plate. It is demonstrated that the effective density of acoustic metamaterial decoupling layer has a great influence on the mechanical impedance of the system. Furthermore, the resonance frequency of locally resonant structure can be effectively predicted by a simple model, and it can be significantly affected by the material properties of the locally resonant structure.     

Tunable dual-band ferrite-based metamaterials with dual negative refractions

We report on three types of tunable dual-band metamaterial with dual negative refraction in this paper. The three types of metamaterial are composed of ferrite slabs and three different metallic resonators, including split-ring resonators (SRR), Ω-like resonators, and short wire pairs. The ferrite slabs under an applied magnetic bias provide one magnetic resonance frequency band and the three metallic resonators provide another magnetic resonance frequency band, respectively. The continuous wires within the metamaterials provide the negative permittivity in a wide frequency band covering the two magnetic resonance bands. We give the design, analysis and numerical demonstrations of three such types of metamaterial in detail. The effective electromagnetic parameters obtained from the simulated S-parameters indicate that the three types of metamaterial indeed exhibit two negative refraction passbands and the two passbands can also be shifted by changing the magnetic bias. Our results open the way to fabricate tunable dual-band metamaterial cloaks, absorbers, and antennas.     

Elastic waves propagation in thin plate metamaterials and evidence of low frequency pseudo and local resonance bandgaps

A comprehensive numerical simulation study on elastic wave propagation for a novel engineered thin plate metamaterial structural system is presented. To enhance the accuracy of model, a mesh convergence study is validated. The wave dispersion spectra with bandgaps for three types of structures are presented. Based on local resonance phenomena, the low frequency pseudo and local resonance bandgaps are reported. Highlights are also included for the Bragg scattering induced directional bandgaps. The effects of material and geometric parameters on bandgaps are discussed. The finite element based frequency response study further validates the reported bandgaps. The conclusions provide a new perspective for designs and applications of thin plate metamaterials for subwavelength wave manipulation including seismic shielding of civil infrastructures.     

Mechanical detection of carbon nanotube resonator vibrations

Bending-mode vibrations of carbon nanotube resonators were mechanically detected in air at atmospheric pressure by means of a novel scanning force microscopy method. The fundamental and higher order bending eigenmodes were imaged at up to 3.1 GHz with subnanometer resolution in vibration amplitude. The resonance frequency and the eigenmode shape of multiwall nanotubes are consistent with the elastic beam theory for a doubly clamped beam. For single-wall nanotubes, however, resonance frequencies are significantly shifted, which is attributed to fabrication generating, for example, slack. The effect of slack is studied by pulling down the tube with the tip, which drastically reduces the resonance frequency.     

交指电容加载的周期性对称负磁导率人工材料研究

利用二端口网络理论和弗洛奎定理, 详细分析了周期性对称磁谐振人工材料的相对布洛赫磁导率与散射矩阵参数的关系, 利用这个关系提取了四种形式的开口谐振环布洛赫磁导率. 全波仿真和磁导率数值提取结果表明, 在开口谐振环的开口处加载交指电容, 磁谐振频率将显著降低. 这些成果将为提取周期性人工材料的布洛赫磁导率提供理论依据, 同时为小型化磁谐振特异人工材料提供新的设计思路.     

Identifying magnetic response of split-ring resonators at microwave frequencies

In this study we provide experimental methods to identify the magnetic resonance of split ring resonantors (SRR) at the microwave frequency regime. Transmission measurements were performed on both single SRR unit cell and periodic arrays of SRRs. The magnetic response of the SRR structure was demonstrated by comparing the transmission spectra of SRRs with closed ring resonators (CRR). Effects of the changes in the effective dielectric constant of the SRR medium on the band-gaps of SRR are investigated experimentally. SRRs not only exhibit a magnetic resonance band gap but also a band gap due to the electric resonance. Finally, we present the effect of electric coupling to the magnetic resonance of bianisotropic SRRs by utilizing SRRs with different orientations, and incident electromagnetic wave polarizations.     

基于平面超材料的Fano谐振可调谐研究

基于两段相同金属分裂环谐振器构成的单层结构, 从理论及实验方面研究了平面超材料的可调谐Fano谐振. 实验测量了平面超材料对TE和TM入射波的电磁响应, 利用电磁波的入射角度控制Fano谐振的强度, 实现了谐振的开关特性, 谐振频率红移可达到21%. 基于有限元法给出了平面超材料的场分布, 强的正常色散表明平面超材料的电磁响应可类比经典电磁诱导透明现象, 仿真与实验结果相符合. 对称结构超材料Fano谐振的开/关特性为超材料性能的可调谐控制提供了有效途径.     

Numerical and experimental analysis of the vibration and band-gap properties of elastic beams with periodically variable cross sections

The band-gap properties of non-uniform periodic beams are analyzed using numerical and experimental methods. The flexural wave equations are established based on the Euler–Bernoulli and Timoshenko beam theories. The beams with periodically variable cross sections are investigated. The transfer matrix method is used to explore the dynamic behaviors of the periodic beams, that is, the natural frequencies of the finite periodic beams with different cross-section ratios between the adjacent sub-cells and the band-gaps of the infinite periodic beams based on the Bloch theory. The validity and accuracy of the band-gaps acquired by the present method are verified by comparing the results with those obtained from the finite element method and the vibration experiments. The effects of the different lengths of adjacent sub-cells on the band-gap properties are then investigated. The research results and conclusions should be useful in the study of vibration control applications.     

基于石墨烯振幅可调的宽带类电磁诱导透明超材料设计

基于石墨烯的电控特性提出了一种由金属线谐振器和"H"型谐振器组成的宽带可调的类电磁诱导透明(类EIT)超材料结构.首先,利用CST Microwave Studio软件对该超材料结构的透射特性进行了仿真.该结构在1.05—1.46 THz内的透射窗由金属线谐振器的等离子谐振和"H"型谐振器的电感-电容谐振干涉相消引起,且暗模式谐振器的数量增多导致了透射窗带宽的增加.其次,仿真模拟了该结构在不同石墨烯费米能级下的透射特性.当石墨烯费米能级由0 eV逐渐增加到1.5 eV时,该结构透射窗在1.05—1.46 THz内的平均透射振幅由87%逐渐减少到25%,实现了宽带可调.同时,通过仿真模拟该结构在1.26 THz下的电场分布对其透射机理进行了分析,并实验制备了类EIT超材料结构样品,且利用太赫兹时域光谱对样品进行了透射性能测试,测试结果与仿真分析的趋势基本一致.     

局域共振型声学超材料薄板带隙特性的能量解法

研究局域共振型声学超材料的带隙特性时,面临的首要问题是寻求一种带隙特性的高效解法。为此,本文以局域共振型声学超材料薄板为研究对象,提出了一种基于能量泛函变分原理及正交多项式级数展开的带隙计算方法。该方法通过合并基体板及共振子的动、势能及外力功建立元胞的能量泛函,经过变分运算得到元胞的振动控制方程,进而引入第一类Chebyshev正交多项式作为基函数将控制方程进行离散。为克服无法直接对离散控制方程中的广义坐标施加周期边界条件的困难,该方法将连续边界条件弱化到若干选定的配点上以离散方式实现,并将对应的一组线性约束条件通过拉格朗日乘子法施加到系统中。仿真结果表明,该方法具有较高的计算精度和效率,并可应用于"局域共振子-夹层板"等复合结构的带隙特性研究。本文方法为局域共振型薄壁超材料的带隙求解提供了新的思路,丰富了声学超材料的振-声学理论,并为薄壁超材料的工程设计和优化提供了技术支撑。      

Temperature-controlled tunable acoustic metamaterial with active band gap and negative bulk modulus

The local resonant band gap and the negative bulk modulus of the acoustic metamaterial with Helmholtz resonators are strongly affected by the temperature of water. In this paper, the acoustic transmission line method (ATLM) is introduced to investigate the influences of the temperature of water on the local resonant band gap and the negative bulk modulus of the acoustic metamaterial. Results show that the relative variations of the local resonant band gap and the negative effective bulk modulus suffering from the change of the temperature of water are approximately equivalent and are up to about 11%. The reason is that the local resonant frequency is proportional to the sound speed of fluid which is strongly effects by the temperature of water. By achieving the unambiguous relationships between these unusual properties of the acoustic metamaterial and the temperature of water, we find that the temperature-controlled acoustic metamaterial with the active band gap and the active negative bulk modulus can be realized in theory. This idea opens a new avenue for the design of the tunable acoustic metamaterial that can modulate the acoustic wave propagation.     

Double topological edge states investigation in sonic metamaterials

We investigate the topologically protected sound propagation in sonic metamaterials, analogous to quantum spin hall effect (QSHE). The sonic metamaterials consist of circular rods and meta-molecules arranged in air with a honeycomb-lattice. The on-demand inversion in topological phase can be achieved by two ways of scatterer controls at locally resonant frequency and Bragg frequency. The Helmholtz resonators in the structure are contributed to the formation of subwavelength double Dirac cones which are more likely to appear due to local resonance enhancement with more number of resonators. By combining two sonic metamaterials with different topological invariants, we demonstrate the robust sound propagation and pseudospin-dependent one-way acoustic propagation at the interface. Experimental measurement of the topologically protected acoustic wave transmission matches well with the simulation result.     

Wave propagation characterization and design of two-dimensional elastic chiral metacomposite

In this work, a chiral metacomposite is proposed by integrating two-dimensional periodic chiral lattice with elastic metamaterial inclusions for low-frequency wave applications. The plane harmonic wave propagation in the proposed metacomposite is investigated through the finite element technique and Bloch's theorem. Band diagrams are obtained to illustrate wave properties of the chiral metacomposite. Effective dynamic properties of the chiral metacomposite are numerically calculated to explain low-frequency bandgap behavior in the chiral metacomposite. Interestingly doubly negative effective density and modulus of the chiral metacomposite are found in a specific frequency range, where a pass band with negative group velocity is observed. Tuning of the resulting low-frequency bandgaps is then discussed by adjusting microstructure parameters of the metamaterial inclusion and lattice geometry. Specifically design of a metacomposite beam structure for the broadband low-frequency vibration suppression is demonstrated.     

可听声频段的声学超材料

制作了一维周期排列的亥姆霍兹共振器超材料,在空气环境下测试了其在可听声频段声学透射行为.实验结果表明,在2.1—3.5 kHz附近该材料具有透射衰减的吸收峰,利用声传输线理论（ATLM）计算的透射率和实验结果一致,同时由计算的等效阻抗分析可知,实验中出现的吸收峰是由HRs共振的回波反射引起的.另外,实验测试的样品中透射信号分布进一步验证了材料的共振效应,也就是会出现与外加激励反相响应.基于前述的共振模型计算出该材料的等效弹性模量为负. 关键词： 亥姆霍兹共振器 声传输线 吸收峰 等效弹性模量     

一维负磁导率材料中的缺陷效应

理论和实验已经表明，金属开口谐振环（split ring resonators,简称SRR）可以实现材料的有效磁导率μeff在某一频率范围内为负.采用波导法实验研究了不同几何尺寸的六边形SRR在X波段微波作用下的近邻相互作用.实验发现，相同尺寸的六边形SRR周期性排列而成的一维负磁导率材料存在一个谐振频率；当缺陷谐振环引入一维负磁导率材料时，主谐振频率和缺陷环谐振频率同时发生移动；主谐振频率和缺陷环谐振频率的移动量随缺陷与双环谐振频率之差的增加而减小，当缺陷环谐振频率与双环谐振频率接近时，环间的相互作用增强，频率的移动量增大. 关键词： 负磁导率 缺陷效应 开口谐振环