局域共振复合单元声子晶体结构的低频带隙特性研究

本文提出了一种新型局域共振复合单元声子晶体结构, 并结合有限元方法对结构的带隙机理及低频共振带隙特性进行了分析和研究. 共振带隙产生的频率位置由所对应的局域共振模态的固有频率决定, 并且带隙宽度与局域共振模态的品质因子及其与基体之间的耦合作用强度有关. 采用局域共振复合单元结构可以实现声子晶体的多重共振, 在低频范围能打开多条共振带隙, 但受到共振单元排列方式的的影响. 由于纵向和横向局域共振模态的简并, 复合单元结构能在200 Hz以下的低频范围打开超过60%宽度的共振带隙, 最低带隙频率低至18 Hz. 这为声子晶体结构获得低频、超低频带隙提供了一种有效的方法. 关键词： 局域共振 低频带隙 复合单元 声子晶体     

Flexural vibration band gaps in thin plates with two-dimensional binary locally resonant structures

The complete flexural vibration band gaps are studied in the thin plates with two-dimensional binary locally resonant structures, i.e. the composite plate consisting of soft rubber cylindrical inclusions periodically placed in a host material. Numerical simulations show that the low-frequency gaps of flexural wave exist in the thin plates. The width of the first gap decreases monotonically as the matrix density increases. The frequency response of the finite periodic thin plates is simulated by the finite element method, which provides attenuations of over 20dB in the frequency range of the band gaps. The findings will be significant in the application of phononic crystals.     

一维光子晶体光学特性的复平面波展开法研究

应用复平面波展开法对一维光子晶体的光子带隙, 透射特性进行了分析. 通过对色散关系和透射系数的数值计算发现一维光子晶体周期结构个数以及折射率分布对光学晶体透射系数以及光子带隙的影响. 对于含有整数个周期结构的光子晶体有共振点出现在光子帯隙外的频率范围内, 共振点的个数比周期结构个数少1. 带隙倾斜斜率等于折射率的比值. 折射率比值越大, 带隙的范围越大.     

一种多频局域共振型声子晶体板的低频带隙与减振特性

设计了一种多频局域共振型声子晶体板结构, 该结构由一薄板上附加周期性排列的多个双悬臂梁式子结构而构成. 由于多个双悬臂梁式子结构的低频振动与薄板振动的相互耦合作用, 这种局域共振型板结构可产生多个低频弯曲波带隙(禁带); 带隙频率范围内的板弯曲波会被禁止传播, 利用带隙可以实现对薄板的多个目标频率处低频减振. 本文针对这种局域共振型板结构进行了简化, 并基于平面波展开法建立了其弯曲波带隙计算理论模型; 基于该模型, 结合具体算例进行了带隙特性理论分析. 设计、制备了一种存在两个低频弯曲波带隙的局域共振型板结构样件, 通过激光扫描测振仪测试证实该结构存在两个低频带隙, 在带隙频率范围的板弯曲振动被显著衰减.     

Boundary element method for calculation of elastic wave transmission in two-dimensional phononic crystals

A boundary element method (BEM) is presented to compute the transmission spectra of two-dimensional (2-D) phononic crystals of a square lattice which are finite along the x-direction and infinite along the y-direction. The cross sections of the scatterers may be circular or square. For a periodic cell, the boundary integral equations of the matrix and the scatterers are formulated. Substituting the periodic boundary conditions and the interface continuity conditions, a linear equation set is formed, from which the elastic wave transmission can be obtained. From the transmission spectra, the band gaps can be identified, which are compared with the band structures of the corresponding infinite systems. It is shown that generally the transmission spectra completely correspond to the band structures. In addition, the accuracy and the efficiency of the boundary element method are analyzed and discussed.     

基于集中质量法的一维声子晶体弹性波带隙计算

通过将一维声子晶体中的原胞简化为有限多个自由度的弹簧振子结构，引入了一种基于集中 质量法的一维声子晶体弹性波带隙计算方法.与传统平面波展开法相比，该方法的计算结果 与之相符合，而且在收敛性方面较之有很大改善.通过使用集中质量法，可在得到同样计算 精度的条件下，显著降低计算量，提高计算速度. 关键词： 声子晶体 弹性波带隙 集中质量法 平面波展开法     

二维声表面波压电声子晶体在射频段的时域有限差分法

对二维声表面波压电声子晶体在射频段的带隙特性,进行了时域有限差分法(FDTD)理论推导和计算,并提出实验方法对比验证。FDTD计算模型考虑了压电效应,引入周期边界条件以节省计算空间和时间,采用完全匹配层以解决声表面波在截断边界处的虚拟反射问题。实验上分别设计有/无二维压电声子晶体的两种宽频带延迟线结构,测量两种延迟线的传输系数取差值,得到了二维压电声子晶体的带隙;其中通过时域加窗函数保留一次传输信号,进行干扰信号的去除。以铝/128°YX-LiNbO3二维压电声子晶体为例,该FDTD方法、商业有限元软件COMSOL、实验方法均得到了100500 MHz射频段内的多个带隙,三种带隙对比证明了FDTD计算带隙与实验测量带隙一致,比COMSOL计算的计算带隙精度更高。      

Propagation characteristics of the laser-generated lower-order lamb waves in one-dimensional periodic thin plates

Using the finite element method (FEM), we study the thermoelastic generation and the transmitted power spectra (TPS) of Laser-generated lower-order Lamb wave mode in an one-dimensional thin aluminum plate engraved by a periodic rectangular grating. The calculation verified that the equally good Lamb waves band gaps can also exist in an one-component periodic structure and the width and location of the band gaps can be regulated by the parameters of the depth of the grooves (h), the ratio of the lattice period to the plate thickness (D/L) and the ratio of the width of the grooves to the lattice period (d/D). Specially, we suggest that Lamb wave band gaps can be substantially enlarged by using multiple periodic systems which consist of several pieces of periodic structure with different D/L.     

Ultrasonic band gaps and negative refraction

The first experimentally observed ultrasonic band gaps in periodic bidimensional composited are reviewed here. The studied basic structure consists of an aluminum alloy plate with a periodic arrangement of cylindrical holes filled with mercury. Localization phenomena in linear and point defects have been observed and an ultrasonic waveguide capable to bend the ultrasonic radiation by 90 degrees has been achieved. We also revisit twinned-square periodic structures for ultrasonic wave bending and splitting. Such devices allow 45 degrees bending of waves, whereas an extreme anomalous refraction law at the grain boundaries has also been experimentally observed. Finally, a preliminary study about the possibility of "left-handed" behaviour in ultrasonic crystals is presented in this work. The device consists of a slab of the above mentioned metallic composite attached to an epoxy wedge. In this system, clues to negative refraction are theoretically shown.     

Band gap structures in underwater screens of periodically spaced porous plates

Acoustic properties of different periodic structures composed of alternating fluid and fluid-saturated porous layers obeying Biot’s theory are investigated. At first, the network of modes and the transmission coefficients of finite structures of six plates are studied in the frequency-angle of incidence plane. It is shown that the network of modes concentrates in localized domains of the plane where the transmission coefficients will take the greatest values. With this minimum of six plates, the structures exhibit the main features as for structures containing more plates, especially those with an infinite number of plates. Then, considering infinite structures the band gap calculations are led using the Bloch–Floquet theorem. The evanescent and propagative zones in the frequency-angle of incidence plane are determined. What is proposed here is a class of underwater porous screens that exhibits band gaps extending over great angular domains and enlarging in the frequency domain when the pores at the interfaces of the porous plates are sealed. The effect of porosity on the band gaps is also investigated.     

Wave localization in two-dimensional porous phononic crystals with one-dimensional aperiodicity

The localization properties of in-plane elastic waves propagating in two-dimensional porous phononic crystals with one-dimensional aperiodicity are initially analyzed by introducing the concept of the localization factor that is calculated by the plane-wave-based transfer-matrix method in this paper. The band structures characterized by using localization factors are calculated for different phononic crystals by altering matrix material properties and geometric structure parameters. Numerical results show that the effect of matrix material properties on wave localization can be ignored, while the effect of geometric structure parameters is obvious. For comparison, the periodic porous system and Fibonacci system with rigid inclusion are also analyzed. It is found that the band gaps are easily formed in aperiodic porous system, but hard for periodic porous system. Moreover, compared with aperiodic system with rigid inclusion, the wider low-frequency band gaps appear in the aperiodic porous system.     

内插扩张室声子晶体管路带隙特性研究

声子晶体管路的带隙特性,可以实现管路系统在特定频率下的噪声控制.利用二维模态匹配法推导出单个内插扩张室元胞的传递矩阵,结合Bloch定理,得到声子晶体管路的能带结构计算方法;验证了二维方法在计算能带结构时的准确性.研究发现,内插扩张室声子晶体管路存在布拉格带隙和局域共振带隙.进一步研究了晶格常数以及内插管长度对能带结构的影响,结果表明,晶格常数主要控制布拉格带隙,而内插管长度对局域共振带隙有较大的影响,并研究了两种参数变化下的带隙耦合.研究结果可以为管路降噪设计提供新的思路.     

Modulating lamb wave band gaps using an elastic metamaterial plate

Modulating band gaps (extending the bandwidths or shifting into a lower frequency range) is a challenging task in phononic crystals. In this paper, elastic metamaterial plates composed of a square array of “hard” stubs or “soft” stubs on both sides of a 2D binary locally resonant plate are proposed, and their band structures are studied. The dispersion relationships and the displacement fields of the eigenmodes are calculated using finite element methods. Numerical results show that the band gaps are shifted to lower frequencies and the bandwidths are enlarged compared to classic elastic metamaterial plates. A conceptual “analogousrigid mode” that includes an “out-of-plane analogous-rigid mode” and an “in-plane analogous-rigid mode” is developed to explain these phenomena. The “out-of-plane analogous-rigid mode” mainly adjusts the band gaps into the lower frequency range, and the “in-plane analogous-rigid mode” mainly enlarges the bandwidth. Furthermore, the band gap effects of composite “hard” stubs and “soft” stubs are investigated. The results show that the location of the band gaps can be modulated into a relatively lower frequency and the bandwidth can be extended by the use of different composite stubs. These elastic wave properties in the proposed structure can be used to optimize band gaps and possibly produce low-frequency filters and waveguides.     

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.     

新型负模量声学超结构的低频宽带机理研究

提出了一种具有负模量特性的新型声学超结构,并揭示了其低频带隙的形成及拓宽机理.通过理论推导给出了该新型结构的归一化有效模量表达式,由于有效模量的零值点与系统参数密切相关,可以调节合适的参数使得零值点降低或带隙下界降低,进一步实现低频带隙.理论结果表明,在一定的频率范围内,系统的弹性模量为负且负模量区域进一步拓宽,从而通过负模量区域的放大而拓宽带隙.这种新的实现低频带隙的方法克服了传统局域共振附加质量过大及惯性放大结构带隙较窄的缺点.同时,通过有限元法得到的周期结构的传输率随着结构参数的变化趋势与理论分析的变化趋势基本一致,并得到了约40—180 Hz的低频宽带.这种实现低频带隙的新思路对低频声波的控制具有很重要的理论指导意义.     

Flexural vibration band gaps in a thin plate containing a periodic array of hemmed discs

Using a periodic expansion by means of the Bloch theorem, the flexural vibration band gaps are studied in a thin plate with two-dimensional ternary locally resonant structures, i.e. a thin epoxy plate containing a periodic square array of lead discs hemmed around by rubber. The full band gaps of flexural vibration in the thin plate are obtained within which sound and vibration will be forbidden. The numerical results are used to show how the width of the first full band gap depends on the radius ratio of lead disc to hemmed disc, filling fraction, lattice constant (distance between the centers of the nearest lead discs) and thickness of the thin plate. It is observed that the gap width can be changed a lot by modulating these physical parameters.     

Analysis on vibration characteristics of large-size rectangular piezoelectric composite plate based on quasi-periodic phononic crystal structure

Based on the theory of composite materials and phononic crystals (PCs), a large-size rectangular piezoelectric composite plate with the quasi-periodic PC structure composed of PZT-4 and epoxy is proposed in this paper. This PC structure can suppress the transverse vibration of the piezoelectric composite plate so that the thickness mode is purer and the thickness vibration amplitude is more uniform. Firstly, the vibration of the model is analyzed theoretically, the electromechanical equivalent circuit diagram of three-dimensional coupled vibration is established, and the resonance frequency equation is derived. The effects of the length, width, and thickness of the piezoelectric composite plate at the resonant frequency are obtained by the analytical method and the finite element method, the effective electromechanical coupling coefficient is also analyzed. The results show that the resonant frequency can be changed regularly and the electromechanical conversion can be improved by adjusting the size of the rectangular piezoelectric plate. The effect of the volume fraction of the scatterer on the resonant frequency in the thickness direction is studied by the finite element method. The band gap in X and Y directions of large-size rectangular piezoelectric plate with quasi-periodic PC structures are calculated. The results show that the theoretical results are in good agreement with the simulation results. When the resonance frequency is in the band gap, the decoupling phenomenon occurs, and then the vibration mode in the thickness direction is purer.     

Hybrid phononic crystal plates for lowering and widening acoustic band gaps

We propose hybrid phononic-crystal plates which are composed of periodic stepped pillars and periodic holes to lower and widen acoustic band gaps. The acoustic waves scattered simultaneously by the pillars and holes in a relevant frequency range can generate low and wide acoustic forbidden bands. We introduce an alternative double-sided arrangement of the periodic stepped pillars for an enlarged pillars’ head diameter in the hybrid structure and optimize the hole diameter to further lower and widen the acoustic band gaps. The lowering and widening effects are simultaneously achieved by reducing the frequencies of locally resonant pillar modes and prohibiting suitable frequency bands of propagating plate modes.     

Extended plane-wave-based transfer-matrix approach to simulating dispersive photonic crystals

It has been difficult to compute the band structures and transmission spectra for photonic crystals (PCs) with dispersive components included in the periodic units. Here we show that by using an extended plane-wave-based transfer-matrix method, we are able to formulate the problem for computing optical properties of dispersive PCs, including magnetic and left-handed PCs. This approach is very general, since it can treat PCs with arbitrary Bravais lattice composed of materials with arbitrary dielectric permittivities and magnetic permeabilities. Combined with the supercell method, this method can further simulate defective PCs such as PC-based waveguides and microcavities.     

二维组合宽带隙材料的研究

运用FDTD(时域有限差分法)研究了弹性波/声波通过二维正方形排列的铁/水声子晶体的传播特性.发现铁/水声子晶体在高频范围存在完全带隙，软包层铁/水声子晶体在低频范围出现共振带隙，它们分别对应于不同的带隙形成机理.通过铁/水声子晶体和软包层铁/水声子晶体的组合，可以得到从高频到低频的组合宽带隙结构，从而达到在更宽频范围内控制弹性波传播的目的；而且通过调整包层的厚度、铁芯的大小、以及填充率等结构参数，可以有效地调节组合宽带隙的频率结构.