Interaction of Love waves with coupled cavity modes in a 2D holey phononic crystal

The interaction of Love waves with square array of pillars deposited on a cavity defined in a 2D holey phononic crystal is numerically investigated using Finite Element Method. First, the existence of SH surface modes is demonstrated separately for phononic crystals that consist of square arrayed holes, or rectangular arrayed Ni pillars, respectively in, or on, a SiO₂ film deposited on a ST-cut quartz substrate. The coupling between SH modes and torsional mode in pillars induces a transmission dip that occurs at a frequency located in the range of the band-gap of the holey phononic crystal. Second, a cavity is constructed by removing lines of holes in the holey phononic crystal and results in a transmission peak that matches the dip. The optimal geometrical parameters enable us to create a coupling of the cavity mode and the localized pillar mode by introducing lines of pillars into the cavity, which significantly improved the efficiency of the cavity without increasing the crystal size. The obtained results will pave the way to implement advanced designs of high-performance electroacoustic sensors based on coupling modes in phononic crystals.     

一维颗粒声子晶体的拓扑相变及可调界面态

基于Su-Schrieffer-Heeger模型,构造了一种一维非线性声子晶体,通过调控外加在声子晶体上的预紧力,可调控声子晶体的拓扑态,从而实现拓扑相变.利用这一效应,把该非线性声子晶体与另一线性声子晶体形成异质结构,可以实现一种新型声学开关:通过调节预紧力即调控非线性声子晶体的拓扑相,可以实现异质结构中界面态从无到有的转变,从而实现了开关效应.利用该效应可望开发新型声学器件,如可调谐振器、可调滤波器、可调隔振器等.     

Velocity of a SAW propagating in a 2D phononic crystal

We have studied the propagation of a surface acoustic waves (SAW), in a structure constituted by a 2D phononic film (a few micrometers thick and having lattice constants of a few hundreds of micrometers in the two directions of the propagation plane) deposited onto a homogeneous semi-infinite substrate. First, we have calculated the dispersion relations of the acoustic modes by using a plane waves expansion method. We found that the surface branch exhibits both the folding effect and a band gap for the propagation along some particular directions. This is a very interesting result which demonstrates that the effects related to the existence of the band gap (sound velocity dispersion, diffraction, refraction, ultrasound tunneling, etc.) can all appear, even if the thickness of the phononic film is much less than the penetration depth of the SAW. Then, we used an all-optical technique to monitor the spectral content of the SAW propagating along the GammaX direction in the reduced Brillouin zone. We show that a wave with frequency in the stop band, is destructively diffracted after it propagates through less than ten periods. Finally, we report on measurements of the Rayleigh wave phase velocity and we show that the transit time is independent of the distance traveled inside the phononic crystal, suggesting that tunneling trough the sample is involved.     

Tailoring of phononic band structures in colloidal crystals

We report an experimental study of the elastic properties of a two-dimensional (2D) colloidal crystal subjected to light-induced substrate potentials. In agreement with recent theoretical predictions [H. H. von Grünberg and J. Baumgartl, Phys. Rev. E 75, 051406 (2007).10.1103/PhysRevE.75.051406] the phonon band structure of such systems can be tuned depending on the symmetry and depth of the substrate potential. Calculations with binary crystals suggest that phononic band engineering can be also performed by variations of the pair potential and thus opens novel perspectives for the fabrication of phononic crystals with band gaps tunable by external fields.     

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.     

Large Lamb wave band gap in phononic crystals thin plates

We suggest that Lamb wave band gaps in one-dimensional phononic crystals can be substantially enlarged by using multiple heterostructures which consist of several pieces of phononic crystal with different ratios of the thickness to the lattice period. This is possible because each substructure shows a different band gap and the band structure of a Lamb wave is strongly affected by the ratio of the plate thickness to the lattice period. This effect has been demonstrated by using finite element simulations on two different one-dimensional systems. PACS 63.20.-e; 62.65.+k; 41.20.Jb; 43.20.+g     

广义Fibonacci准周期结构声子晶体透射性质的研究

提出了一维广义Fibonacci准周期结构的声子晶体模型. 对弹性波通过该一维准周期结构声子晶体的透射系数进行数值计算,并与周期结构和标准Fibonacci准周期结构声子晶体的透射系数进行比较. 结果表明,利用一维广义Fibonacci准周期结构的声子晶体可获得比周期结构和标准Fibonacci准周期结构声子晶体更大的带隙范围,同时在带隙内有更丰富的局域模式存在. 对局域模性质的研究有助于声波或弹性波滤波器的制作. 关键词： 广义Fibonacci准周期结构 声子晶体 局域化     

Quality enhancement and insertion loss reduction of a rectangular resonator by employing an ultra-wide band gap diamond phononic crystal

We report on an ‘in plane mode’ band gaps investigation of a novel diamond CRS (circle-rectangle-square) shaped holey phononic crystals in the desired operating frequency ranges. An ultra-wide band gap for diamond in the ‘in plane mode’ is observed. We also investigate an ultra-wide acoustic band gap for a finite one-dimensional (1D) diamond CRS phononic crystal (PnC) in the ‘out of plane mode’, and an ultra-wide acoustic band gap of a finite two-dimensional (2D) diamond CRS phononic crystal (PnC) in the ‘out of plane mode’ based on the FEA (Finite Element Analysis) method. We analyze that the transmission response of diamond in the length extension and width extension manner is more reasonable. Ultra-wide peak attenuations in the transmission spectra of a CRS shaped diamond phononic crystal successfully reveal the complete band gaps. The wide band gap of a CRS shaped diamond phononic crystal and the wide peak attenuation strongly agree in the same frequency region. It is analyzed that when a CRS-diamond phononic crystal is employed for MEMS resonators with different tether widths the quality Q of the resonators improved, and the energy losses decrease with extremely low insertion loss. In addition, it is observed that the vibrational displacement of a resonator is reduced by employing a diamond phononic crystal.     

Designing a broad locally-resonant bandgap in a phononic crystals

Producing a broad locally-resonant bandgap for low frequencies in a phononic crystals is a challenging task, using conventional methods. In this paper, we describe the design of a broad, locally-resonant, bandgap in a phononic crystals using a numerical simulation. The structure consists of periodic double-sided novel composite sonators, deposited on a 2D locally-resonant phononic-crystals plate made of a rubber-filler array, which is embedded in an epoxy plate. Using the finite element method, we calculate the dispersion relations, the power-transmission spectra, and the displacement fields for the eigenmodes. Our results confirm that, the new structure facilitates a significant increase in absolute bandwidth (by a factor of 4.2) compared to conventional phononic crystals. It also broadens the range of elastic wave attenuation. The formation mechanisms that generates the broad locally-resonant bandgap is explored numerically. The simulation indicates that the formation of this bandgap is possible due to coupling between the entire vibration mode of the novel composite-resonator and the Lamb-wave mode of the 2D locally-resonant phononic-crystals plate. The bandwidth of the locally-resonant bandgap is determined by the resonator mode. This study opens new possibilities to broaden locally-resonant bandgaps of phononic crystals for low frequencies. The results can potentially be used to reduce vibration and noise in many applications.     

Analysis of dispersion characteristics of phononic structures

A general theory for calculating the dispersion of bulk acoustic waves in 3D and 2D phononic crystals made of anisotropic materials is presented, which is based on the plane-wave expansion method. Two approaches to separating acoustic modes in the dispersion diagrams are proposed. The pattern of the acoustic field distribution is studied as depending on the wavevector direction for various types of modes. Degeneracy of acoustic modes in directions different from the axes of symmetry of the phononic crystal is demonstrated. Possibilities of the proposed method are illustrated by the application to 3D and 2D silicon-based phononic crystal structures.     

Individual and collective vibrational modes of nanostructures studied by picosecond ultrasonics

We report on picosecond ultrasonic measurements obtained on aluminum and platinum nanostructures with variable dot size and lateral periodicity which realized a 2D phononic crystal. Performing investigations at different resolution scales, we have identified individual modes of vibration depending on the dot size, and mode of vibration strongly correlated with the bi-dimensional organization. The platinum dots sputtered on an aluminum layer have shown a behavior of isolated oscillators without any coupling between neighbor elements in this phononic crystal. The frequency of such normal modes, extracted from time resolved measurements are in good agreement with 3D finite element simulations. In contrast, with aluminum dot systems where the coupling is more efficient we observe a complex spectrum of vibrational modes related to the band structure induced by the bi-dimensional patterning.     

二维空心散射体声子晶体板的低频带隙特性及其形成机理

利用有限元方法,对设计的涂有硅橡胶包裹层的空心铅柱体嵌入到4个环氧树脂短连接板中构成的声子晶体板的低频带隙特性进行了研究,分析了其能带结构、传输损失及位移场。与正方连接板粘连结构、嵌入结构和细连接短板粘连结构这3种传统声子晶体板的带隙特性作对比,说明具有包裹层、短连接板结构的声子晶体板更容易产生低频宽带;观察位移矢量场的振动模态,并结合弹簧质量模型,解释了带隙形成的机理;通过讨论连接板的宽度、散射体的内外半径及高度对第一完全带隙的影响,说明连接板宽度越窄,厚度越小,散射体内半径越小,外半径越大,高度越高,越有利于带隙的扩展。      

Band structures of Fibonacci phononic quasicrystals

The paper studies the band structures of a two-component Fibonacci phononic quasicrystal which is considered as a phononic crystal disordered in a special way. Oblique propagation in an arbitrary direction of the in-plane elastic waves with coupling of longitudinal and transverse modes is considered. The transfer matrix method is used and the well-defined localization factors which are used to study the ordered and disordered phononic crystals are introduced to describe the band gaps of the phononic quasicrystals. The transmission coefficients are also calculated and the results show the same behaviours as the localization factor does. The results show the merits of using the localization factors. The band gaps of the phononic quasicrystal and crystals with translational and/or mirror symmetries are presented and compared to the perfect phononic crystals. More band structures are exhibited when symmetries are introduced to the phononic quasicrystals.     

Large complete band gap in two-dimensional phononic crystal slabs with elliptic inclusions

Phononic band structure with periodic elliptic inclusions for the square lattice is investigated based on the plane wave expansion method. The numerical results show the systems composed of tungsten (W) elliptic rods embedded in a silicon (Si) matrix can exhibit a larger complete band gap than the conventional circular phononic crystal (PC) slabs. The phononic band structure of the plate-mode waves and the width of the first complete band gap can be tuned by varying the ratio of the minor axis and the major axis, the orientation angle of the elliptic rods and the thickness of the PC slabs. We also study the band structure of plate-mode waves propagating in two-dimensional (2D) slabs with periodic elliptic inclusions coated on uniform substrate.     

Symmetric and Anti-Symmetric Lamb Waves in a Two-Dimensional Phononic Crystal Plate

It is weft known that Lamb waves in a plate with a mirror plane can be separated into two uncoupled sets： symmetric and anti-symmetric modes. Based on this property, we present a revised plane wave expansion method （PWE） to calculate the band structure of a phononie crystal （PC） plate with a mirror plane. The developed PWE method can be used to calculate the band structure of symmetric and anti-symmetric modes separately, by which the depending relationship between the partial acoustic band gap （PABG）, which belongs to the symmetric and anti-symmetric modes alternatively, and the position of the scatterers can be determined. As an example of its application, the band structure of the Lamb modes in a two-dimensional PC plate with two layers of void circular inclusions is investigated. The results show that the band structure for the symmetric and anti-symmetric modes can be changed by the position of the scatterers drastically, and larger PABGs will be opened when the scatterers are inserted into the area of the plate, where the elastic potential energy is concentrated.     

Band gap structures for viscoelastic phononic crystals based on numerical and experimental investigation

Many materials used as phononic crystals (PCs) are viscoelastic one. It is believed that viscosity results in damping to attenuate wave propagation, which may help to tune the defect modes or band gaps of viscoelastic phononic crystals. To investigate above phenomenon, firstly, we have extended the application of boundary element method (BEM) to the study of viscoelastic phononic crystals with and without a point defect. A new developed BEM within the framework of Bloch theory can easily deal with viscoelastic phononic crystals with arbitrary shapes of the scatterers. Experimental methods have been put forward based on the self-made viscoelastic phononic crystals. Verified by the experimental results, systematic comprehensive parametric studies on the band structure of viscoelastic phononic crystals with varying factors (final–initial value ratio, relaxation time, volume fraction of scatterers, shapes of scatterers) have been discussed by the numerical simulation. To further address the possibility to change the defect modes, the band structure of viscoelastic phononic crystals with a point defect has been studied based on the numerical and experimental methods. From present research work, it can be found that by adjusting the two viscous parameters combined with considering the effect of volume fraction and shapes, a wider and lower initial forbidden frequency or lower and higher quality factor resonant frequency can be obtained.     

Propagation of thickness-twist waves in elastic plates with periodically varying thickness and phononic crystals

We study the propagation of thickness-twist (TT) waves in a crystal plate of AT-cut quartz with periodically varying, piecewise constant thickness. The scalar differential equation by Tiersten and Smythe is employed. The problem is found to be mathematically equivalent to the motion of an electron in a periodic potential field governed by Schrodinger’s equation. An analytical solution is obtained. Numerical results show that the eigenvalue (frequency) spectrum of the waves has a band structure with allowed and forbidden bands. Therefore, for TT waves, plates with periodically varying thickness can be considered as phononic crystals. The effects of various parameters on the frequency spectrum are examined.     

Focusing and waveguiding of Lamb waves in micro-fabricated piezoelectric phononic plates

This paper presents results on the numerical and experimental studies of focusing and waveguiding of the lowest anti-symmetric Lamb wave in micro-fabricated piezoelectric phononic plates. The phononic structure was based on an AT-cut quartz plate and consisted of a gradient-index phononic crystal (GRIN PC) lens and a linear phononic plate waveguide. The band structures of the square-latticed AT-cut quartz phononic crystal plates with different filling ratios were analyzed using the finite element method. The design of a GRIN PC plate lens which is attached with a linear phononic plate waveguide is proposed. In designing the waveguide, propagation modes in square-latticed PC plates with different waveguide widths were studied and the results were served for the experimental design. In the micro-fabrication, deep reactive ion etching (Deep-RIE) process with a laboratory-made etcher was utilized to fabricate both the GRIN PC plate lens and the linear phononic waveguide on an 80 μm thick AT-cut quartz plate. Interdigital transducers were fabricated directly on the quartz plate to generate the lowest anti-symmetric Lamb waves. A vibro-meter was used to detect the wave fields and the measured results on the focusing and waveguiding of the piezoelectric GRIN PC lens and waveguide are in good accordance with the numerical predictions. The results of this study may serve as a basis for developing an active micro plate lens and related devices.     

超元胞方法研究平移群对称性对声子带隙的影响

采用基于超元胞的平面波展开法，计算了由水银(水)正四棱柱体按正方格子排列于水(水银)基体中所组成的两种声子晶体的能带结构.通过改变两相邻的柱体底面边长之比来改变声子晶体的平移群对称性.结果发现，改变相邻柱体的底面边长之比，具有很好的调节声学带隙的作用.研究表明，声子晶体的平移群对称性对于其带隙的形成具有重要影响,同时还表明,超元胞方法也是研究声子晶体平移群对称性影响声子带隙形成的一种有效方法. 关键词： 声子晶体 带隙 对称性     

一维准周期结构声子晶体透射性质的研究

提出了一维准周期结构的声子晶体模型.对弹性波通过该一维准周期结构声子晶体的透射系数进行了数值计算，并与周期结构的透射系数进行了比较.计算结果表明，弹性波通过一维准周期结构声子晶体时，同样会有带隙的出现，且带隙所在频率范围与周期结构的情形完全一样，不同的是在准周期结构声子晶体中，带隙内有很强的局域共振模.对此局域模性质的研究有助于声波或弹性波滤波器的制作. 关键词： 准周期结构 声子晶体 局域化