复合兰姆波声子晶体中超宽部分禁带

兰姆波在声子晶体薄板中的传播特性因其在无损检测、 减振技术和传感器件等领域的潜在应用价值而受到越来越多的关注. 本文采用超原胞平面波展开法和有限元法系统地研究了复合对称结构声子晶体薄板中的兰姆波超宽部分禁带. 结果表明: 对于在薄板侧面对称地嵌入双层矩形空气柱构成的复杂系统, 低阶兰姆波部分带隙结构极为丰富. 将晶格常数(L)和板厚(H) 比值具有匹配关系的兰姆波声子晶体衔接构成复合结构, 低阶兰姆波部分禁带宽度因各组分结构的部分禁带交叠而得到显著拓宽, 可在低频超宽频带内实现对特定低阶兰姆波模式良好的模式选择功能. 该研究结果对兰姆波缺陷无损检测中模式优化选择及兰姆波单向导通器件设计等方面具有重要意义.     

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.     

Investigation of a silicon-based one-dimensional phononic crystal plate via the super-cell plane wave expansion method

The super-cell plane wave expansion method is employed to calculate band structures for the design of a silicon-based one-dimensional phononic crystal plate with large absolute forbidden bands. In this method, a low impedance medium is introduced to replace the free stress boundary, which largely reduces the computational complexity. The dependence of band gaps on structural parameters is investigated in detail. To prove the validity of the super-cell plane wave expansion, the transmitted power spectra of the Lamb wave are calculated by using a finite element method. With the detailed computation, the band-gap of a one-dimensional plate can be designed as required with appropriate structural parameters, which provides a guide to the fabrication of a Lamb wave phononic crystal.     

Transmission mode of one-dimensional phononic crystal based on coupling of total evanescent waves

In order to obtain the transmission properties of one-dimensional phononic crystal under total evanescent waves, we design structure model. Basing on the basic acoustic wave equations and boundary condition as well as the Bloch theory, we study the band structure of one-dimensional phononic crystal. We summarize the properties of the mode based on the coupling of total evanescent waves and explain its physical mechanism. There are three transmission modes in phononic crystal. Based on the coupling of total evanescent waves, the number of perfect transmission peaks is just equal to the number of structure period, and the thickness of period can be much less than the wave length.     

Propagation of guided elastic waves in 2D phononic crystals

The phononic band structure of two-dimensional phononic guides is numerically studied. A plane wave expansion method is used to calculate the dispersion relations of guided elastic waves in these periodic media, including 2D phononic plates and thin layered periodic arrangements. We show that, for any guided elastic wave, Lamb or generalised Lamb modes, stop bands appear in the dispersion curves, displaying a phononic band structure in both cases.     

Lamb waves in two-dimensional phononic crystal plate with anisotropic inclusions

An analysis is given to the band structure of the two-dimensional phononic crystal plate constituted of a square array of elastic anisotropic, circular Pb cylinders embedded in elastic isotropic epoxy. The numerical results show that the band gap can be tuned by rotating the anisotropic material orientation. It is found that the influence of anisotropy on band gap of Lamb wave is clearly different from that on the band gap of bulk waves. The thickness of the system under study is a sensitive parameter to affect the influence of anisotropic materials on the normalized gap width.     

Low-frequency band gaps in one-dimensional thin phononic crystal plate with periodic stubbed surface

Using supercell plane wave expansion method, the Lamb wave band structure of one-dimensional thin plate with periodic stubs is investigated. The numerical results show that flat bands will appear and band gap can exist in a low-frequency domain. The position of the flat bands and width of the low-frequency Lamb wave band gap can be tuned by the stub height, plate thickness and filling fraction. The band gap is obtained by opening the folding points of the same plate modes not the crossing point of different plate mode when the stub height is small.     

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.     

Lamb wave band gaps in locally resonant phononic crystal strip waveguides

Using finite element method, we have made a theoretically study of the band structure of Lamb wave in a locally resonant phononic crystal strip waveguide with periodic soft rubber attached on the two sides of epoxy main plate. The numerical results show that the Lamb wave band gap based on local resonant mechanism can be opened up in the stub strip waveguides, and the width of the local resonant band gap is narrower than that based on the Bragg scattering mechanism. The results also show that the stub shape and width have influence on the frequency and width of the Lamb wave band gap.     

Temperature effects on the band gaps of Lamb waves in a one-dimensional phononic-crystal plate (L)

This study investigates the temperature-tuned band gaps of Lamb waves in a one-dimensional phononic-crystal plate, which is formed by alternating strips of ferroelectric ceramic Ba(0.7)Sr(0.3)TiO(3) and epoxy. The sensitive and continuous temperature-tunability of Lamb wave band gaps is demonstrated using the analyses of the band structures and the transmission spectra. The width and position of Lamb wave band gaps shift prominently with variation of temperature in the range of 26 °C-50 °C. For example, the width of the second band gap increases from 0.066 to 0.111 MHz as the temperature is increased from 26 °C to 50 °C. The strong shift promises that the structure could be suitable for temperature-tuned multi-frequency Lamb wave filters.     

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.     

Enhanced plane wave expansion analysis for the band structure of bulk modes in two-dimensional high-contrast solid–solid phononic crystals

Plane wave expansion analyses that use the inverse rule to obtain the Fourier coefficients of the elastic tensor instead of the more conventional Laurent's rule, exhibit faster convergence rates for solid–solid phononic crystals. In this work, the band structure convergence of calculations using the inverse rule is investigated and applied to the case of high acoustic impedance contrast solid–solid phononic crystals, previously known for convergence difficulties. Results are contrasted to those obtained with the conventional plane wave expansion method. The inverse rule is found to converge at a much rate for all ranges of impedance contrast, and the ratio between the computational times needed to obtain a convergent band structure for a high-contrast solid–solid phononic crystal with the conventional plane wave expansion method using 1369 reciprocal lattice vectors is as large as 6800:1. This ratio decreases for material sets with lower impedance contrast; however, the inverse rule is still faster for a given error threshold for even the lowest impedance contrast phononic crystals reported in the literature. This convergence enhancement is a major factor in reconsidering the plane wave expansion method as an important tool in obtaining propagating elastic modes in phononic crystals.     

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.     

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.     

弹性波通过一维复合材料系统的透射性质

提出了不同结构的一维弹性波复合材料系统模型,包括一维周期结构声子晶体、标准Fibonacci准周期结构声子晶体、广义Fibonacci准周期结构声子晶体以及完全无序结构的复合材料系统. 采用模式匹配理论法,数值计算了弹性波通过一维复合材料系统的透射系数. 计算结果表明,利用特殊的准周期结构声子晶体可获得比周期结构声子晶体更宽的带隙范围,准周期结构排列的复合材料系统相当于在周期结构中引入了缺陷体一样,带隙内出现了丰富的局域模式. 对弹性波/声波在复合材料系统中局域态性质的研究有助于弹性波/声波滤波器、导波器 关键词： 弹性波复合材料 局域化     

Lamb waves in phononic crystal slabs: truncated plane parallels to the axis of periodicity

A theoretical study is presented on the propagation properties of Lamb wave modes in phononic crystal slabs consisting of a row or more of parallel square cylinders placed periodically in the host material. The surfaces of the slabs are parallel to the axis of periodicity. The dispersion curves of Lamb wave modes are calculated based on the supercell method. The finite element method is employed to calculate the band structures and the transmission power spectra, which are in good agreement with the results by the supercell method. We also have found that the dispersion curves of Lamb waves are strongly dependent on the crystal termination, which is the position of the cut plane through the square cylinders. There exist complete or incomplete (truncated) layers of square cylinders with the change of the crystal termination. The influence of the crystal termination on the band gaps of Lamb wave modes is analyzed by numerical simulations. The variation of the crystal termination leads to obvious changes in the dispersion curves of the Lamb waves and the widths of the band gaps.     

Complete band gaps of phononic crystal plates with square rods

Much of previous work has been devoted in studying complete band gaps for bulk phononic crystal (PC). In this paper, we theoretically investigate the existence and widths of these gaps for PC plates. We focus our attention on steel rods of square cross sectional area embedded in epoxy matrix. The equations for calculating the dispersion relation for square rods in a square or a triangular lattice have been derived. Our analysis is based on super cell plane wave expansion (SC-PWE) method. The influence of inclusions filling factor and plate thickness on the existence and width of the phononic band gaps has been discussed. Our calculations show that there is a certain filling factor (f = 0.55) below which arrangement of square rods in a triangular lattice is superior to the arrangement in a square lattice. A comparison between square and circular cross sectional rods reveals that the former has superior normalized gap width than the latter in case of a square lattice. This situation is switched in case of a triangular lattice. Moreover, a maximum normalized gap width of 0.7 can be achieved for PC plate of square rods embedded in a square lattice and having height 90% of the lattice constant.     

一维指数形变截面有限周期声子晶体的研究

本文利用集中质量法对弹性纵波在一维指数形截面有限周期声子晶体中的传播进行了研究, 得到了频率响应函数的表达式. 与一维等截面的声子晶体相比, 指数形变截面声子晶体带隙内的衰减值随着输出端截面积的增大而减小, 同时带隙的起始频率降低而截止频率升高, 也即带隙的宽度会得到拓展. 晶格常数和材料组份比变化时, 变截面声子晶体带隙的起始频率和截止频率的变化趋势与等截面时的声子晶体相同. 希望本文的研究能够推动声子晶体在减振降噪等领域中的应用.     

Wavelet-based method for computing elastic band gaps of one-dimensional phononic crystals

A wavelet-based method was developed to compute elastic band gaps of one-dimensional phononic crystals. The wave field was expanded in the wavelet basis and an equivalent eigenvalue problem was derived in a matrix form involving the adaptive computation of integrals of the wavelets. The method was then applied to a binary system. For comparison, the elastic band gaps of the same one-dimensional phononic crystals computed with the wavelet method and the well-known plane wave expansion (PWE) method are both presented in this paper. The numerical results of the two methods are in good agreement while the computation costs of the wavelet method are much lower than that of PWE method. In addition, the adaptability of wavelets makes the method possible for efficient band gap computation of more complex phononic structures. Supported by the National Natural Science Foundation of China (Grant No. 10632020)     

The influence of the micro-topology on the phononic band gaps in 2D porous phononic crystals

The phononic band structures of two-dimensional metal porous phononic crystals consisting of different lattices (the lattice structures transformed from square to triangle), and pores of various shapes (circle, square, and triangle) and sizes are studied numerically by using Finite Difference Time Domain (FDTD) scheme. It is found that for x-y mode waves, the absolute phononic band gaps (PBGs) rely more on the pore shapes. For triangular pores, the PBG is opening in the whole process of the lattice transformation, and for circular ones, the PBG is closed after a certain lattice structure. No PBG forms in the crystals with square pores. The PBG can be varied by adjusting the size of the pores. But a critical porosity exists for the opening of the PBG.