Trapping of electromagnetic wave in single-negative metamaterial waveguides

We study the trapping properties of transverse magnetic (TM) waves in single-negative metamaterial waveguides including epsilon-negative (ENG) metamaterial and mu-negative (MNG) metamaterial. The relationship between effective refractive index and reduced core width is analyzed when the permittivities of ENG and MNG metamaterials are different, and the inflection on this curve can be regarded as the trapping point. Simulation results show that the properties in an ENG–MNG–ENG metamaterial waveguide are contrary to that in a MNG–ENG–MNG metamaterial waveguide. The sensitivity of trapping point to the change of permittivity makes the single-negative metamaterial waveguides to be an effective method to detect the permittivity variation and can be used as a new kind of waveguide sensor.     

Coupled-mode analysis for linear fiber Bragg grating made of metamaterial

We derive the coupled-mode equations for a metamaterial fiber Bragg gratings (FBGs). The coupled-mode theory describing wave propagation in periodic structures such as FBG is generalized for studying the transmission and reflection of electromagnetic waves through a FBG containing metamaterial layers. This approach shows that the band gap becomes broader in comparison with a conventional FBG. It is observed that the central frequency of the band gap has a shift in regard of changing metamaterial thickness. We verify this investigation through attaining the transmission and reflection spectra of a conventional FBG while we are setting related parameters. Furthermore, this proposed structure can be applied as a tunable filter.     

Tunable band gaps in an inertant metamaterial plate with two-degree-of-freedom local resonance

This article presents an inertant metamaterial plate with two-degree-of-freedom (TDOF) local resonance. It is theoretically investigated with dispersion relation, effective density, and group velocity, and phase velocity to show the unique acoustic performance. Results show that the metamaterial plate can generate two tunable band gaps with a single mass attached by tuning the distance of springs to the centroid of mass due to the extra rotation of the mass. Simultaneously, the band gaps can also be tuned to the lower frequency range by exploiting the inerter. Effective mass density shows negative within the band gaps, and is also tuned by the attached spring-mass and inerter. Finally, within specific frequency ranges, the group velocity is negative which manifests the metamaterial plate behaves abnormal dispersion.     

Determining the retardation of a wave plate by using spectroscopic method

A method for determining the retardation of a wave plate is presented. The method is based on polychromatic polarization interference technique. Through accurate judgment of the intersection points' wavelengths of the two orthogonal polarization transmittance spectrum curves, the apparent retardation, the absolute retardation values and the physical thickness of a wave plate can be measured at a wide spectral range from 400 nm to 800 nm. Experimental results show that the proposed method has very high precision. In addition, the method has a significant advantage that has high misalignment tolerance. The method reported here should have applications in fabrication and measurement of a wave plate.     

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.     

New type of an acoustic plate mode: quasi-longitudinal normal wave

A new type of an acoustic wave belonging to the family of the normal plate modes is discovered numerically and verified experimentally in ST, x-quartz plates with free surfaces. It exists within restricted bands of the normalized plate thickness H/λ, where H is the thickness, λ is the wavelength, separated by forbidden H/λ-bands attributed to the common plate modes. Polarization of the wave over the whole plate thickness is almost longitudinal. Velocity of the wave is close to or equal to the velocity of the longitudinal bulk wave, propagating in the same direction. The proximity or/and equality of the velocities is a necessary, but not sufficient condition of the existence of the new wave.     

基于波传播法的周期复合板振动带隙衰减特性研究

运用波传播法对有限和无限周期对边简支复合板的振动带隙衰减特性进行了研究.在建立相邻板结构边界连续方程的基础上, 分别运用传递矩阵和Bloch定理建立了有限和无限周期复合板的耦合运动方程, 并详细对比分析了有限和无限周期复合板带隙衰减特性的关联关系.研究表明: 周期板结构的振动带隙频率范围与激励方式和激励位置是相关的, 若周期复合板在宽度方向按某阶模态进行线激励, 则该激励下的振动带隙与无限周期复合板在该阶模态下的振动带隙是一致的; 若周期板在点激励作用, 则该点激励下的振动带隙是参与振动的各阶模态振动带隙的交集. 此外, 还进一步研究了结构阻尼对振动衰减带隙的影响. 关键词： 周期复合板 带隙衰减特性 波传播法 结构阻尼     

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.     

二维正方排列圆柱状亥姆赫兹共振腔阵列局域共振声带隙的研究

通过对二维正方排列圆柱状亥姆赫兹共振腔阵列声性质的研究,指出局域共振型声子晶体中存在两类耦合作用, 即共振单元与基体的弱耦合作用及共振单元间的耦合作用.其中前一种耦合作用可以通过改变共振单元的品质因子而改变, 逐渐减小这种耦合作用可以实现从局域共振到布拉格共振的连续转变;后一种耦合是通过共振单元周围的近场耦合实现的, 通过减小共振单元的间距可以增大其耦合强度,因而增大带隙宽度,但带隙中波的衰减深度却是随这种耦合强度的增大而减小的.     

含气泡液体中声传播的解析解及其强非线性声特性

声波在含气泡的液体中传播时,气泡的受迫振动会引起强的声散射,并且由于振动的非线性,使得气泡产生的次级波不仅含有基频成分,而且还会有高次谐波。本文从理论上描述了气泡个数随尺并给出了含气泡液体的等效非线性声参数Ｂ／Ａ的计算公式理论与已有的实验观测符合较好,文中对含气泡水的声速和声衰减等特性也进行了讨论。     

Simple method for simultaneous determination of the phase retardation and fast axis of a wave plate

A simple method for simultaneous determination of the phase retardation and fast axis of a wave plate is presented. In this method, double light path compare system is adopted to achieve better accuracy. In the main optical path, laser beam passes successively through a polarizer, a wave plate to be measured, an analyzer, and then is incident on a detector. In the reference optical path, another detector is used to monitor the fluctuation of the light source. With rotation of the wave plate, the maximum and minimum output light intensity, rotation angle of the wave plate are detected in the main light path; corresponding light intensity are simultaneously detected in the reference light path. Based on the light intensity and the rotation angle, the phase retardation and fast axis of the wave plate can be determined simultaneously. The main advantage of this method is its simplicity of apparatus, easy operation, low cost, and high accuracy. We believe that the method reported in this paper should be a useful approach to measure a wave plate without requiring any complex and expensive components.     

动态质量密度和声学超常介质

复合介质的质量密度通常认为是组成它的各种成分的质量密度的体平均值.体平均质量密度常常被用于计算在长波长极限下的声波速度,在此极限下波长比复合介质中的特征尺度要大得多.作者通过严格的数学推导证明,计算(长波长极限下的)波速时所用到的动态质量密度与静态的体平均质量密度有显著的不同.这一发现与最近的实验结果符合得非常好,并且使得声学超常介质的实现成为可能.这两种质量密度之所以不同的物理根源就在于,在波场中复合介质中的各个成分之间有相对的运动.也就是说,隐含的假定——在长波长极限下复合介质中的各个成分必定会全体同相地运动——将不再正确,尤其是当各个成分的声学阻抗之间有较大的差异时.实验和理论显示,对于局域共振声学材料而言,动态质量密度甚至还会变成是负的.文章探讨了这一发现的物理意义,以及它在声学超常介质领域的应用.     

动态质量密度和声学超常介质

复合介质的质量密度通常认为是组成它的各种成分的质量密度的体平均值.体平均质量密度常常被用于计算在长波长极限下的声波速度,在此极限下波长比复合介质中的特征尺度要大得多.作者通过严格的数学推导证明,计算（长波长极限下的）波速时所用到的动态质量密度与静态的体平均质量密度有显著的不同.这一发现与最近的实验结果符合得非常好,并且使得声学超常介质的实现成为可能.这两种质量密度之所以不同的物理根源就在于,在波场中复合介质中的各个成分之间有相对的运动.也就是说,隐含的假定——在长波长极限下复合介质中的各个成分必定会全体同相地运动——将不再正确,尤其是当各个成分的声学阻抗之间有较大的差异时.实验和理论显示,对于局域共振声学材料而言,动态质量密度甚至还会变成是负的.文章探讨了这一发现的物理意义,以及它在声学超常介质领域的应用.     

Nonlocal wave propagation in an embedded DWBNNT conveying fluid via strain gradient theory

Based on the strain gradient and Eringen’s piezoelasticity theories, wave propagation of an embedded double-walled boron nitride nanotube (DWBNNT) conveying fluid is investigated using Euler–Bernoulli beam model. The elastic medium is simulated by the Pasternak foundation. The van der Waals (vdW) forces between the inner and outer nanotubes are taken into account. Since, considering electro-mechanical coupling made the nonlinear motion equations, a numerical procedure is proposed to evaluate the upstream and downstream phase velocities. The results indicate that the effect of nonlinear terms in motion equations on the phase velocity cannot be neglected at lower wave numbers. Furthermore, the effect of fluid-conveying on wave propagation of the DWBNNT is significant at lower wave numbers.     

板厚对无障薄板声辐射特性影响的分析

分析无障薄板的声辐射特性时通常忽略板厚对格林函数的影响而采用双层势计算.本文考虑板厚引起的声辐射阻抗,采用混合势计算结构表面声压与振速,并分析板厚对声辐射参数的影响。根据交界相容性条件,采用边界积分方程分别表示平板上下表面的声压和振速,并合并同类项.进一步将结构的动力方程代入混合势形式的振速方程中,离散声压差值和板的位移为振动模态叠加的形式,获得二重积分形式的声辐射阻抗,从而求解振动模态系数,确定声辐射特性参数.以水下简支矩形板为例计算对比了声辐射参数,并讨论了其对板厚的敏感性。结果表明:板厚引起的声辐射阻抗对声辐射参数的大小影响较小,但随着频率的增加致使共振频率发生较大偏移;在相同阶数的共振频率范围内,板厚度越大,采用双层势计算的误差越大。     

Reliability assessment of different plate theories for elastic wave propagation analysis in functionally graded plates

The importance of elastic wave propagation problem in plates arises from the application of ultrasonic elastic waves in non-destructive evaluation of plate-like structures. However, precise study and analysis of acoustic guided waves especially in non-homogeneous waveguides such as functionally graded plates are so complicated that exact elastodynamic methods are rarely employed in practical applications. Thus, the simple approximate plate theories have attracted much interest for the calculation of wave fields in FGM plates. Therefore, in the current research, the classical plate theory (CPT), first-order shear deformation theory (FSDT) and third-order shear deformation theory (TSDT) are used to obtain the transient responses of flexural waves in FGM plates subjected to transverse impulsive loadings. Moreover, comparing the results with those based on a well recognized hybrid numerical method (HNM), we examine the accuracy of the plate theories for several plates of various thicknesses under excitations of different frequencies. The material properties of the plate are assumed to vary across the plate thickness according to a simple power-law distribution in terms of volume fractions of constituents. In all analyses, spatial Fourier transform together with modal analysis are applied to compute displacement responses of the plates. A comparison of the results demonstrates the reliability ranges of the approximate plate theories for elastic wave propagation analysis in FGM plates. Furthermore, based on various examples, it is shown that whenever the plate theories are used within the appropriate ranges of plate thickness and frequency content, solution process in wave number-time domain based on modal analysis approach is not only sufficient but also efficient for finding the transient waveforms in FGM plates.     

Numerical analysis for smoothing of CW multimode beam transformed by time-varying random phase plate

The numerical analysis of CW multimode laser beam transformed by time-varying random phase plate is presented in this paper. The method is based on diffraction integral formula. The dependence of the intensity distribution on the element size, changing frequency and duty ratio is discussed in detail. The numerical results account for the experimental results satisfactorily.     

An analysis of surface acoustic wave propagation in a plate of functionally graded materials with a layered model

In a homogeneous plate, Rayleigh waves will have a symmetric and anti-symmetric mode regarding to the mid-plane with different phase velocities. If plate properties vary along the thickness, or the plate is of functionally graded material (FGM), the symmetry of modes and frequency behavior will be modified, thus producing different features for engineering applications such as amplifying or reducing the velocity and deformation. This kind of effect can also be easily realized by utilizing a layered structure with desired material properties that can produce these effects in terms of velocity and displacements, since Rayleigh waves in a solid with general material property grading schemes are difficult to analyze with known methods. Solutions from layered structures with exponential and polynomial property grading schemes are obtained from the layered model and comparisons with known analytical results are made to validate the method and examine possible applications of such structures in engineering. Supported by the National Natural Science Foundation of China (Grant Nos. 10432030, 10125209, and 10572065) and the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions, Ministry of Education of China, and also supported by Qianjiang River Fellow Fund established by Zhejiang Provincial Government and Ningbo University and administered by Ningbo University, Zhejiang, China     

Reconstruction of the acoustic impedance profile in a plate using an inverse spectral procedure

An inverse spectral procedure was applied to reconstruct the acoustic impedance profile along the thickness direction of a plate using its thickness resonance frequencies, density and thickness. For a successful reconstruction, the material-property profile must be symmetric about the mid-plane of the plate. Several cases of numerical simulations, including plates with a few layers and with a high number of layers are described. The calculated resonance frequencies were used to reconstruct the acoustic impedance profile, a process that was successful for all cases. We assume that a plate with a high number of layers, each with a different but constant acoustic impedance, simulates a plate with a smoothly varying acoustic impedance profile. It can be concluded that such a plate, which generates small, virtually undetectable, internally reflected waves, can also be reconstructed. In the special case of a plate of unknown thickness and unknown but constant density, the method is still useful, because a relative variation of the material property can be reconstructed using only the resonance frequencies. An experiment using a resonance-mode electromagnetic acoustic transducer (resonance-mode EMAT) is also described. EMAT is a non-contact ultrasonic method that can measure thickness resonance frequencies, making it appropriate for this method. Some examples of applications are measurement of the temperature profile inside a rolled metal sheet, measurement of a clad metal plate, and monitoring of a metal casting.