固体板中SH板波非线性效应的实验观察

采用微扰近似和导波的模式展开分析方法,从理论上简要分析了SH板波的二次谐波发生效应;尽管在无限大固体介质中单个切变波的二次谐波发生效应非常微弱,但在一定条件下由两个切变波构成的SH板波可具有强烈的非线性效应;本文的主要工作就是对此结论加以实验验证。试制了激发SH板波的切变波斜劈换能器和接收二次谐波信号的液体斜劈换能器,建立了非线性SH板波的实验研究系统;通过详细的理论分析和对比实验研究,阐明了在一定条件下实验观察到的显著二次谐波信号来源于SH板波传播过程中的强烈非线性效应。此外,针对不同的SH板波传播距离,在远场条件下分别测量了相应的二次谐波幅频曲线;在基频SH板波与二倍频对称兰姆波相速度相等所对应的频率值附近,分析了二次谐波的振幅随传播距离的变化关系,结果证明在一定条件下SH板波的二次谐波振幅可随传播距离积累增长,即SH板波可具有强烈的非线性效应。      

Reflection of Lamb waves obliquely incident on the free edge of a plate

The reflection of obliquely incident symmetric and anti-symmetric Lamb wave modes at the edge of a plate is studied. Both in-plane and Shear-Horizontal (SH) reflected wave modes are spawned by an obliquely incident in-plane Lamb wave mode. Energy reflection coefficients are calculated for the reflected wave modes as a function of frequency and angle of incidence. This is done by using the method of orthogonal mode decomposition and by enforcing traction free conditions at the plate edge using the method of collocation. A PZT sensor network, affixed to an Aluminum plate, is used to experimentally verify the predictions of the analysis. Experimental results provide support for the analytically determined results.     

Effect of anisotropy on acoustoelastic birefringence in wood

The ultrasonic velocity of shear waves propagating through radial direction of a wood plate specimen, transversely to the loading direction, was measured. By rotating an ultrasonic sensor, the oscillation direction of the shear waves was varied with respect to the wood plate axis and loading direction. The relationship between shear wave velocity and oscillation direction was examined to discuss the effect of anisotropy on the acoustoelastic birefringence in wood. The results obtained were summarized as follows. When the oscillation direction of the shear wave corresponded to the tangential direction of the wood specimen regardless of the stress direction, shear wave velocity decreased markedly and the relationship between shear wave velocity and rotation angle tended to become discontinuous. That is, when the shear waves oscillated in the anisotropic axis of the wood, the shear wave velocity peaked unlike in the case of oscillation in the stress direction. In an isotropic material (acrylic, aluminum 5052), on the contrary, when the shear waves oscillated in the stress direction of the specimen, the shear wave velocity peaked regardless of the main-axis direction of the specimen. On the basis of the discussion of these results, the ultrasonic shear wave propagating in wood under stress is confirmed to be polarized in the anisotropic axis of the wood.     

Nondestructive testing in human teeth using a leaky Lamb wave device

A Lamb wave interdigital transducer mounted on a layered substrate composed of two plates, a thin piezoelectric ceramic plate and an acrylic plate, operating at a liquid-solid boundary, is investigated for ultrasonic nondestructive testing of the layer thickness in human teeth. A higher-order mode having a phase velocity higher than the longitudinal wave velocity in the human teeth can be used for nondestructive testing. In the combination of the two layers, the fourth mode of leaky Lamb wave is most favorable for a frequency-controllable radiation angle of an ultrasound beam into a water layer as an acoustic coupler. In the configuration of an acoustic delay line, the layer-thickness measurement in vivo, evaluated from the time interval between two reflected ultrasound echoes, is successfully realized under a thin water layer as the acoustic coupler.     

轨道板中超声兰姆波传播的有限元计算和实验*

该文针对我国高速铁路轨道板缺陷的非接触动态检测问题,研究了空气耦合超声兰姆波在轨道板中的传播规律。首先,给出了轨道板中超声兰姆波的相速度和群速度频散曲线,结果表明:随着频厚积的增加,频散现象越明显,并且A0相速度收敛于Rayleigh波的波速。然后,建立轨道板中波传播的有限元模型,计算得到兰姆波传播的群速度为2220 m/s,且二维傅里叶变换系数的较大值沿Rayleigh波的频散曲线分布。最后,在沪杭高铁嘉兴南站进行了现场测试,以8.8°倾斜角向轨道板激励产生超声兰姆波,激发产生的兰姆波模态群速度为2325 m/s,且二维傅里叶变换分析其系数的较大值沿Rayleigh波的频散曲线分布。有限元计算结果和实验结果均与理论计算结果一致。该研究为后续轨道板缺陷的非接触动态检测提供了理论依据和实验方法。     

Capillary-gravity waves in the presence of infinite porous plates

Summary The wave motion generated by a porous plate immersed in a non-wetting liquid of infinite depth is investigated. The boundary value problem for the velocity potentials is solved using Taylor's assumption on the plate and a contact-line condition that accounts for the dynamic variation of the angle of contact and the vorticity there. The amplitude of the radiated waves and the energy dissipated are calculated both when the plate is oscillating horizontally and vertically with a prescribed velocity. Also the scattering of a harmonic wave incident normally to the plate is considered and the reflexion and transmission coefficients are obtained.     

The effect of initial stress on the propagation behavior of SH waves in piezoelectric coupled plates

This study analytically investigates the propagation of shear waves (SH waves) in a coupled plate consisting of a piezoelectric layer and an elastic layer with initial stress. The piezoelectric material is polarized in z-axis direction and perfectly bonded to an elastic layer. The mechanical displacement and electrical potential function are derived for the piezoelectric coupled plates by solving the electromechanical field equations. The effects of the thickness ratio and the initial stress on the dispersion relations and the phase and group velocities are obtained for electrically open and mechanically free situations. The numerical examples are provided to illustrate graphically the variations of the phase and group velocities versus the wave number for the different layers comparatively. It is seen that the phase velocity of SH waves decreases with the increase of the magnitude of the initial compression stress, while it increases with the increase of the magnitude of the initial tensile stress. The initial stress has a great effect on the propagation of SH waves with the decrease of the thickness ratio. This research is theoretically useful for the design of surface acoustic wave (SAW) devices with high performance.     

Flexural and transversal wave motion in homogeneous isotropic thermoelastic plates by using asymptotic method

The present investigation is concerned with the flexural and transversal wave motion in an infinite, transversely isotropic, thermoelastic plate by asymptotic method. The governing equations for the flexural and transversal motions have been derived from the system of three-dimensional dynamical equations of linear theory of coupled thermoelasticity. The asymptotic operator plate model for free vibrations; both flexural and transversal, in a homogenous thermoelastic plate leads to fifth degree and cubic polynomial secular equations, respectively, that governs frequency and phase velocity of various possible modes of wave propagation at all wavelengths. All the coefficients of differential operator have been expressed as explicit functions of the material parameters. The velocity dispersion equations for the flexural and transversal wave motion have been deduced from the three-dimensional analog of Rayleigh-Lamb frequency equation for thermoelastic plate waves. The approximations for long and short waves and expression for group velocity have also been derived. The thermoelastic Rayleigh-Lamb frequency equations for the considered plate are expanded in power series in order to obtain polynomial frequency and velocity dispersion relations whose equivalence is established with that of asymptotic method. The dispersion curves for phase velocity, group velocity and attenuation coefficient of various flexural and transversal wave modes are shown graphically for aluminum-epoxy material elastic and thermoelastic plates.     

Generalized thermoelastic extensional and flexural wave motions in homogenous isotropic plate by using asymptotic method

In this paper the asymptotic method has been applied to investigate propagation of generalized thermoelastic waves in an infinite homogenous isotropic plate. The governing equations for the extensional, transversal and flexural motions are derived from the system of three-dimensional dynamical equations of linear theories of generalized thermoelasticity. The asymptotic operator plate model for extensional and flexural free vibrations in a homogenous thermoelastic plate leads to sixth and fifth degree polynomial secular equations, respectively. These secular equations govern frequency and phase velocity of various possible modes of wave propagation at all wavelengths. The velocity dispersion equations for extensional and flexural wave motion are deduced from the three-dimensional analog of Rayleigh-Lamb frequency equation for thermoelastic plate. The approximation for long and short waves along with expression for group velocity has also been obtained. The Rayleigh-Lamb frequency equations for the considered plate are expanded in power series in order to obtain polynomial frequency and velocity dispersion relations and its equivalence established with that of asymptotic method. The numeric values for phase velocity, group velocity and attenuation coefficients has also been obtained using MATHCAD software and are shown graphically for extensional and flexural waves in generalized theories of thermoelastic plate for solid helium material.     

SH wave propagation in a piezoelectric/piezomagnetic plate with an imperfect magnetoelectroelastic interface

In this paper, we investigate the SH wave propagation in a layered piezoelectric (PE) and piezomagnetic (PM) plate with an imperfect magnetoelectroelastic interface. A linear magnetoelectroelastic spring model is used to describe the weakness of the imperfect interface. On the basis of this model, dispersion curves and mode shapes of the SH waves are computed. In particular, a PZT-5A/CoFe₂O₄ composite plate is considered in the numerical examples to calculate the dispersion curves and the mode shapes for different combinations of the magnetic, electrical and elastic spring constants. The effects of the layer thickness ratio and the electric-magnetic boundary conditions on the dispersion curves are discussed in details. Our results show that for a general weak bonding case, the high modes of the dispersion curves are not monotonous in the range of small wave numbers. With the layer thickness ratio increasing, the wave velocities of the SH waves increase. The electric boundary conditions mainly determine the dispersion curves of the SH waves in the case of a small layer thickness ratio, i.e. a large thickness of the PE layer. The present results have relevant applications in the nondestructive testing and evaluation of the layered PE/PM plate-like wave devices.     

SH Acoustic Waves in a Lithium Niobate Plate and the Effect of Electrical Boundary Conditions on Their Properties

It is theoretically and experimentally confirmed that the electromechanical coupling coefficient of SH waves propagating in a Y-cut lithium niobate plate along the X direction can exceed 30% when the plate thickness satisfies the condition h/λ= 0.02–0.15. This value of the coupling coefficient is approximately six to seven times greater than the maximal value obtained for SAW in the same material. Such a high value of K ² offers a possibility to control the wave velocity by varying the electrical boundary conditions, e.g., by moving a conducting screen toward the plate surface. The effect of such a screen on the properties of the SH waves is studied both theoretically and experimentally. On the whole, the results of the study show that the use of SH waves offers considerable improvements in the parameters of the known SAW devices and also opens up the possibilities for the development of new devices and sensors that have to operate in contact with a liquid medium.     

激光衍射法测量表面张力和毛细波波速与温度的关系

利用激光衍射对液体表面张力和毛细波波速与温度的关系进行了研究.当激光斜入射到毛细波上,观察到稳定的、清晰的衍射图样,运用光栅衍射理论对该实验现象进行了分析,测量了不同温度下蒸馏水的表面张力和毛细波波速,用最小二乘法对实验数据进行拟合,给出了表面张力和毛细波波速与温度的解析关系,发现表面张力和毛细波波速随着温度的增加而减小,并和温度呈近似线性关系.根据其机理,建立了激光衍射法实时的和非接触的测量不同温度下液体表面张力和毛细波波速的方法.     

SH wave propagation in magnetic–electric periodically layered plates

In this paper, dispersive behavior and band structure of SH waves in magnetic–electric (ME) periodically layered plate are investigated by the transfer matrix method. Two kinds of unit cell form, one is piezoelectric (PE)/piezomagnetic (PM)/PE, and the other is PM/PE/PM, are considered in detailed. A peculiar case of the generalized single-celled plate is first presented and then the multi-celled periodical layered plates for discussion on the propagation behaviors and the band characteristics of SH waves, respectively. The effects on dispersive curves of four kinds of ME boundary conditions at the free surface of plates are discussed. Numerical examples for phase velocities or frequencies all show that the zero-order mode is non-dispersive both for single-celled and multi-celled periodically layered plates. The high modes of dispersive curves tend to the shear wave velocity of the slower sub-layer as frequencies increase both for these two structures. The frequency pass-band and frequency band gaps appear in multi-layered ME periodically layered plates. Electrical and magnetic boundary conditions, respectively, determine the dispersive curves for SH waves in the PE/PM/PE and PM/PE/PM periodically layered plates.     

圆管结构中周向导波非线性效应的模式展开分析

在二阶微扰近似条件下, 采用导波模式展开分析方法研究了圆管结构中周向导波的非线性效应. 伴随基频周向导波传播所发生的二次谐波, 可视为由一系列二倍频周向导波模式叠加而成. 从动量定理出发, 结合柱坐标系下非线性应力张量及其散度的数学表达式, 针对圆管中某一基频周向导波模式, 推导出相应的二倍频应力张量及二倍频彻体驱动力的数学表达式, 建立了确定二倍频周向导波模式展开系数的控制方程, 得到了伴随基频周向导波传播所发生的二次谐波声场的形式解. 理论分析和数值计算表明, 当构成二次谐波声场的某一二倍频周向导波模式与基频周向导波的相速度匹配时, 该二倍频周向导波模式的位移振幅表现出随传播周向角积累增长的性质; 当两者的相速度失配时, 二倍频周向导波的振幅随传播周向角表现出“拍”效应.     

Study of second-harmonic generation of shear horizontal modes using modal analysis

In this work a modal analysis was employed to study generation of the second harmonics of shear horizontal (SH) modes in a solid plate. Under second order perturbation, second-harmonic generation will occur accompanying SH mode propagation due to the bulk elastic non-linearity of plate material. In solid plate the total second-harmonic fields of a SH mode propagation are regarded as sum of the fields of a series of double frequency Lamb modes (DFLMs). The contribution of each DFLM component to the total second-harmonic fields is dependent of the difference of phase velocities of the corresponding DFLM and SH mode. The analysis results show that the DFLM field component may have cumulative growth effect once its phase velocity exactly or approximately equals that of a SH mode. It is also found that the fields of the total second harmonics of a SH mode are only symmetrical. The examples of field distributions of several DFLMs on the plate surface are considered.     

半波片角度失配对通道调制型偏振成像效果的影响及补偿

通道调制型偏振成像系统能够实时地对目标进行全偏振成像,是当前偏振成像领域的研究热点之一.基于萨瓦板的通道调制型偏振仪中半波片的光轴方向对成像结果的准确性有较大的影响.本文分析了半波片失配角的大小对探测器采集到的光强分布的影响,得到了二者之间的表达式,根据该表达式提出通过测量半波片失配角对系统进行定标并利用测得的半波片失配角对偏振成像的解调结果进行修正和补偿的方法.计算机仿真结果显示失配角为0.5?时,S1,S2和S3的解调结果准确度在经过修正补偿后分别提高了0.06%,3.49%和3.49%.表明该方法能够较好地对解调出的偏振斯托克斯参数图像进行补偿,得到更精确的成像结果,对提高通道调制型偏振成像的质量具有重要的意义.     

金属板中Lamb波波速与应力关系的实验研究

本文给出了金属板中Lamb波波速对同向应力变化率测量的装置,探讨分析了测量原理及误差,并对Lamb波的波速与应力关系进行了实验研究。结果表明Lamb波的波速对应力有较好的线性关系,Lamb波相速度对应力的变化率的实验值与理论值符合很好。     

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.     

波片复合旋光器研究

利用矩阵光学方法，分析了波片复合旋光器的理论基础，给出了二元和三元复合波片旋光器的条件及其旋光角的大小的数学表达式，并根据此理论作了典型设计。结果表明，旋光角的大小与各波片的延迟量和它们的快轴同X轴的夹角有关。     

Single SH guided wave mode generation method for PPM EMATs

Using periodic permanent magnet(PPM) electromagnetic acoustic transducers(EMATs), different shear horizontal(SH) guided wave modes can form simultaneously in some situations, which can interfere with the inspection. The main cause of this phenomenon(typically named multiple modes) is related to the frequency bandwidth of excitation signals and the transducer spatial bandwidth. Simply narrowing the frequency bandwidth cannot effectively limit the number of different SH modes. Previous researches showed that unnecessary SH wave modes can be eliminated by using dual EMATs.However, in practical applications, it is more convenient to change the excitation frequency than to use dual EMATs. In this paper, the stress boundary conditions of the PPM-EMAT are analyzed, the analytical expression of SH guided wave is established, and the magnitude of SH guided wave mode under continuous tone and tone-burst input is obtained. A method to generate a single SH mode by re-selecting an operating point is proposed. Furthermore, the influence of the frequency bandwidth of the tone-burst signal is analyzed. Finally, a single SH mode excitation is achieved with tone-burst input.