Determination of mechanical stresses in solids by an acoustic method

Different versions of linearized problems of the elastic wave propagation in prestressed bodies are considered. The influence of the version of the linearized elasticity theory chosen for calculating the magnitude of the acoustoelastic effect on the result of calculation is analyzed for longitudinal and shear waves and for Rayleigh surface waves. The results of theoretical calculations are compared with the experiment. Experimental data on the effect of bending stresses on the propagation velocity of Rayleigh waves are presented. These results extend the range of problems that can be solved by using the acoustoelastic effect.     

Experimental study on the surface stress measurement with Rayleigh wave detection technique

In this paper, experimental study on the surface stress measurement of a metallic material based on the Rayleigh wave acoustoelastic theory is introduced. A Rayleigh wave acoustoelastic formula deduced by Husson is optimized to estimate the surface stress of the material. Two micro Rayleigh wave transducers with 5 MHz frequency one of which is used for acoustic pulse emitter and another for receiver are used to determine the time of flight of Rayleigh wave propagating in a certain distance along the surface of the material. The difference in time of flight between two ultrasonic signals obtained in stressed and unstressed object surface is identified by the digital correlation method. A specimen made of Q235 steel and applied with tensile load is used for calibration to obtain the acoustoelastic coefficients of Q235 steel. Furthermore, some principal factors which may result in errors in the experiment are discussed and some measurements are proposed to prevent these errors. Finally the surface stress of a cantilever beam is detected by the Rayleigh wave acoustoelastic technique and the experimental result is well compared with the theoretical value.     

Numerical solutionsfor acoustic Rayleigh wave problems in anisotropic and layered media

A finite difference iterative formulation which has already been applied successfully to acoustic surface wave scattering problems in homogeneous and layered isotropic as well as non-linear media, is extended to cover Rayleigh type mode propagation in anisotropic materials. The transmission, reflection and conversion into bulk modes of Rayleigh waves are studied as a function of relative step height. The waves are incident normally at upward and downward step discontinuities formed by the sudden termination of an uniform aluminium layer on a semi-infinite fused quartz substrate. In terms of the severity of Rayleigh wave scattering, the layered upward step has the most drastic effects, followed by the layered downward and the homogeneous downward steps respectively. Rayleigh wave scattering at a break in a layered waveguide is discussed.     

分层半空间表面非线性瑞利波的激发*

针对非线性瑞利波在均匀分层半空间结构中的激发和传播规律进行研究。根据摄动理论和模态分解将分层半空间结构中瑞利波的二次谐波声场表示为二倍频瑞利波模式的线性组合,经由互易关系得到各模式的展开系数表达式。对不同分层半空间结构中瑞利波二次谐波的激发和传播特性进行讨论,结果表明相速度匹配的瑞利波模式其二次谐波分量随传播距离线性增长,非匹配模式的二次谐波分量则沿传播方向周期震荡传播。此外,文中定义非线性参数表征瑞利波模式产生的非线性程度,这有利于选择出具有明显非线性效应的匹配点,为后续检测工作提供理论依据,具有指导意义。     

Rayleigh wave and detection of low-velocity layers in a stratified half-space

The excitation and propagation of the guided waves in a stratified half-space and a Rayleigh wave exploration method in shallow engineering seismic exploration are studied in this paper. All the modes of the guided waves are calculated by the bisection method in the case where the low velocity layers are contained in a stratified half-space. Cases when the formation shear wave velocity gradually decreases from the top to the bottom layers are also studied. The dispersion curves obtained in actual Rayleigh wave exploration are usually noncontinual zigzag curves, but the dispersion curves given by the elastic theory for given modes of the guided waves are smooth and continual curves. In this paper, the mechanism of zigzag dispersion curves in Rayleigh wave exploration is investigated and analyzed thoroughly. The zigzag dispersion curves can give not only the possible positions of the low-velocity layers but also the other information on the formation structure (fractures, oil, gas, etc.). It is found that the zigzag dispersion curves of the Rayleigh wave are the result of the leap of the modes and the existence of low velocity layers in a stratified half-space. The effects of the compressional wave velocity, shear wave velocity, and density of each layer on zigzag dispersion curves and the relationship of the low velocity layers to zigzag dispersion curves are also investigated in detail. Finally, the exploration depth of the Rayleigh wave is discussed. The exploration depth of the Rayleigh wave is equal to the wavelength multiplied by a coefficient that is variable and usually given by the work experience and the formation properties of the local work area.     

Simulation on laser-induced surface acoustic wave on isotropic cylinders by finite element method

Based on the thermoelastic theory, a finite element model is developed to simulate the process of laser inducing ultrasonic field in isotropic cylinders, which can take the temperature dependence of thermal parameters into account. Using the finite element model, we have simulated the ultrasonic fields induced by a pulse laser line source impacting on the generatrix of aluminum cylinders with different diameters. And the intact waveforms of surface acoustic wave (SAW including cylindrical Rayleigh and Whispering gallery (WG) modes) are presented, which are in very good agreement with the calculated and experimental waveforms in other literatures. Furthermore, the dispersion properties of cylindrical Rayleigh waves are analyzed by the method of phase spectral analysis, and the results show that with the increasing frequency, the phase velocity of cylindrical Rayleigh wave rapidly increases to the maximum value, and then gradually decreases to that of plane Rayleigh wave. With the diameter of cylinder decreasing, the maximum value of phase velocity and the corresponding frequency increase.     

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     

Dispersion of waves and characteristic wave surfaces in functionally graded piezoelectric plates

An inhomogeneous layer element method is presented to analyze the dispersion of waves and characteristic wave surfaces in plates of functionally graded piezoelectric material (FGPM). In this method, the FGPM plate is divided into a number of layered elements. The elemental elastic and electric properties are assumed as linear functions of the thickness to adopt the variety of the material property of FGPM. The Hamilton principle is applied to determine the governing equations. The phase velocity surface, phase slowness surface, phase wave surface, group velocity surface, group slowness surface, and group wave surface for FGPM plate are formulated using Rayleigh quotient and the orthogonality condition of the eigenvectors. These six surfaces are then used to illustrate the characteristics of waves in FGPM plates. Numerical examples are presented using the present formulations to analyze dispersions and characteristics of waves in FGPM plates.     

谱有限元数值分析各向异性复合板中导波色散特性

提出谱有限元方法研究层状各向异性复合板中导波的色散特性和波结构。基于三维弹性动力学方程,用有限元方法离散波导截面,波传播方向的位移用简谐波表示,得到了导波色散的特征方程。分析了单层和双层复合板中导波沿不同方向传播的色散特性和波结构,讨论了双层复合板中层厚比对相速度的影响。数值研究结果表明:导波的对称模态沿纤维方向传播时在较宽的频率范围内保持弱色散状态。双层复合板中导波基本模态的相速度在低频时受层厚比的影响较明显,随着频率的增加趋向于相速度较低的材料。数值模拟结果为导波用于复合材料定量无损检测和性能评价提供理论依据。      

Incredible negative values of effective electromechanical coupling coefficient for surface acoustic waves in piezoelectrics

The extraordinary case of increase in velocity of surface acoustic waves (SAW) caused by electrical shorting of the surface of the superstrong piezoelectric crystal potassium niobate, KNbO3, is numerically found. The explanation of this effect is based on considering SAWs as coupled Rayleigh and Bleustein-Gulyaev modes. A general procedure of approximate decoupling of the modes is suggested for piezoelectric crystals of arbitrary anisotropy. The effect under study takes place when the phase velocity of uncoupled sagittally polarized Rayleigh waves is intermediate between the phase velocities of uncoupled shear-horizontal Bleustein Gulyaev waves at the free and metallized surfaces. In this case, the metallization of the surface by an infinitely thin layer may cause a crossover of the velocity curves of the uncoupled waves. The presence of the mode coupling results in splitting of the curves with transition from one uncoupled branch to the other. This transition is responsible for the increase in SAW velocity, which appears to be greater than its common decrease produced by electrical shorting of the substrate surface.     

FEM simulation of Rayleigh waves for CMOS compatible SAW devices based on AlN/SiO2/Si(1 0 0)

A simulation study of Rayleigh wave devices based on a stacked AlN/SiO₂/Si(1 0 0) device was carried out. Dispersion curves with respect to acoustic phase velocity, reflectivity and electromechanical coupling efficiency for tungsten W and aluminium Al electrodes and different layer thicknesses were quantified by 2D FEM COMSOL simulations. Simulated acoustic mode shapes are presented. The impact of these parameters on the observed Rayleigh wave modes was discussed. High coupling factors of 2% and high velocities up to 5000 m/s were obtained by optimizing the AlN/SiO₂ thickness ratio.     

Near field Rayleigh wave on soft porous layers

Simulations performed for a typical semi-infinite reticulated plastic foam saturated by air show that, at distances less than three Rayleigh wavelengths from the area of mechanical excitation by a circular source, the normal frame velocity is close to the Rayleigh pole contribution. Simulated measurements show that a good order of magnitude estimate of the phase speed and damping can be obtained at small distances from the source. Simulations are also performed for layers of finite thickness, where the phase velocity and damping depend on frequency. They indicate that the normal frame velocity at small distances from the source is always close to the Rayleigh pole contribution and that a good order of magnitude estimate of the phase speed of the Rayleigh wave can be obtained at small distances from the source. Furthermore, simulations show that precise measurements of the damping of the Rayleigh wave need larger distances. Measurements performed on a layer of finite thickness confirm these trends.     

Effect of the surface free energy on the behaviour of surface and guided waves

The aim of this paper is to evaluate the influence of the surface free energy upon the propagation of the eigenmodes of structures, by studying successively (a) the Rayleigh wave for an elastic half-space, (b) the Lamb waves for an elastic layer, and (c) the guided modes for a tri-layer structure (e.g., metal/adhesive/metal). The surface free energy is a parameter which appears in the jump conditions of stresses and displacements at each interface, and which consequently modifies the eigenmodes, solutions of the boundary conditions system. As expected, the Rayleigh wave is dispersive and its velocity increases when the surface free energy increases. In the same way, the velocity of Lamb waves also increases except at normal angle of propagation where the surface free energy does not arise. Moreover, near the Rayleigh angle, the behaviour of the A₀ and S₀ Lamb modes varies strongly according to the surface free energy. Similar results are observed for the tri-layer structure.     

分层固体板中导波的激发与频散特性

针对无限大弹性分层固体板,研究了结构中导波的频散和激发特性。首先使用传递矩阵法推导分层板模型中导波的频散方程,然后用二分法求取导波各模式的频散曲线,进而分析结构中导波的频散特性。结果表明:在速度递增或递减的分层板中,基阶模式和高阶模式的高频极限分别等于低速层的瑞利波速和横波波速。对于含低速夹层的分层板,所有模式的高频极限都等于低速层的横波速度。在导波激发特性方面,研究了在具有一定宽度的法向力源作用下的分层板中导波各模式在结构中的法向位移谱。发现在速度递增的分层板结构中基阶模式是主导模式,而对于速度递减和含低速夹层模型,主导模式在不同的频段范围内对应不同的导波模式。      

超声双折射法测试铝合金的内部应力

声各向同性的金属材料在应力作用下表现出声各向异性,这是用声弹性法分析材料内部应力的基础。本文用偏振方向平行或垂直于应力方向的超声纯横波对LY11型铝合金进行测试。实验结果表明:材料在拉、压单轴应力作用下,偏振方向平行和垂直于应力方向的超声纯横波的声速都发生了变化。实验在分析材料声各向异性的基础上计算材料声弹性双折射系数,得到测试LY11型铝合金内部应力的理论公式,并对其内部的残余应力进行评估。实验中利用双换能器回振法测量声速,时间测试精确度可达10^-11s,可精确测量声速的微小变化量。     

Subsonic leaky Rayleigh waves at liquid-solid interfaces

The paper is devoted to the study of leaky Rayleigh waves at liquid-solid interfaces close to the border of the existence domain of these modes. The real and complex roots of the secular equation are computed for interface waves at the boundary between water and a binary isotropic alloy of gold and silver with continuously variable composition. The change of composition of the alloy allows one to cross a critical velocity for the existence of leaky waves. It is shown that, contrary to popular opinion, the critical velocity does not coincide with the phase velocity of bulk waves in liquid. The true threshold velocity is found to be smaller, the correction being of about 1.45%. Attention is also drawn to the fact that using the real part of the complex phase velocity as a velocity of leaky waves gives only approximate value. The most interesting feature of the waves under consideration is the presence of energy leakage in the subsonic range of the phase velocities where, at first glance, any radiation by harmonic waves is not permitted. A simple physical explanation of this radiation with due regard for inhomogeneity of radiated and radiating waves is given. The controversial question of the existence of leaky Rayleigh waves at a water/ice interface is reexamined. It is shown that the solution considered previously as a leaky wave is in fact the solution of the bulk-wave-reflection problem for inhomogeneous waves.     

Viscosity and Diffusion Effects at the Boundary Surface of Viscous Fluid and Thermoelastic Diffusive Solid Medium

This paper concentrates on the wave motion at the interface of viscous compressible fluid half-space and homogeneous isotropic, generalized thermoelastic diffusive half-space. The wave solutions in both the fluid and thermoelastic diffusive half-spaces have been investigated; and the complex dispersion equation of leaky Rayleigh wave motion have been derived. The phase velocity and attenuation coefficient of leaky Rayleigh waves have been computed from the complex dispersion equation by using the Muller's method. The amplitudes of displacements, temperature change and concentration have been obtained. The effects of viscosity and diffusion on phase velocity and attenuation coefficient of leaky Rayleigh waves motion for different theories of thermoelastic diffusion have been depicted graphically. The magnitude of heat and mass diffusion flux vectors for different theories of thermoelastic diffusion have also been computed and represented graphically.     

Critical surface wave velocity near phase transitions

The temperature dependent Rayleigh wave velocity is discussed for crystals with a surface layer of depth equal to the correlation length, ξ, with special reference to a critical region near phase transitions. For finite qξ the Rayleigh wave velocity reflects the specific critical properties of the surface layer. Under such conditions the temperature dependence of Rayleigh waves cannot be predicted on the temperature dependence of constants. A phenomenological analysis is made for qξ ≦? 1. Experimental results on SrTiO₃ show bulk-dominated critical Rayleigh wave velocities due to the short correlation length in this material.     

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。     

左手介质中电磁波的传播速度

在同向介质中,电磁波的群速度一般是能量传播的方向,并且电磁波的相速度和群速度在大部分情况下都满足瑞利关系.为了研究左手介质的电磁特性,本文从理论上导出了左手介质中电磁波的相速度、群速度及其关系,得出左手介质中电磁波的群速度为负,并介绍了左手介质的一些应用前景.