激光在近表面弹性性质梯度变化的材料中激发超声波的数值分析

激光激发超声波为评价材料近表面弹性性质提供了有效的手段. 考虑到由于冲击硬化、表面热处理、表面氧化等引起的金属材料近表面层弹性性质的变化，建立了一种激光在基底上的梯度材料中激发超声波的理论模型. 用有限元方法模拟了热弹条件下脉冲激光作用于材料上表面激发出的超声波及其传播过程，研究了近表面层离散的层数对超声波的产生和传播的影响，并分别讨论了表面层“变硬”和“变软”两种情况下声表面波的模式变化及用二维傅里叶变换得到各模式的色散曲线. 为进一步研究近表面层的弹性性质建立合理的计算模型及材料性质的反演提供了理论依 关键词： 超声波 有限元法 近表面弹性性质 色散     

近表面弹性性质连续变化材料中激光声表面波的理论研究

基于金属材料近表面层弹性性质（杨氏模量）的连续变化,建立了一种激光在基底上的梯度材料中激发声表面波的理论模型,并用有限元方法模拟了脉冲激光作用于材料上表面激发出的超声波及其传播过程.讨论了表面层厚度的变化以及表面层弹性性质的变化对热弹条件下产生的声表面波波形特征的影响,并分别计算了两种情况下的声表面波的相速度色散,得到了两种情况下声表面波的变化规律.     

Improved MLPG_R method for simulating 2D interaction between violent waves and elastic structures

Interaction between violent water waves and structures is of a major concern and one of the important issues that has not been well understood in marine engineering. This paper will present first attempt to extend the Meshless Local Petrov Galerkin method with Rankine source solution (MLPG_R) for studying such interaction, which solves the Navier–Stokes equations for water waves and the elastic vibration equations for structures under wave impact. The MLPG_R method has been applied successfully to modeling various violent water waves and their interaction with rigid structures in our previous publications. To make the method robust for modeling wave elastic–structure interaction (hydroelasticity) problems concerned here, a near-strongly coupled and partitioned procedure is proposed to deal with coupling between violent waves and dynamics of structures. In addition, a novel approach is adopted to estimate pressure gradient when updating velocities and positions of fluid particles, leading to a relatively smoother pressure time history that is crucial for success in simulating problems about wave–structure interaction. The developed method is used to model several cases, covering a range from small wave to violent waves. Numerical results for them are compared with those obtained from other methods and from experiments in literature. Reasonable good agreement between them is achieved.     

Investigation of surface acoustic waves in laser shock peened metals

Laser shock peening is a well-known method for extending the fatigue life of metal components by introducing near-surface compressive residual stress. The surface acoustic waves (SAWs) are dispersive when the near-surface properties of materials are changed. So the near-surface properties (such as the thickness of hardened layers, elastic properties, residual stresses, etc.) can be analyzed by the phase velocity dispersion. To study the propagation of SAWs in metal samples after peening, a more reasonable experimental method of broadband excitation and reception is introduced. The ultrasonic signals are excited by laser and received by polyvinylindene fluoride (PVDF) transducer. The SAW signals in aluminum alloy materials with different impact times by laser shock peening are detected. Signal spectrum and phase velocity dispersion curves of SAWs are analyzed. Moreover, reasons for dispersion are discussed.     

Love waves in functionally graded piezoelectric materials by stiffness matrix method

A numerical matrix method relative to the propagation of ultrasonic guided waves in functionally graded piezoelectric heterostructure is given in order to make a comparative study with the respective performances of analytical methods proposed in literature. The preliminary obtained results show a good agreement, however numerical approach has the advantage of conceptual simplicity and flexibility brought about by the stiffness matrix method. The propagation behaviour of Love waves in a functionally graded piezoelectric material (FGPM) is investigated in this article. It involves a thin FGPM layer bonded perfectly to an elastic substrate. The inhomogeneous FGPM heterostructure has been stratified along the depth direction, hence each state can be considered as homogeneous and the ordinary differential equation method is applied. The obtained solutions are used to study the effect of an exponential gradient applied to physical properties. Such numerical approach allows applying different gradient variation for mechanical and electrical properties. For this case, the obtained results reveal opposite effects. The dispersive curves and phase velocities of the Love wave propagation in the layered piezoelectric film are obtained for electrical open and short cases on the free surface, respectively. The effect of gradient coefficients on coupled electromechanical factor, on the stress fields, the electrical potential and the mechanical displacement are discussed, respectively. Illustration is achieved on the well known heterostructure PZT-5H/SiO₂, the obtained results are especially useful in the design of high-performance acoustic surface devices and accurately prediction of the Love wave propagation behaviour.     

MR detection of mechanical vibrations using a radiofrequency field gradient

A new method for NMR characterization of mechanical waves, based upon radiofrequency field gradient for motion encoding, is proposed. A binomial B1 gradient excitation scheme was used to visualize the mobile spins undergoing a periodic transverse mechanical excitation. A simple model was designed to simulate the NMR signal as a function of the wave frequency excitation and the periodicity of the NMR pulse sequence. The preliminary results were obtained on a gel phantom at low vibration frequencies (0-200 Hz) by using a ladder-shaped coil generating a nearly constant RF field gradient along a specific known direction. For very small displacements and/or B1 gradients, the NMR signal measured on a gel phantom was proportional to the vibration amplitude and the pulse sequence was shown to be selective with respect to the vibration frequency. A good estimation of the direction of vibrations was obtained by varying the angle between the motion direction and the B1 gradient. The method and its use in parallel to more conventional MR elastography techniques are discussed. The presented approach might be of interest for noninvasive investigation of elastic properties of soft tissues and other materials.     

The radiation impedance and the energy partition among wave fields generated by a normal force strip radiator on isotropic solid surface

I.IntroductionTheacousticbeams'f0cusingandscanninggeneratedbytransducerarraysonso1idsurfacep1ayaveryimportantroleinacousticimagingandultrasonoc1ectronicdevices.InourpreviouSworkt'-'],weinvestigatcdtheproperties0ftheacousticbeams'focusingandscanninga1ongthesymmetricalaxis,acousticfic1ddistributioninthewho1espaceandnearthefocus.Andwealsogaverigoroustheoretica1ana1ysis,numcrica1simu1ationandexperimenta1obscrvation.Butra-diationimpedanceandenergyofthesurfaceradiatorshavenotbeendiscussedyetbynow.…     

Leaky wave detection at air-solid interfaces by laser interferometry

A recently developed optical heterodyne interferometer is proved to be sensitive to detect ultrasonic waves leaking out from metals (and from non-metals as well) several centimeters away from the metal surface in air. This measurement is based on the detection of the optical index variation in air due to the leaky wave. Experiments were carried out using both ultrasonic leaky Rayleigh and leaky Lamb waves in the low-megahertz region. Optical measurements of these leaky wave velocities in semi-infinite materials and plates, which are related to elastic constants of the materials, showed a good correlation to the predicted values. Optical measurements of the amplitude of the leaky waves were used to obtain attenuation coefficients, which correlate to the structural integrity of the materials. Surface and near-surface defects were also detected. This optical method can be used for metals with low-reflectivity surfaces. Thus, it can be used for non-polished surfaces and can be extended for non-contact, non-destructive evaluation applications.     

A numerical study on the propagation of Rayleigh and guided waves in cortical bone according to Mindlin's Form II gradient elastic theory

Cortical bone is a multiscale heterogeneous natural material characterized by microstructural effects. Thus guided waves propagating in cortical bone undergo dispersion due to both material microstructure and bone geometry. However, above 0.8 MHz, ultrasound propagates rather as a dispersive surface Rayleigh wave than a dispersive guided wave because at those frequencies, the corresponding wavelengths are smaller than the thickness of cortical bone. Classical elasticity, although it has been largely used for wave propagation modeling in bones, is not able to support dispersion in bulk and Rayleigh waves. This is possible with the use of Mindlin's Form-II gradient elastic theory, which introduces in its equation of motion intrinsic parameters that correlate microstructure with the macrostructure. In this work, the boundary element method in conjunction with the reassigned smoothed pseudo Wigner-Ville transform are employed for the numerical determination of time-frequency diagrams corresponding to the dispersion curves of Rayleigh and guided waves propagating in a cortical bone. A composite material model for the determination of the internal length scale parameters imposed by Mindlin's elastic theory is exploited. The obtained results demonstrate the dispersive nature of Rayleigh wave propagating along the complex structure of bone as well as how microstructure affects guided waves.     

研究激光激发的声表面波与材料近表面缺陷的振荡效应

根据激光激发声表面波的热弹运动方程及热传导方程, 采取有限元技术对方程进行求解, 得到声表面波传播波形图. 当声表面波经过近表面缺陷时, 声表面波与近表面缺陷之间产生一种振荡效应, 通过近表面缺陷的振荡波形幅值存在一个逐渐增加后又逐渐减小的过程. 当声表面波经过不同深度的近表面缺陷时, 振荡信号中心频率存在一定的变化规律. 数值仿真结果表明: 当近表面缺陷深度从0.1 mm到0.5 mm变化时, 振荡效应产生的振荡信号中心频率从0.4 MHz到0.76 MHz变化, 振荡信号中心频率与近表面缺陷深度呈近似线性关系, 这为近表面缺陷的定量检测提供了一种理论基础.     

The study of guided waves in surfaces and thin supported films using surface Brillouin scattering and acoustic microscopy

This paper reviews the use of surface Brillouin scattering (SBS) and acoustic microscopy (AM) in studying the surface dynamics of solids in order to obtain information about the near-surface elastic properties of solids and thin supported films. The vibrational modes that are probed by these means include Rayleigh surface and pseudo-surface acoustic waves, longitudinal lateral waves (surface skimming bulk longitudinal waves) and various thin film guided modes, such as Sezawa and Love waves. SBS is the inelastic scattering of light, mediated by thermodynamic fluctuations in the surface elevation and near surface elastic strains. The scattering cross-section is conveniently expressed in terms of Fourier domain elastodynamic Green's functions. AM depends on the insonification of a surface through a coupling fluid, and the resulting excitation and subsequent decay of the various surface modes. The complex reflectivity of the fluid-loaded surface, and the line and point force surface Green's functions are invoked in the interpretation of different modalities of AM, yielding much the same information about the surface dynamics. The focus in this paper is on the Green's function approach. A number of illustrative examples, drawn from the authors' research, are provided.     

Propagation in an elastic wedge using the virtual source technique

The virtual source technique, which is based on the boundary integral method, provides the means to impose boundary conditions on arbitrarily shaped boundaries by replacing them by a collection of sources whose amplitudes are determined from the boundary conditions. In this paper the virtual source technique is used to model propagation of waves in a range-dependent ocean overlying an elastic bottom with arbitrarily shaped ocean-bottom interface. The method is applied to propagation in an elastic Pekeris waveguide, an acoustic wedge, and an elastic wedge. In the case of propagation in an elastic Pekeris waveguide, the results agree very well with those obtained from the wavenumber integral technique, as they do with the solution of the parabolic equation (PE) technique in the case of propagation in an acoustic wedge. The results for propagation in an elastic wedge qualitatively agree with those obtained from an elastic PE solution.     

High-performance modeling acoustic and elastic waves using the parallel Dichotomy Algorithm

A high-performance parallel algorithm is proposed for modeling the propagation of acoustic and elastic waves in inhomogeneous media. An initial boundary-value problem is replaced by a series of boundary-value problems for a constant elliptic operator and different right-hand sides via the integral Laguerre transform. It is proposed to solve difference equations by the conjugate gradient method for acoustic equations and by the GMRES(k) method for modeling elastic waves. A preconditioning operator was the Laplace operator that is inverted using the variable separation method. The novelty of the proposed algorithm is using the Dichotomy Algorithm [26], which was designed for solving a series of tridiagonal systems of linear equations, in the context of the preconditioning operator inversion. Via considering analytical solutions, it is shown that modeling wave processes for long instants of time requires high-resolution meshes. The proposed parallel fine-mesh algorithm enabled to solve real application seismic problems in acceptable time and with high accuracy. By solving model problems, it is demonstrated that the considered parallel algorithm possesses high performance and efficiency over a wide range of the number of processors (from 2 to 8192).     

基于迟滞应力应变关系的非线性声学检测理论与方法研究

本文将传统PM(Preisach-Mayergoyz)模型由一维介质拓展到二维介质,引入迟滞细观弹性单元概念,得到迟滞变化的应力应变关系.并采用一阶有限差分方程进行了声场计算和分析,发现空间声场中含有明显的高阶奇次谐波成分.对接收到的全波信号进行滤波、放大、时间反转后加载到接收换能器对应阵元上再进行发射,观察到高次谐波在微损伤区域实现聚焦.这为利用非线性高次谐波检测微损伤提供了可能的途径,也为疲劳损伤等缺陷的早期检测提供了理论和方法依据.     

利用Taylor展开法研究Lamb波在功能梯度材料中的传播特性

超声技术可用于对功能梯度材料(FGMs)的性质进行评估. 由于FGMs性质的非均匀性,采用分布函数来描述FGMs弹性常数和密度沿厚度方向的变化趋势,并提出利用Taylor展开的方法来解决分布函数为任意函数时的FGMs中Lamb波的传播问题. 利用本征函数展开法得到了铁基氧化铝FGMs中Lamb波的相速度色散曲线,讨论了材料性质分布对铁基氧化铝FGMs中Lamb波传播特性的影响. 为FGMs性质(沿板厚方向变化)的反演提供了理论依据. 关键词： 功能梯度材料 Lamb波 Legendre多项式 分布函数     

Resonance effects of the axisymmetrical mode propagation in composite cylindrical solids with nematic coatings

The dispersion curves for harmonic waves in composite cylindrical elastic solids with a coating, made of non traditional soft material (nematic elastomer) are investigated. The obtained earlier low frequency effective model of nematics is used with taking into account the anisotropy, viscosity and internal rotation of long molecules of material. The impedance matrices, dispersion equations and asymptotics of speeds and wavenumbers in the long-wave approximation are derived for the further numerical analysis. The obtained quasi resonance effects of the first and of the second kinds are discussed for waves of different polarization.     

Enhancement of phononic band gaps in ternary/binary structure

Based on the transfer matrix method (TMM) and Bloch theory, the interaction of elastic waves (normal incidence) with 1D phononic crystal had been studied. The transfer matrix method was obtained for both longitudinal and transverse waves by applying the continuity conditions between the consecutive unit cells. Dispersion relations are calculated and plotted for both binary and ternary structures. Also we have investigated the corresponding effects on the band gaps values for the two types of phononic crystals. Furthermore, it can be observed that the complete band gaps are located in the common frequency stop-band regions. Numerical simulations are performed to investigate the effect of different thickness ratios inside each unit cell on the band gap values, as well as unit cells thickness on the central band gap frequency. These phononic band gap materials can be used as a filter for elastic waves at different frequencies values.     

The radiation power of elastic waves excited in a solid half-space by a subsurface time-harmonic source

The method of Fourier transforms is used to solve the problem of excitation of longitudinal, transverse, and Rayleigh surface waves by a time-harmonic point source placed in a homogeneous isotropic, perfectly elastic half-space and acting along the normal surface. Expressions for the time-average radiation powers of the aforementioned waves are obtained by the method of radiation reaction without using any approximations. The distribution of radiation power over different types of waves depending on their velocities and the source’s depth is investigated in detail.     

Characterization of mechanical properties of a hollow cylinder with zero group velocity Lamb modes

Hollow cylinders used in the industry must be regularly inspected. Elastic guided waves, similar to Lamb modes in a plate, can propagate in the axial direction or around the circumference. They are sensitive to geometrical and mechanical parameters of the cylindrical shell. The objective of this paper is to show that zero group velocity (ZGV) Lamb modes can be used to bring out anisotropy and to measure elastic constants of the material. This study provides experimental and numerical investigations on a Zirconium alloy tube extensively used by the nuclear industry in reactor core components. A non-contact method, based on laser ultrasound techniques and ZGV Lamb modes, demonstrates that the difference observed between axial and circumferential guided waves cannot be explained by an isotropic model. Then, a transverse isotropic model is used for the Zircaloy tube. Four of the five elastic constants are directly extracted from ZGV resonance frequencies. The last one is deduced from the measured dispersion spectra. With this complete set of constants, a good agreement is obtained between theoretical and experimental dispersion curves for both axially and circumferentially propagating guided waves.     

Numerical simulation of laser-generated ultrasound in non-metallic material by the finite element method

The use of a pulsed laser for the generation of the elastic waves in non-metallic materials in the thermoelastic regime is investigated by using finite element method (FEM), taking into account not only thermal diffusion and the finite spatial and temporal shape of the laser pulse, but also optical penetration and the temperature dependence of material properties. The optimum finite element model is established based on analysis of two important parameters, meshing size and time step, and the stability of solution. Temperature distributions and temperature gradient fields in non-metallic material for different time steps are obtained, this temperature field is equivalent to a bulk force source to generate ultrasonic wave. The laser-generated ultrasound waveforms at the epicenter and surface acoustic waveforms (SAWs) are obtained and the influence of optical penetration into the material on the temperature field and the ultrasound waveforms are analyzed. The numerical results indicate that the heat penetration into non-metallic material is caused mainly by the optical penetration, and the ultrasound waveforms, especially the shape of the precursor, are strongly dependent on the optical penetration depth into non-metallic material.