Propagation of time-reversed Lamb waves in acrylic cylindrical tubes as cortical-bone-mimicking phantoms

The present study aims to investigate the propagation of time-reversed Lamb waves in acrylic cylindrical tubes as cortical-bone-mimicking phantoms. Time-reversed Lamb waves could be successfully launched in 6 acrylic tubes with wall thicknesses from 2 to 12 mm by using a modified time reversal method. The group velocities of the time-reversed Lamb waves in the acrylic tubes were measured by using the axial transmission technique. They decreased very slightly with increasing wall thickness, showing good agreement with the theoretical group velocity of the A0 Lamb wave in the acrylic plate. These results suggest that the time-reversed Lamb waves in the acrylic tubes would essentially behave as the A0 Lamb wave, consistent with the behavior of the slow guided wave in long cortical bones. It is expected that the application of the time-reversed Lamb waves in long bones would enhance clinical potential of ultrasonic technologies for the diagnosis of osteoporosis.     

Analysis of Second-Harmonic Generation of Low-Frequency Dilatational Lamb Waves in a Two-Layered Composite Plate

We analyze the effect of second-harmonic generation(SHG) of primary Lamb wave propagation in a two-layered composite plate, and then investigate the influence of interfacial properties on the said effect at low frequency. It is found that changes in the interfacial properties essentially affect the dispersion relation and then the maximum cumulative distance of the double-frequency Lamb wave generated. This will remarkably influence the efficiency of SHG. To overcome the complications arising from the inherent dispersion and multimode natures in analyzing the SHG effect of Lamb waves, the present work focuses on the analysis of the SHG effect of low-frequency dilatational Lamb wave propagation. Both the numerical analysis and finite element simulation indicate that the SHG effect of low-frequency dilatational Lamb wave propagation is found to be much more sensitive to changes in the interfacial properties than primary Lamb waves. The potential of using the SHG effect of low-frequency dilatational Lamb waves to characterize a minor change in the interfacial properties is analyzed.     

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。     

Second Harmonic Generation of Lamb Wave in Numerical Perspective

The influences of phase and group velocity matching on cumulative second harmonic generation of Lamb waves are investigated in numerical perspective.Finite element simulations of nonlinear Lamb wave propagation are performed for Lamb wave mode pairs with exact and approximate phase velocity matching,with and without group velocity matching,respectively.The evolution of time-domain second harmonic Lamb waves is analyzed with the propagation distance.The amplitudes of primary and second harmonic waves are calculated to characterize the acoustic nonlinearity.The results verify that phase velocity matching is necessary for generation of the cumulative second harmonic Lamb wave in numerical perspective,while group velocity matching is demonstrated to not be a necessary condition.     

Characterization of surface properties of a solid plate using nonlinear Lamb wave approach

A nonlinear Lamb wave approach is presented for characterizing the surface properties of a solid plate. This characterization approach is useful for some practical situations where ultrasonic transducers cannot touch the surfaces to be inspected, e.g. the inside surfaces of sealed vessels. In this paper, the influences of changes in the surface properties of a solid plate on the effect of second-harmonic generation by Lamb wave propagation were analyzed. A surface coating with the different properties was used to simulate changes in the surface properties of a solid plate. When the areas and thicknesses of coatings on the surface of a given solid plate changed, the amplitude-frequency curves both of the fundamental waves and the second harmonics by Lamb wave propagation were measured under the condition that Lamb waves had a strong nonlinearity. It was found that changes in the surface properties might clearly affect the efficiency of second-harmonic generation by Lamb wave propagation. The Stress Wave Factors (SWFs) in acousto-ultrasonic technique were used for reference, and the definitions of the SWFs of Lamb waves were introduced. The preliminary experimental results showed that the second-harmonic SWF of Lamb wave propagation could effectively be used to characterize changes in the surface properties of the given solid plate.     

Cumulative second-harmonic generation of Lamb waves propagating in a two-layered solid plate

The physical process of cumulative second-harmonic generation of Lamb waves propagating in a two-layered solid plate is presented by using the second-order perturbation and the technique of nonlinear reflection of acoustic waves at an interface. In general, the cumulative second-harmonic generation of a dispersive guided wave propagation does not occur. However, the present paper shows that the second-harmonic of Lamb wave propagation arising from the nonlinear interaction of the partial bulk acoustic waves and the restriction of the three boundaries of the solid plates does have a cumulative growth effect if some conditions are satisfied. Through boundary condition and initial condition of excitation, the analytical expression of cumulative second-harmonic of Lamb waves propagation is determined. Numerical results show the cumulative effect of Lamb waves on second-harmonic field patterns.     

铝板中Lamb波检测的实验研究

Lamb波在传播过程中具有频散及多模态特性,若相关参数选择不当,会导致在实际应用中信号相互叠加而无法识别。本文基于Lamb波的频散曲线是其频散方程实数解分布的特点,采用二分法绘制了铝板中Lamb波的频散曲线、波结构曲线和入射角曲线。根据曲线选择S0模态的Lamb波对1mm厚铝板中不同类型的缺陷进行检测。实验结果表明,S0模态的Lamb波对裂纹型缺陷和贯穿型缺陷十分敏感,但对于裂纹型缺陷,其幅值变化并不与缺陷大小成线性关系,并且S0模态Lamb波的声场指向性十分集中,在偏离声束轴线时无法检测到缺陷。     

Absorption of zero Lamb waves in an elastic layer by mechanical resonators with friction

The propagation of zero Lamb waves in a plate with mechanical resonators attached to its surfaces is studied. It is shown that, in a plate that is single-mode for symmetric (antisymmetric) waves, the zero symmetric (antisymmetric) Lamb wave can be absorbed by mechanical resonators with a certain friction. The single-mode (for symmetric or antisymmetric waves) plate can be not thin compared to the wavelength of the transverse wave.     

Calculation and visualization of Lamb wave motion

Lamb wave propagation was calculated by using hybrid boundary element method (HBEM) that is the combination of the analytical mode expansion and boundary element method. HBEM makes it possible to simulate Lamb wave propagation in large plates with shorter computational time. The numerical results, e.g. displacements and stresses, were collected at every time step for the inner grid points and visualized as mpeg movies or jpeg pictures. The generation mechanism of Lamb waves is investigated as a numerical example.     

基于群速度失配的超声兰姆波二次谐波的时域测量方法

考虑到发射和接收换能器对超声兰姆波时域二次谐波信号所带来的不可避免的影响,提出一种基于基频与二倍频兰姆波群速度失配的超声兰姆波二次谐波的时域测量方法。当基频与二倍频超声兰姆波的相速度匹配而群速度失配时,在超声兰姆波传播过程中所发生的二次谐波信号,在时域上可与源于斜劈换能器的二次谐波信号相分离。采用仅源自于基频兰姆波的时域二次谐波的积分振幅,定量描述兰姆波二次谐波的发生效率。以铝板中传播的兰姆波为例,给出了时域二次谐波的具体测量过程。本文提出的测量方法放宽了超声兰姆波二次谐波的测量条件,且扣除了换能器对二次谐波信号所带来的影响,所测得的二次谐波信号完全来自于基频兰姆波时域信号的二次谐波发生效应。      

多通道超声兰姆波检测板状结构中的裂纹

超声兰姆(Lamb)波在结构缺陷检测方面愈来愈受到重视,但目前Lamb波的应用局限于单信号源激励,单通道接收的方法,容易受到噪声干扰,其后续的信号分析处理也比较复杂。本文旨在采用多通道Lamb波对板状结构中的裂纹进行定量分析与诊断。在铝板的表面凿刻出不同深度的凹槽作为裂纹,通过线阵换能器采集在一定传播距离内的多通道Lamb波信号,并采用二维傅里叶变换分析在不同深度的裂纹下,Lamb波模式能量的变化规律。结果表明,相对于完好铝板中的Lamb波信号,裂纹的存在会使Lamb波发生模式转换现象,并且转换模式能量百分比随裂纹深度的增加而线性增加。其结果为Lamb波评价板状结构中的裂纹状况提供了一种可能的方法。     

非线性兰姆波在阶梯板中传播的有限元仿真

在非线性兰姆波检测中,累积二次谐波是重要的检测信号.该文利用有限元法仿真了非线性兰姆波在阶梯板中的产生和传播过程,通过二维离散傅里叶变换分析了兰姆波的传播模态和各个模态通过波导横截面的能流大小,给出了各个模态在阶梯板中的反射、透射系数,总结了其随阶梯板厚度的变化规律.研究发现,随着台阶增高,散射效应使得兰姆波更难入射波...     

General solution of cumulative second harmonic by Lamb wave propagation in a solid plate

A straightforward approach has been developed for the general solution of cumulative second harmonic by Lamb wave propagation in a solid plate. The present analyses of second-harmonic generation by Lamb waves focus on the cases where the phase velocity of the fundamental Lamb wave is exactly or approximately equal to that of the double frequency Lamb wave （DFLW）. Based on the general solution obtained, the numerical analyses show that the cumulative second-harmonic fields are associated with the position of excitation source and the difference between the phase velocity of the fundamental Lamb wave and that of the dominant DFLW component.     

金属板疲劳损伤非线性兰姆波混频检测

针对金属板结构安全运行需要,开展了金属板结构疲劳损伤非线性兰姆波混频检测方法研究.通过数值仿真,研究了两列A0兰姆波与材料损伤间的非线性相互作用.结果 表明,两列共线A0兰姆波在结构材料损伤处产生单向传播的和频S0波,且和频波幅值随传播距离具有积累增长效应.对不同疲劳程度金属板试件进行了共线混频兰姆波检测实验,结果表明...     

The propagation of coupled Lamb waves in multilayered arbitrary anisotropic composite laminates

Based on linear three-dimensional elasticity theory, the wave equations of coupled Lamb waves in multilayered arbitrary anisotropic composite laminates are derived using a Legendre orthogonal polynomial approach. The elastodynamic solution for the propagation of coupled Lamb waves in composite plates is also presented to determine the characteristics of coupled Lamb waves. To verify the applicability and validity of the method, two cases of bi-layered plates formed with isotropic components and anisotropic components, respectively, are primarily manipulated for comparison with earlier known results. Next, the dispersion curves, displacements and stress distributions of Lamb waves in multilayered anisotropic laminates are calculated. The effects of coupling and fiber orientation on the characteristics of the Lamb waves are illustrated. The potential usefulness of the fundamental modes of the coupled Lamb waves is discussed in detail.     

The propagation of Lamb waves in a plate bordered with layers of a liquid.

The influence of liquid layers on the propagation of Lamb waves in a plate of finite thickness is studied theoretically. The dispersion equations of Lamb waves in a plate bordered with layers of liquids are derived. Numerical solutions of the equations show that the phase velocity of Lamb waves changes with the thickness of the liquid layers. For the lowest antisymmetrical mode of very thin plates, the numerical results calculated from the dispersion equations are compared with those derived from the bending wave acoustic impedance approach. The limitation of the latter is discussed. Applications of Lamb waves pertinent to biosensing are also presented.     

Guided waves in elastic plates with Gaussian section variation: experimental and numerical results

Experimental and numerical results are presented on the behavior of guided waves in elastic plates in plane strain that include a Gaussian variation of their section, located between two areas of constant thickness. The area of varying section is wide compared to the used wavelengths, which allows wave propagation inside this area. The experimental results show that an incident Lamb wave is indeed converted into an adiabatic wave inside the varying section domain. A trapped wave in the Gaussian domain is also observed, depending on the incident mode and on the Gaussian maximum height. Outside the varying section domain, conversion into different Lamb waves is observed. This conversion phenomenon is experimentally quantified by the measurement of the Lamb wave normal displacement and of its carried energy. A numerical study, based on the Finite Elements Method is performed, and successfully compared to the experimental results.     

Simultaneous measurement of the phase and group velocities of Lamb waves in a laser-generation based imaging method

This paper describes a novel approach to the simultaneous measurement of the phase and group velocities of Lamb waves based on images of their propagation. The laser-generation based imaging method was first introduced to obtain images of Lamb wave propagation. The time series of snapshot images is used to make a position-time diagram, and the velocities can be estimated based on the slopes of the position curves. Thus, the phase and group velocities can be obtained by measuring the phase advance and energy flow of the Lamb wave, respectively. Details of the principle of simultaneous measurement are presented herein. Experimental verification was also performed in the range of 0.2-3.0 MHz-mm using aluminum plates. The average errors between experiment and theory in the phase and group velocities were 3.31% and 5.68%, respectively.     

两侧有固体层负载时板中Lamb波的传播

本文研究了薄板二面有固体导负载时板中Ｌａｍｂ波的传播，从弹性波理论出发并结合应的边界条件，导出板中Ｌａｍｂ波的色散方程，数值计算表示，不管作为自由状态时板中Ｌａｍｂ波相速（板厚取定时）是大于或小于外层固体的声表面波波速，板中对称及反对称模式的Ｌａｍｂ波相速都随着外层固体层厚度增加而变化并且渐近于外层固体的声表面波波速，数值计算又表明，对很薄的板，板中对称及反对称模式的相速均随负载板的厚度呈线性变化     

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.