兰姆波在搭接焊缝上的反射和透射

采用数值模拟方法和实验研究了兰姆波在搭接焊缝上的反射和透射。数值模拟了频率500 kHz的兰姆波S0与.A0模态,分别在2 mm厚不锈钢板上的不同宽度搭接焊缝模型上的反射和透射,并计算了相应的反射系数和透射系数。发现:当搭接焊缝宽度小于4 mm时,S0模态的反射系数和焊缝宽度具有近似的线性关系,而焊缝余高和两板之间的间隙对S0模态反射系数的影响很小。基于兰姆波S0模态反射系数与焊缝宽度的线性关系。提出了通过测量S0模态反射系数快速测量搭接焊缝宽度的方法。实验测得的2 mm厚不锈钢板上不同宽度搭接焊缝对500 kHz的入射兰姆波S0模态的反射系数,验证了上述线性关系,说明了可用兰姆波反射回波测量搭接焊缝宽度。      

Ultrasonic Lamb wave method for sizing of spot welds

Two spot-welded thin sheets can be treated as two elastic waveguides coupled by a small common welded region. It is proposed to use Lamb waves to evaluate the quality of the weld. The feasibility of selecting the working frequency and mode number of the Lamb wave so that no resonance of the elastic vibrations appears in the weld region is considered analytically. This condition ensures a one-to-one correspondence between the mean diameter of the spot-weld region and the coefficient of transmission of the Lamb waves through it.A simple technique is suggested for determining the transmission coefficient and the scattering patterns of Lamb waves at the weld region. Experiments indicate that, to a satisfactory approximation, the wave transmission coefficient is proportional to the cube of the weld diameter. This allows a unique determination of the dimension of the welded region on the basis of the amplitude of the transmitted signal.     

Modal decomposition method for modeling the interaction of Lamb waves with cracks

The interaction of the low-order antisymmetric (a0) and symmetric (s0) Lamb waves with vertical cracks in aluminum plates is studied. Two types of slots are considered: (a) internal crack symmetrical with respect to the middle plane of the plate and (b) opening crack. The modal decomposition method is used to predict the reflection and transmission coefficients and also the through-thickness displacement fields on both sides of slots of various heights. The model assumes strip plates and cracks, thus considering two-dimensional plane strain conditions. However, mode conversion (a0 into s0 and vice versa) that occurs for single opening cracks is considered. The energy balance is always calculated from the reflection and transmission coefficients, in order to check the validity of the results. These coefficients together with the through-thickness displacement fields are also compared to those predicted using a finite element code widely used in the past for modeling Lamb mode diffraction problems. Experiments are also made for measuring the reflection and transmission coefficients for incident a0 or s0 lamb modes on opening cracks, and compared to the numerical predictions.     

Reflection and transmission coefficients for guided waves reflected by defects in viscoelastic material plates

The paper presents a Fourier transform-based signal processing procedure for quantifying the reflection and transmission coefficients and mode conversion of guided waves diffracted by defects in plates made of viscoelastic materials. The case of the S(0) Lamb wave mode incident on a notch in a Perspex plate is considered. The procedure is applied to numerical data produced by a finite element code that simulates the propagation of attenuated guided modes and their diffraction by the notch, including mode conversion. Its validity and precision are checked by the way of the energy balance computation and by comparison with results obtained using an orthogonality relation-based processing method.     

Experimental study of the A0 and S0 Lamb waves interaction with symmetrical notches

The aim of this work is to study the fundamental Lamb modes interaction with defects in isotropic plates. For these experimental investigations, symmetrical notches with various depths milled in aluminum plates are considered. Moreover, the incident Lamb wave of a specific mode is generated by means of two identical thin piezoceramic transducers placed at the opposite sides of the plate. The waves scattered by the notch are recorded with conventional transducers located on the plate surface in front and behind the defect. The selection of the A₀ or the S₀ modes is obtained by exciting the transducers with anti-phased or in-phased signals, respectively. Furthermore, a calibration process is investigated to correct errors caused by the presence of the receiver between the emitters and the defects. The power reflection and transmission coefficients are then obtained and the power balance is verified. Finally, these measurements are compared successfully with those obtained by a numerical method using the finite-element modeling described in a previous work.     

3D analysis of interaction of Lamb waves with defects in loaded steel plates

The objective of the research presented here is the investigation of the interaction of guided waves with welds, defects and other non-uniformities in steel plates loaded by liquid. The investigation has been performed using numerical simulation for 2D and 3D cases by the finite differences method, finite element method and measurement of 3D distributions of acoustic fields. Propagation of the S(0) mode in a steel plate and its interaction with non-uniformities was investigated. It was shown that using the measured leaky wave signals in the water loading of the steel plate and by application of signal processing, the 3D ultrasonic field structure inside and outside of the plate can be reconstructed. The presence of leaky wave signals over the defect caused by the mode conversion of Lamb waves has been proved using the numerical modelling and experimental investigations. The developed signal and data processing enables to visualise dynamics of ultrasonic fields over the plate, and also to estimate spatial positions of defects inside the steel plates.     

Simulation of Lamb wave reflections at plate edges using the semi-analytical finite element method

In typical Lamb wave simulation practices, effects of plate edge reflections are often not considered in order to simplify the wave signal interpretations. Methods that are based on infinite plates such as the semi-analytical finite element method is effective in simulating Lamb waves as it excludes the effect of plate edges. However, the inclusion of plate edges in a finite plate could render this method inapplicable, especially for transient response simulations. Here, by applying the ratio of Lamb mode reflections at plate edges, and representing the reflection at plate edges using infinite plate solutions, the semi-analytical finite element method can be applied for transient response simulation, even when the plate is no longer infinite.     

Lamb wave topological imaging for blind hole defects in isotropic plates

The research aims at validating the ability of topological imaging to blind holes in isotropic plates using Lamb waves. Due to the defect is not symmetric around the midplane of the plate, the effect of Lamb mode conversion will have to be taken into account.The imaging method is based on two computations of ultrasonic fields, one forward and one adjoint, performed for the defect-free reference medium. The excited signal and scattered Lamb waves caused by the blind hole, are used as emitting sources to compute the forward problem and the adjoint problem, respectively. With the help of the finite element simulations,the natural refocusing process of the multimode Lamb waves at the defect location is visually demonstrated by the transient acoustic field snapshots at the different moments to strengthen the physical mechanism of the topological imaging method. The numerical results demonstrate that topological imaging has relatively stronger applicability to the blind hole in contrast to classical Delay And Sum(DAS) method and Time Reversal(TR) method. The topological imaging could handle complex Lamb wave signals containing mode conversions without the imaging quality being affected. The proposed imaging method presents a certain developing potential for detecting and imaging asymmetric defects in plate-like configurations using Lamb waves.     

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.     

覆黏弹层加肋双层板的声反射

为评估覆盖层的吸声性能,研究黏弹层在无限大周期加肋双层板背衬下的声反射。首先通过弯曲波与Lamb波的比较,揭示了板近似理论不适用于黏弹性板的原因。为此采用(黏)弹性理论处理(黏)弹性板,而肋板的处理则采用板近似理论,并用Hull提出的方法解决肋板和平板的耦合问题,得到反射声场的解。与板近似理论计算加肋双层板声反射的结果进行比较验证了本文方法的正确性,对反射系数进行计算分析了背衬对声反射的影响,定义平均反射系数比较了不同覆盖层的性能。结果表明,频率较低时覆盖层无法有效抑制背衬的影响,板间流体层与双层板的耦合作用引起共振散射,肋板与双层板的耦合作用降低声反射。      

各向同性板中盲孔缺陷的兰姆波拓扑成像

将拓扑成像用于各向同性板中盲孔缺陷的兰姆波检测。由于缺陷关于板中面是非对称的,兰姆波模式转换的影响不能忽略。成像方法是基于无缺陷参考媒质中两个超声场(直接声场和伴随声场)的计算。以传感器激励信号为声源,计算直接声场;以盲孔引起的兰姆波散射信号为声源,计算伴随声场。拓扑成像通过直接声场与伴随声场的相乘,可消除无缺陷处多模式混叠的干扰,提高成像分辨率。建立有限元模型,通过不同时刻的瞬态声场图可视化地显示多模式兰姆波在缺陷处的聚焦过程,揭示拓扑成像方法的物理机理。数值结果表明,相对于经典的延迟求和以及时间反转方法,拓扑成像对盲孔缺陷有更强的适应能力。即使对于复杂的包含模式转换的兰姆波信号,拓扑图像的质量依然没有受到影响。文中提出的成像方法对板类结构中非对称缺陷的兰姆波检测具有一定的应用潜力。      

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.     

Micro-crack detection of nonlinear Lamb wave propagation in three-dimensional plates with mixed-frequency excitation

We propose a nonlinear ultrasonic technique by using the mixed-frequency signals excited Lamb waves to conduct micro-crack detection in thin plate structures. Simulation models of three-dimensional(3D) aluminum plates and composite laminates are established by ABAQUS software, where the aluminum plate contains buried crack and composite laminates comprises cohesive element whose thickness is zero to simulate delamination damage. The interactions between the S_0 mode Lamb wave and the buried micro-cracks of various dimensions are simulated by using the finite element method.Fourier frequency spectrum analysis is applied to the received time domain signal and fundamental frequency amplitudes,and sum and difference frequencies are extracted and simulated. Simulation results indicate that nonlinear Lamb waves have different sensitivities to various crack sizes. There is a positive correlation among crack length, height, and sum and difference frequency amplitudes for an aluminum plate, with both amplitudes decreasing as crack thickness increased, i.e.,nonlinear effect weakens as the micro-crack becomes thicker. The amplitudes of sum and difference frequency are positively correlated with the length and width of the zero-thickness cohesive element in the composite laminates. Furthermore,amplitude ratio change is investigated and it can be used as an effective tool to detect inner defects in thin 3D plates.     

Transmission analysis of ultrasonic Lamb mode conversion in a plate with partial-thickness notch

Mode conversions of Lamb waves can occur upon encountering damage or defect such as a notch, leading to newly-converted modes apart from wave reflection and transmission. In this paper, the transmission of the fundamental Lamb modes symmetrical S0 and anti-symmetrical A0 with anti-symmetrical notches were investigated in steel plates within the relatively short propagation distance. The group velocity and modal energy of the converted modes were analyzed using simulations and experiments. Two-dimensional finite difference time domain (2D-FDTD) method was employed to calculate the scattering field and extract numerical trends for simulation study and experimental confirmation. Both simulations and experiments revealed that the apparent group velocities of the converted modes in the transmitted signals subject to the notch positions. To describe the mode conversion degree and evaluate the notch severity, wave packets of the originally-transmitted modes and newly-converted modes were separated and corresponding mode energy percentages were analyzed at different notch severities. Frequency-sweeping measurements illustrated that the modal energy percentages varied monotonically over the notch-depth increase with a statistically consistency (R = 1.00, P < 0.0004).     

复合兰姆波声子晶体中超宽部分禁带

兰姆波在声子晶体薄板中的传播特性因其在无损检测、 减振技术和传感器件等领域的潜在应用价值而受到越来越多的关注. 本文采用超原胞平面波展开法和有限元法系统地研究了复合对称结构声子晶体薄板中的兰姆波超宽部分禁带. 结果表明: 对于在薄板侧面对称地嵌入双层矩形空气柱构成的复杂系统, 低阶兰姆波部分带隙结构极为丰富. 将晶格常数(L)和板厚(H) 比值具有匹配关系的兰姆波声子晶体衔接构成复合结构, 低阶兰姆波部分禁带宽度因各组分结构的部分禁带交叠而得到显著拓宽, 可在低频超宽频带内实现对特定低阶兰姆波模式良好的模式选择功能. 该研究结果对兰姆波缺陷无损检测中模式优化选择及兰姆波单向导通器件设计等方面具有重要意义.     

Transient Lamb waves: comparison between theory and experiment

This paper presents an experimental investigation of the generation of transient Lamb waves inside an immersed plate by a time limited signal. The transient Lamb waves are the solutions of the characteristic equation of the plate for complex frequency and real slowness, in contrast to the leaky Lamb waves, for which the slowness is complex and the frequency is real. By using a large transducer in agreement with the real slowness assumption, the excitation of these transient Lamb waves is observed experimentally both in reflection and transmission for a tone burst excitation. Particular attention is paid to the A0 mode for which the amplitude increases exponentially in time. As a result, the total reflected waveform contains in this case a transient contribution, coming from the generation of the A0 mode, that precedes the forced regime. It is shown that there is a very good agreement between the theoretical and the experimental time exponential amplitude variations of the transient Lamb waves. For the A0 mode, the transient signal is qualitatively explained by a group velocity higher than the phase velocity.     

电磁超声换能器激发超声兰姆波的模式展开分析

提出一种用于研究电磁超声换能器(EM.AT)激发超声兰姆波的模式展开分析方法。从EMAT曲折线圈的电流分布出发,推导出铝板表面洛伦兹切向应力的形式解;对其进行空间傅里叶变换,得到激发超声兰姆波的表面驱动应力之波数谱密度。在此基础上采用导波激发的模式展开分析方法,推导出与EMAT线圈的几何参数密切相关的兰姆波模式展开系数的数学表达式,为严格分析EMAT的兰姆波激发问题奠定了理论基础。数值分析结果表明,通过改变EMAT线圈的几何参数,可对兰姆波的模式展开系数进行适当调整,从而实现有效抑制不需要兰姆波模式的目的,这一结果为采用EMAT激发纯度高的单一兰姆波模式提供了理论依据。      

Modal expansion analyses of ultrasonic Lamb waves generated by electromagnetic ultrasonic transducers

A modal expansion approach has been proposed for investigating generation of ultrasonic Lamb waves by electromagnetic acoustic transducers（EMATs）.Based on the current distribution of the EMAT＇s meandering coil,the formal solution for the Lorentz surface stress applied on the plate surface has been derived.Then the function of the wave-number spectral density of the Lorentz surface stress for generating ultrasonic Lamb waves has been obtained using the spatial Fourier transform.On this basis,with the modal expansion approach for waveguide excitation,the mathematical expression of the Lamb wave＇s mode expansion coefficient has been deduced,which is closely related with the geometrical parameters of the EMAT＇s meandering coil.The mathematical relationship between the Lamb wave＇s mode expansion coefficient and the EMAT＇s geometrical parameters,obtained in this paper,lays a theoretical foundation for exactly analyzing generation of Lamb waves by EMATs.Further,the numerical analyses performed indicate that the Lamb wave＇s mode expansion coefficient can be appropriately adjusted by changing the geometrical parameters of the EMAT＇s coil,and thus the unwanted Lamb wave modes can be effectively restrained.This result provides a theoretical basis for generating a single and pure Lamb wave mode by the meandering coil EMAT.     

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...     

压电晶片传感器监测金属薄板的腐蚀

激励压电晶片传感器产生Lamb波并用于监测金属板材的腐蚀,由信号的相关系数表征腐蚀对在板中Lamb波传播特性的影响。实验结果表明在Lamb波模态中A₀模式受腐蚀影响大,适合用于监测金属的腐蚀。Lamb波通过腐蚀区域后由于频散以及信号幅度和相位的变化对采集的损伤信号与健康状态信号的相关系数有影响。在腐蚀区域直径一定的情况下,对应的相关系数并不随腐蚀深度的增加而单调递减;在腐蚀深度一定时,相关系数随腐蚀区域直径增加而单调递减。