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.     

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.     

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...     

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.     

The influence of backward wave transmission on quantitative ultrasonic evaluation using Lamb wave propagation

In view of the various novel quantitative ultrasonic evaluation techniques developed using Lamb wave propagation, the influence of an important related phenomenon, backward transmission, is investigated in this paper. Using the discrete layer theory and a multiple integral transform method, the surface displacement and velocity responses of isotropic plates and cross-ply laminated composite plates due to the Lamb waves excited by parabolic- and piston-type transmitting transducers are evaluated. Analytical expressions for the surface displacement and velocity frequency response functions are developed. Based on this a large volume of calculations is carried out. Through examining the characteristics of the surface displacement and velocity frequency response functions and, especially, the different propagation modes' contributions to them, the influence of the backward wave transmission related to quantitative ultrasonic nondestructive evaluation applications is discussed and some important conclusions are drawn.     

Fast beating null strip during the reflection of pulsed Gaussian beams incident at the Rayleigh angle

It is well known that harmonic bounded Gaussian beams undergo a transformation into two bounded beams upon reflection on a solid immersed in a liquid. The effect is known as the Schoch effect and can be found at the Rayleigh angle for thick plates and at the different Lamb angles for thin plates. Here, a study is made on the effect of pulsed Gaussian beams reflected on solids. It is found experimentally that the Rayleigh wave phenomenon still generates two reflected bounded beams, whereas Lamb wave phenomena do not generate this effect. This fact may be explained intuitively by realizing that the Rayleigh phenomenon is a coincidental phenomenon that is generated in situ, whereas the Lamb wave phenomenon is a non-coincidental phenomenon that is generated only after incident sound is influenced by both sides of a thin plate. Another explanation is the fact that Rayleigh waves are not dispersive, whereas stimulation and propagation of Lamb waves is frequency dependent. A pulse contains many frequencies and therefore only a fraction of the incident pulse is transformed into a Lamb wave. In this paper, numerical simulations are performed that show that actually the Schoch effect does occur neither for Rayleigh waves, nor for Lamb waves. As a matter of fact, a pulse, incident at the Rayleigh angle, generates two reflected lobes with a null zone of a different kind. The null zone is beating several times during the passage of each pulse. This results in a 'null zone' having a lower mean intensity than any of the two lobes, still less outspoken than for the case of harmonic incident bounded beams. This effect does only occur for Rayleigh wave generation and is much less outspoken for Lamb wave generation.     

Scattering of the fundamental anti-symmetric Lamb wave at delaminations in composite laminates

An analysis of the scattering characteristics of the fundamental anti-symmetric (A(0)) Lamb wave at a delamination in a quasi-isotropic composite laminate is presented. Analytical solutions for this problem do not exist due to the anisotropic nature and multilayer characteristics of composite laminates. This study uses a three-dimensional finite element (FE) method and experimental measurements to provide physical insight into the scattering phenomena. Good agreement is found between simulations and experimental measurements. The results show that the A(0) Lamb wave scattering at a delamination in composite laminates is much more complicated than the scattering at a defect in isotropic plates. Scatter amplitudes and scatter directivity distributions depend on the delamination size to wavelength ratio and the through-thickness location of the delamination damage. The study also investigates the feasibility of the common experimental practice of simulating delamination damage by bonding masses to the surface of composite laminates for guided wave damage detection and characterization methodologies verifications. The results suggest that care is required to use bonded masses to simulate delamination damage for verifying and optimizing damage characterization techniques. In summary, the results of the investigation help to further advance the use of the A(0) Lamb wave for damage detection and characterization.     

Prolonged acousto-optic interaction with Lamb waves in crystalline plates

The propagation and acousto-optic interaction of Lamb modes in an anisotropic plate of tellurium dioxide (TeO2) are studied numerically and analytically. In the case of a Y-cut X-propagating TeO2 plate, the very high elastic anisotropy of the crystal greatly modifies the dispersion curves, giving rise to their multiple oscillations. The existence ranges of backward Lamb modes increase with the mode order contrary to the case of isotropic plates. The quasi-collinear light scattering by Lamb waves is considered. Owing to the structure of Lamb wave field, a simultaneous light diffraction at two different optical frequencies can take place while Lamb waves are excited only at the single frequency. It is demonstrated with the Z-cut (110)-propagating plate that a small change in the acoustic frequency can result in a significant shift in the frequency of the scattered light.     

一种定征固体板表面性质的兰姆波方法

基于Ritec-SNAP系统建立了兰姆波实验系统，分析了用兰姆波幅频特性定征固体板表面性质的可行性。实验结果表明，用高阶、多模兰姆波的幅频特性可准确定征固体板表面性质的变化。     

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.     

The reflection and transmission of Lamb waves at overlap joints

The reflection and transmission of Lamb waves at overlap joints are researched by the numerical method and the experiments. The numerical method is used to simulate the reflection and transmission of Lamb waves at welds with different widths on 2 mm-thick stainless steel plates. The reflection and transmission coefficients are calculated as well. When the welds width is less than 4 mm, a quasi-linear correlation is observed between the reflection coefficient of SO mode and the weld width. In contrast to the weld width, both the gap between two plates and the reinforcement height of weld do not have obvious effect on the reflection coefficient. Based on the results, we propose that the weld width could be rapidly measured through examining the echo amplitude of SO mode. Experiments further confirm the quasilinear correlation and the feasibility of our proposed method.     

超声Lamb波二次谐波发生效率分析与模式选择

在导波模式展开分析方法的基础上,提出激发效率参量来定量表征超声Lamb波积累二次谐波的发生效率。以P92钢板为例,理论计算得到了与频散曲线对应的理论激发效率参量分布图谱,从图谱中选择理论激发效率参量大小不同的两种基频Lamb波模式:纵波型S1模式和交点型A2/S2模式,分别测量这两种基频Lamb波模式在钢板中传播时产生的二次谐波信号。理论计算和实验测量结果表明,这两种基频Lamb波模式的理论和实验激发效率参量的比值基本一致,且激发效率参量较大的纵波型S1模式能激发出效率更高的二次谐波信号。研究结果表明激发效率参量可以有效的用于Lamb波二次谐波发生效率的表征及模式选择。      

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。     

Combined spectral estimator for phase velocities of multimode Lamb waves in multilayer plates

A novel combined spectral estimate (CSE) method for differentiation and estimation the phase velocities of multimode Lamb waves whose wave numbers are much close or overlap one another in multiplayer plates is presented in this paper, which based on auto-regressive (AR) model and 2-D FFT. Simulated signals in brass plate were processed by 2-D FFT and CSE. And experiments are performed by using two conventional angle probes as emitter and receiver on the same surface of three-layered aluminum/xpoxy/aluminum plates, which include symmetrical and unsymmetrical plates. The multimode Lamb waves are excited in these laminates, and the received signal is processed by 2-D FFT and CSE, respectively. The results showed that the phase velocities of multimode signals whose wave numbers are much closed cannot be differentiated by 2-D FFT, but CSE has strong spatial resolution. Compared the measured phase velocities with the theoretical values, the error is smaller than 2% on the whole. It promises to be a useful method in experimental signals processing of multimode Lamb waves.     

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.     

Lamb and torsional waves and their use in flaw detection in tubes

Five separate issues concerning Lamb wave propagation are discussed: (1) the actual motion of the particles in sheet material; (2) the mechanism of the initiation of Lamb waves in plates; (3) the effect of pulse propagation as opposed to continuous waves; (4) wave propagation on the inner and outer surfaces of tubes; and (5) the propagation of waves in tubes at large angles of incidence, beyond the Lamb wave regime.     

Design of optimal configuration for generating A0 Lamb mode in a composite plate using piezoceramic transducers

This work concerned a technique for a health monitoring system based on the generation and sensing of Lamb waves in composite structures by thin surface-bonded piezoceramic transducers. The objective was to develop transducers that are adapted for the damage detection in orthotropic composites. The key problem with the investigated Lamb waves was to select a mode to be sensitive to the damage. A hybrid modeling technique was therefore used to conceive transducers that were adapted to achieve such a feature. This modeling technique enabled studying the influence of the transducer characteristics on the Lamb waves propagating in orthotropic plates. It was demonstrated that a Lamb mode could be generated dominantly to other modes by using a multi-element transducer. The effectiveness of this technique was successfully verified experimentally on composite plates. It was shown that the dominant Lamb mode, obtained by use of dual-element transducers, was an appropriate mode for successfully detecting a damage in composites.     

Normal mode expansion method for laser-generated ultrasonic Lamb waves in orthotropic thin plates

A quantitative theory for modeling the laser-generated transient ultrasonic Lamb waves, which propagates along arbitrary directions in orthotropic plates, is presented by employing an expansion method of generalized Lamb wave modes. The displacement field is expressed by a summation of the symmetric and antisymmetric modes in the surface stress-free orthotropic plate, and therefore the theory is particularly appropriate for waveform analyses of Lamb waves in thin plates because one needs only to evaluate several lower modes. The transient waveforms excited by the thermoelastic expansion and the oil-coating evaporation are analyzed for a transversely isotropic thin plate. The results show that the theory provides a quantitative analysis to characterize anisotropic elastic stiffness properties of orthotropic plates by laser-generated Lamb wave detection.     

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。     

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。