Investigation on the Design of Piezoelectric Actuator/Sensor for Damage Detection in Beam with Lamb Waves

Piezoelectric wafer type actuator/sensor is widely used to generate and sense Lamb waves for Structural Health Monitoring (SHM). However, multiple Lamb waves modes are generally excited with this type of transducer. As a result, there is some difficulty in using Lamb waves for damage detection. To selectively generate a single A₀/S₀ Lamb mode, the tuned excitation of Lamb waves has been studied by some researchers. This paper investigates the design of the PZT actuator/sensor bonded to beam-like structure for generating single A₀/S₀ Lamb mode. In the study it is found that some factors, including the bonding layer, the unknown material properties and dynamical characteristics of the beam, will influence the design of PZT actuator/sensor. Piezoelectric impedance technique is introduced to facilitate the design of PZT actuator/sensor. Crack detection in beam using the tuned A₀/S₀ Lamb waves is performed.     

Numerical modeling of PZT-induced Lamb wave-based crack detection in plate-like structures

This paper presents the numerical modeling and simulations of PZT-induced Lamb wave propagation in plate-like structures by using the spectral finite element method. A novel spectral plate finite element, which can efficiently model the three-dimensional (3D) behavior of Lamb waves, is proposed. In the formulation, linear displacement distributions in the thickness direction are assumed for both the PZT layer and the base plate. A way to avoid the thickness locking is proposed and used in the formulations. Two examples, one for the validation of the proposed two-dimensional (2D) spectral finite element and the other for the demonstration of crack detection in plates, are presented and discussed. The contact between the two faces of crack is considered. Numerical results show that (1) only the anti-symmetric mode is prone to thickness locking thus remedy should be made only on this part, (2) the proposed 2D spectral finite element can adequately model the Lamb wave propagation in plate-like structures and the complex scattering for the crack, and (3) crack location can be well determined by a PZT-induced Lamb wave-based diagnosis algorithm.     

Nondestructive testing method based on lamb waves for localization and extent of damage

Based on Lamb wave analysis of propagation in plate-like structures, a damage detection method is proposed that not only locates the position of the damage accurately but also estimates its size. Similar damage detection methods focus only on localization giving no quantitative estimation of extent. To improve detection, we propose two predictive circle methods for size estimation. Numerical simulations and experiments were performed for an aluminum plate with a hole. Two PZT configurations of different sizes were designed to excite and detect Lamb waves. From cross-correlation analysis, the damage location and extent can be determined. Results show that the proposed method enables a better quantitative resolution in detection, the size of the inspection area influences the accuracy of damage identification, and the closer is the inspected area to the damage, the more accurate are the results. The method proposed can be developed into a multiple-step detection method for multi-scale analysis with prospective accuracy.     

Lamb波理论及层合板冲击损伤的实验研究

从理论上分析了板中Lamb波信号的传播特性,并给出Lamb波在板中传播的频散方程。理论分析及实验均表明,Lamb波的频散特性与复合材料结构损伤有着直接的联系,而且最低阶的对称和反对称Lamb波模态对层合板的损伤比较敏感,但应用Lamb波的频散效应监测结构的损伤在检测技术上还难以实现。根据板中导波形成Lamb波的共振原理,板中应力波的幅频特性很大程度上反映了Lamb波的谐振特征。因此,利用压电元件的压电阻抗谱分析应力波的各阶模态频率及振幅对结构损伤的变化,能够反映材料内部损伤与Lamb波的频散特性。文中针对表面粘贴压电元件的层合板智能结构,建立了包含Lamb波谐振模式的压电阻抗计算模型。冲击损伤试件的实验表明,由于结构损伤的出现压电阻抗谱中的模态频率及其阻抗幅值等特征信息将发生变化。因此,引入应力波损伤因子可以对结构冲击损伤的存在和程度进行初步评价。该方法基于结构的机-电动态阻抗特性,不受结构的几何形状限制,测试用的压电元件成本低,方法简单可行,有望在智能结构的健康诊断方面获得应用。     

Characterization of Laser Generated Lamb Wave Modes after Interaction with a Thickness Reduction Discontinuity Using Ray Tracing Theory

The effect that a circular discontinuity (due to thickness reduction) in an Aluminum plate has on the direction of Lamb wave propagation was experimentally and theoretically studied. Broadband Lamb waves were generated by a pulsed Nd:YAG laser and optically detected with a photo-EMF detector to increase spatial resolution. The experimental results show that thickness reduction modifies the time of flight (TOF) for S0 and A0 vibration modes and generates a change in direction of the ultrasonic Lamb wave. The change in the TOF as a function of distance and thickness reduction was numerically determined using ray theory and then compared to experimental results. It is shown that the change in the direction of propagation depends on the vibrational mode and frequency of the Lamb waves and this can affect the detection and characterization of a hidden discontinuity.     

Boundary element modeling for defect characterization potential in a wave guide

Wave scattering analysis implemented by boundary element methods (BEM) and the normal mode expansion technique is used to study the sizing potential of two-dimensional shaped defects in a wave guide. Surface breaking half-elliptical shaped defects of three opening lengths (0.3, 6.35 and 12.7 mm) and through-wall depths of 10–90% on a 10 mm thick steel plate were considered. The reflection and transmission coefficients of both Lamb and shear horizontal (SH) waves over a frequency range 0.05–2 MHz were studied. A powerfully practical result was obtained whereby the numerical results for the S₀ mode Lamb wave and n₀ mode SH wave at low frequencies showed a monotonic increase in signal amplitude with an increase in the defect through-wall depth. At high frequency (usually above the cut-off frequency of the A₁ mode for Lamb waves and the n₁ mode for SH waves, respectively), the monotonic trend does not hold in general due to the energy redistribution to the higher order wave modes. Guided waves impinging onto an internal stringer-like an inclusion were also studied. Both the Lamb and SH waves were shown to be insensitive to the stringer internal inclusions at low frequency. Experiments with piezoelectric Lamb wave transducers and non-contact SH wave electro-magnetic acoustic transducers (EMAT) verified some of the theoretical results.     

一种用于计算板中缺陷兰姆波散射的混合边界元法

本文介绍了一种将传统边界元法和兰姆波的本征模式函数相结合的混合边界元法，用此方法解决兰姆波在板材中传播时遇到缺陷发生的散射问题，计算了兰姆波通过缺陷后的反射与透射系数。文中给出了若干兰姆波信号幅度与板中不同深度缺陷的相互关系。     

Observation of Piezoelectrically Induced Lamb Wave Propagation in Thin Plates by Use of Speckle Interferometry

Lamb waves have shown to be favorably applicable in the development of health monitoring systems in structural mechanics since they show reflections, refractions, as well as mode conversions at fault locations. For the observation of the wave propagation, the double pulsed electronic speckle pattern interferometry (ESPI) as a high precision, full-field, and non-contact measurement technique is under investigation in this work. First, it is shown that symmetric and antisymmetric Lamb waves can be captured in a faultless plate. Moreover, mode conversions are observed at stiffness discontinuities in a specially prepared plate. Finally, a riveted lightweight structure is under investigation. In these experiments, mode conversions indicate the location of the rivets.     

Lamb wave scattering by a symmetric pair of surface-breaking cracks in a plate

The scattering problem of a Lamb wave incident on a symmetric pair of surface-breaking transverse cracks in a plate is considered. The Lamb wave is assumed to be obliquely incident on the crack plane. Since the cracks are part-through, the scattered field will contain reflected as well as transmitted waves. The energy of the incoming wave is partitioned into reflected and transmitted wave modes. Energy coefficients of the reflected and transmitted waves are calculated as a function of incident frequency and crack depth. The incidence angle of the incoming wave is also treated as a parameter. Both the reflected and transmitted wave fields are considered as linear superpositions of all real and complex wave modes in the plate. Decomposition of modes is achieved with the help of an orthogonality condition based on the principle of reciprocal work. Continuity of displacement and stress fields is imposed at the crack plane. Energy coefficients for reflection and transmission are obtained from the mode amplitudes. Energy coefficients are shown to be a strong function of incident frequency and crack depth. Experiments are conducted with a PZT transducer network interacting with a symmetric pair of machined cracks in an aluminum plate. Trends predicted by the analysis are reflected in the experimental results.     

Nonlinear Lamb waves in plate/shell structures

鉴于常规超声检测技术对分布式材料细微损伤和接触类结构损伤的检测效果不佳,近年来非线性超声技术逐渐引起广泛关注.超声波在板壳结构中通常以兰姆波的形式进行传播,然而由于兰姆波的频散及多模特性,使得非线性兰姆波的理论和实验研究进展缓慢.本文从经典非线性理论出发,总结了源于材料固有非线性诱发的非线性兰姆波的理论和实验两个方面的研究进展,并综述了兰姆波的二次谐波发生效应在材料损伤评价方面的若干应用;从接触声非线性理论出发,讨论了目前由于接触类结构损伤诱发的非线性兰姆波的研究现状.最后展望了非线性兰姆波的未来研究重点及发展趋势.     

基于传递函数法的兰姆波解析模拟

本文研究了兰姆波传播的解析模型。薄压电传感器（PZT）被用于兰姆波的激发。为模拟PZT的激励,采用PZT边缘的分布式点源近似等效PZT的激励,建立了解析模型的边界条件。结合傅里叶变换,在频率波数域求解了三维波动方程,得到了在单位周期激励下兰姆波的频域响应。结合传递函数法,可以得到任意激励下兰姆波的频域响应。利用傅里叶逆变换,进一步求解了兰姆波在时间-空间域的全局波场。为了验证解析模型,将解析模拟与实验进行了比对。试验测量值与解析模拟结果相吻合。     

基于频率-波数域偏移的损伤被动成像识别研究

提出了一种应用Lamb波对板结构中多部位损伤源进行被动成像识别的方法.基于Mindlin板理论,推导了板结构中弥散性Lamb波频率-波数域的快速偏移方法,结合爆炸成像原理,对损伤源发出的Lamb波信号进行回传成像.由于损伤源的发生时刻未知,将使用不同假设发生时刻(即不同长度)的Lamb波信号生成一系列图像,通过最小熵原理从中确定最优图像,识别出损伤源的位置和发生时刻.进行了数值仿真研究来表明所提出方法的有效性.     

The Potential of Ultrasonic Non-Destructive Measurement of Residual Stresses by Modal Frequency Spacing using Leaky Lamb Waves

This paper investigates the potential of ultrasonic non-destructive measurements of residual stresses using the modal frequency spacing method based on the interference spectrum of leaky Lamb waves as an alternative to the commonly used flight-time approach in ultrasonic methods. Extensive experiments were carried out to verify the viability and robustness of the technique using an instrumented leaky Lamb wave setup with uniaxial stressed samples and welded steel samples. To improve the signal-to-noise ratio, multiple sets of raw signals of specularly reflected and leaky Lamb waves were acquired and then averaged in the time domain. The acquired data in the time domain were then transformed into the frequency domain to form the interference spectrum of leaky Lamb waves with a good repeatability. The acoustoelastic coefficient of carbon steel is then derived from the measured relationship of wave velocity and applied stress. Finally, a welded steel plate was examined and residual stress was evaluated. The current work demonstrates the feasibility and the potential of the proposed method in measuring residual stresses in welded plates and thin-walled structures.     

激光热弹激励流-固泄漏Lamb波的有限元模拟

根据变分原理,得到热弹体运动方程和热传导方程相对应的有限元方程. 通过数值积分方法求解有限元方程,得到脉冲激光线源在水/铝、空气/铝这两种流-固界面上热弹激励的泄漏Lamb波瞬态波形. 计算结果表明,泄漏Lamb波不但存在于液-固界面,而且存在于气-固界面;和Lamb波相反,泄漏Lamb波的S_0模态是反对称的,而A_0模态是对称的;但由于这两种流-固界面的性质差异导致泄漏Lamb波的波形和幅度不同.      

钢轨轨底垂直振动模式导波检测技术的实验研究

现有铁路钢轨超声探伤车技术无法检测线路钢轨轨底缺陷,给铁路运输安全带来很大隐患.本文开展了钢轨轨底超声导波传播特性和垂直振动模式导波检测技术研究,采用半解析有限元方法分析了我国60型钢轨轨底的各振动模态导波频散曲线和波结构.应用模态锤技术对自由状态钢轨轨底垂直振动模态导波传播特性进行了实验测量,结果表明,在0～100kHz频率范围内,钢轨轨底垂直振动模态优势模式与厚度为14 mm板中的A0模式兰姆波具有等效性.进一步研究了激励频率、激励脉冲周数、传播距离对轨底垂直振动模态导波传播的影响,设计了导波斜探头,选择合适的参数在钢轨轨底激励出垂直振动模态导波并检测出了轨底的人工缺陷.本文的研究结果为线路钢轨轨底的导波检测技术奠定了一定的基础.     

兰姆波测试信号的数字滤波处理

为了增加兰姆波测试信号特征提取的精度,降低噪声的影响,信号的预处理是必要的.本文采用一发一收兰姆波测试技术,在含有人工槽型缺陷的3mm厚铝板上进行了实验.选择带通无限长脉冲响应滤波器对兰姆波信号进行降噪.考虑到兰姆波的激发频率为250kHz,ⅡR滤波器的通带设置为160～330kHz.采用Hilbert变换获取滤波后信号的包络,结果显示,与滤波前兰姆波信号的包络相比,滤波后信号的包络更加平滑和清晰,各个波包的峰值可以唯一确定,为后续兰姆波信号的走时提取提供了方便.在此基础上,根据入射波与S0反射波峰值之间的时间间隔计算S0模式的群速度,结果与理论值较为接近,由此显示了滤波处理在兰姆波测试信号分析中的重要作用.     

基于匹配追踪算法的复合材料冲击损伤成像技术

基于Lamb波和匹配追踪算法,提出了一种损伤成像方法,对复合材料冲击损伤进行在线的连续 监测。首先针对Lamb波监测的特点,提出了匹配追踪方法的快速实现方案,将信号分解为多个Chirplet原 子的线性组合,建立了Lamb的弥散效应与Chirplet原子的调频斜率之间的关系,模拟结果表明Chirplet原 子能准确地匹配失真变形的窄带脉冲信号;根据损伤前与损伤后的信号差别,提出了一种基于Lamb波能量 特征差异提取的损伤指标;进一步采用改进的RAPID算法进行损伤成像,将损伤情况可视化。结果表明所 提方法可行和有效。     

Lamb wave mode decomposition for structural health monitoring

Lamb waves propagate over large distances in plate-like thin structures and they have received great attention in the structural health monitoring (SHM) field as an efficient means to inspect a large area of a structure by using only a small number of sensors. The times-of-flight of the Lamb wave modes are useful for detecting damage generated in a structure. However, due to the dispersive and multi-mode nature of Lamb waves, it is very challenging to decompose Lamb wave modes into symmetric and anti-symmetric modes for potential applications to structural health monitoring. Thus, we propose an efficient Lamb wave mode decomposition method based on two fundamental rules: the group velocity ratio rule and the mode amplitude ratio rule. The group velocity ratio rule means that the ratio of the group velocities of _A0$A_0$ and _S0$S_0$ modes must be constant. The mode amplitude ratio rule means that the ratio of the magnitudes of _A0$A_0$ and _S0$S_0$ modes in a measured response signal must be always greater than one once the center frequency of the input signal is determined, such that the magnitude of the _A0$A_0$ mode in the excited signal is larger than that of the _S0$S_0$ mode, and vice versa. The proposed method is verified through experiments conducted for a plate specimen.     

Stress Evaluation Using Ultrasonic Interference Spectrum of Leaky Lamb Waves

This paper presents a nondestructive stress evaluation technique using the ultrasonic interference spectrum of leaky Lamb waves. By using a specific pitch-catch ultrasonic setup, the symmetric and antisymmetric modes of Lamb waves in a finite plate are decoupled, leading to simple relationships between the modal frequency spacing of two adjacent modes in the interference spectrum and the acoustic wave velocities that are functions of stress. As a result, the stress in the plate can be determined by measuring the modal frequency spacing instead of the relative flight times to calculate the acoustic wave velocity. Extensive experiments were carried out to verify the viability and robustness of the new technique using a simple testing system. It has been demonstrated that the new technique is about 25 times more accurate than existing flight-time approaches using the same testing system. The experimental results agree well with the results obtained by other ultrasonic methods using expensive equipment.     

WAVE PROPAGATION IN PIEZOELECTRIC/PIEZOMAGNETIC LAYERED PERIODIC COMPOSITES

This paper is concerned with the dynamic behaviors of wave propagation in layered periodic composites consisting of piezoelectric and piezomagnetic phases. The dispersion relations of Lamb waves axe derived. Dispersion curves and displacement fields are calculated with different piezoelectric volume fractions. Numerical results for BaTiO3/CoFe2O4 composites show that the dispersion curves resemble the symmetric Lamb waves in a plate. Exchange between the longitudinal （i.e. thickness） mode and coupled mode takes place at the crossover point between dispersion curves of the first two branches. With the increase of BaTiO3 volume fraction, the crossover point appears at a lower wave number and wave velocity is higher. These findings are useful for magnetoelectric transducer applications.