Multiple-mode Lamb wave scattering simulations using 3D elastodynamic finite integration technique

We have implemented three-dimensional (3D) elastodynamic finite integration technique (EFIT) simulations to model Lamb wave scattering for two flaw-types in an aircraft-grade aluminum plate, a rounded rectangle flat-bottom hole and a disbond of the same shape. The plate thickness and flaws explored in this work include frequency-thickness regions where several Lamb wave modes exist and sometimes overlap in phase and/or group velocity. For the case of the flat-bottom hole the depth was incrementally increased to explore progressive changes in multiple-mode Lamb wave scattering due to the damage. The flat-bottom hole simulation results have been compared to experimental data and are shown to provide key insight for this well-defined experimental case by explaining unexpected results in experimental waveforms. For the rounded rectangle disbond flaw, which would be difficult to implement experimentally, we found that Lamb wave behavior differed significantly from the flat-bottom hole flaw. Most of the literature in this field is restricted to low frequency-thickness regions due to difficulties in interpreting data when multiple modes exist. We found that benchmarked 3D EFIT simulations can yield an understanding of scattering behavior for these higher frequency-thickness regions and in cases that would be difficult to set up experimentally. Additionally, our results show that 2D simulations would not have been sufficient for modeling the complicated scattering that occurred.     

基于模式分离的兰姆波逆时偏移成像

应用频率域逆时偏移方法实现各向同性和各向异性板中缺陷的兰姆波成像.由于缺陷引起的多模态散射信号会在重建图像中形成伪像,根据基本导波模式振动对称性的差别进行了模式分离预处理.基于多元阵列超声技术,开展了铝板和复合板内缺陷频率域逆时偏移超声成像方法的数值仿真研究.首先,建立有限元模型,采用环形传感器数值采集由缺陷引起的兰姆波散射信号,然后,将采集到的多模式散射信号进行模式分离处理,再将模式分离后的兰姆波散射信号经时间反转后并在相应的接收器处重新激励,在频域中运用格林函数反向传播兰姆波散射信号,获取监测区域的声场信息,与正向传播声场进行互相关,重建缺陷图像.首先对铝板中单缺陷以及复合材料板中相邻的两个相同缺陷进行数值仿真,对比有无模式分离处理的缺陷逆时偏移成像效果,体现出模式分离的重要性.在此基础上,采用逆时偏移方法对复合板材内位置邻近、深度不同的双缺陷进行识别.数值结果表明,模式分离预处理后的缺陷重建图像能够有效去除多模式干扰产生的伪像.文中提出的成像方法对各向同性板和各向异性板内缺陷的检测和成像具有很好的发展潜力,可以准确地探测多个缺陷的形状、尺寸和深度.     

Separation of multimode Lamb waves overlapped in time and frequency domains by using fractional differential

To separate multimode Lamb wave overlapped both in time and frequency domains,a multimode Lamb wave signal separation method by using fractional differential is proposed.The Tsallis function is used as the model of the amplitude spectrum.The amplitude spectra of Lamb wave signals are divided into fractional order differential.The characteristic parameters of each mode are extracted by using the polynomial between the maximum amplitude and the differential order as well as the polynomial between the peak frequency and the differential order.The corresponding phase spectrum of each mode is derived from the dispersion characteristics.The signal of each mode is constructed through the amplitude spectrum and phase spectrum.The simulated results of S1 and A1 modes in a 1 mm-thick steel plate show that the relative errors of amplitude and bandwidth of both modes are less than 6%,and that the relative errors of central frequency of both modes are less than 0.25%.Therefore,this method could be used to separate the time-frequency overlapped multimode Lamb wave signals.It is helpful for the analysis and recognition of multimode Lamb wave signals.     

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。     

基于频散补偿和分数阶微分的多模式兰姆波分离

由于兰姆波的多模和频散特性,实际检测时在同一激发频率下存在多种模式的混合信号,而各模式信号有不同的频散特性,使得在时频混叠的情况下兰姆波的检测变得十分复杂.本文在频散补偿的基础上,通过时延函数建模,依靠不同模式频散趋势的差异性,将时频混叠信号的分离问题转化为部分模式混叠信号的分离问题.基于分数阶微分的理论,用信号幅值谱分数阶微分极大值和对应频率分别与微分阶次拟合多项式实现特征参数的提取并依靠特征参数重建幅值谱.结合相位谱重构时域信号以实现部分混叠信号中频散补偿后的模式的分离.最后恢复频散获得分离后的兰姆波信号.仿真和实验结果表明,本文方法不仅可以实现时频混叠多模式兰姆波信号的分离,更能保证分离精度,有助于复杂多模式频散信号的分离与处理的进一步研究.     

用分数阶微分实现时频重叠多模式兰姆波的模式分离

为了分离时频重叠多模式超声兰姆波,提出了一种用分数阶微分理论实现多模式兰姆波模式分离的方法。以时频重叠的S1和A1模式混合信号为例,用赛利斯分布作为幅值谱的模型,首先对信号做频散补偿,由补偿后信号幅值谱分数阶微分推导了幅值谱特征参数的计算式并根据信号模型重建幅值谱,然后结合兰姆波的频散特性推导出对应的相位谱,并通过幅值谱和相位谱重构各模式的信号,实现模式分离。对1 mm钢板中仿真时频重叠的S₁和A₁模式信号分离结果显示分离出信号的幅值和带宽相对误差小于6%,中心频率相对误差小于0.25%。实验结果也证实了方法的可行性。因此当混合信号幅值谱不完全交叠时,本方法可以实现多模式兰姆波信号的分离,有助于多模式兰姆波频散信号的分析和识别。      

Scattering of Lamb waves by a circular cylinder.

Following our previous attempt at the scattering from a cylinder in a slab to the incidence of a guided shear wave, we hereby discuss the scattering by an elastic cylinder embedded in an isotropic plate for a variety of bonding states to incidence of the fundamental Lamb wave modes S0 and A0 at the low-frequency regime. The plate is divided up into three regions by introducing two imaginary planes located symmetrically some distance from the cylinder and perpendicular to surfaces of the plate. The wave fields in various regions are expanded either into cylinder wave modes or into Lamb wave modes. A system of equations determining the coefficients of expansion is obtained according to the traction-free boundary conditions on the plate walls and the displacement and stress continuity conditions across the virtual planes. By taking an appropriate finite number of terms of the infinite expansion series and some selected points on the two properly chosen imaginary planes and the surfaces of the plate through convergence and precision tests, a matrix equation to numerically evaluate the expansion coefficients is found. Coefficients of the reflection and transmission versus the normalized radius of the cylinder in welded, slip, and cracked interfacial conditions are numerically computed. In the low-frequency range, the relative errors are found to be less than 1%. Contrast curves of the reflection coefficient for the cylinder of nearly all permissible size in perfect and imperfect interfacial bonding are shown and prominent differences are noted.     

Localization of notches with Lamb waves

A time-frequency representation (TFR) is used to analyze the interaction of a multimode and dispersive Lamb wave with a notch, and then serves as the basis for a correlation technique to locate the notch. The experimental procedure uses a laser source and a dual-probe laser interferometer to generate and detect Lamb waves in a notched plate. The high fidelity, broad-bandwidth, point-like and noncontact nature of laser ultrasonics are critical to the success of this study, making it possible to experimentally measure transient Lamb waves without any frequency biases. A specific TFR, the reassigned spectrogram, is used to resolve the dispersion curves of the individual modes of the plate, and then the slowness-frequency representation (SFR) of the plate is calculated from this reassigned spectrogram. By considering the notch to be an additional (second) source, the reflected and transmitted contributions of each Lamb mode are automatically identified using the SFRs. These results are then used to develop a quantitative understanding of the interaction of an incident Lamb wave with a notch, helping to identify mode conversion. Finally, two complementary, automated localization techniques are developed based on this understanding of scattering of Lamb waves.     

Acoustic scattering from a finite plate: generation of guided Lamb waves S(0), A(0) and A

In the domain of renewable energies, marine current turbines constitute one of the possibilities of producing electrical energy. Naked-eye inspection, or with the aid of video monitoring systems of these machines to ensure their perfect working order, can be difficult in a turbid environment. Acoustic methods are conceivable. The study focuses on the blades of these machines, by considering rectangular plates. The propagation of Lamb waves in a plate is studied by analyzing experimental time signals obtained from acoustic scattering. These signals are analyzed employing the ray theory. In vacuum, the flexural wave is the A(0) Lamb wave, whilst in water this wave splits in a bifurcation: the A wave with a phase velocity always smaller than the sound speed in water, and the A(0) wave with a phase velocity always higher than the sound speed in water. In the central bandpass of the transducers used in the experiments, mainly the A and S(0) waves exist. However, signals observed in the third harmonic bandpass of the transducers are also analyzed. In order to complement these results, resonance frequencies of the plate studied are calculated taking into account the boundary conditions and compared with the resonance frequencies of the experimental spectra.     

The band gaps of Lamb waves in a ribbed plate: A semi-analytical calculation approach

In this paper a semi-analytical method is proposed to investigate the transmission band gaps of Lamb waves through repetitive structures in a waveguide. For a unit cell the scattering matrix is obtained by the Lamb mode matching technique at each artificially sliced interface and then substituted into the Bloch theorem to solve the eigenproblem incurred by cell repetition. The method is implemented on a ribbed plate. The band gaps in the dispersion curves are confirmed by the dips of Lamb wave transmission coefficients, and attributed to the coupled vibrations of Lamb modes in different sliced sections of the unit cell.     

兰姆波结构健康监测中的概率损伤成像

应用概率成像方法对兰姆波结构健康监测中板的损伤进行识别。根据兰姆波损伤散射信号的传播时间以及传感器网络中一对发射-接收传感器的空间位置来确定一个椭圆轨迹,该轨迹显示了损伤可能出现的位置。将监测区域均匀网格化,计算各网格节点到椭圆轨迹的最短距离,将此距离映射为损伤出现的概率。采用灰度等级对所有网格节点处的概率值进行量化,则由每一个发射接收传感器对就确定了一个灰度图像。为了突出损伤,应用图像融合技术对传感器网络中所有发射接收传感器对所构成的灰度图像进行融合。对铝板中横穿孔损伤的实验结果显示了该方法能够有效地确定损伤的位置和范围,有助于推动兰姆波结构健康监测的实用化。      

Experimental study and signal analysis in the Lamb wave conversion at a bevelled edge

This paper deals with a quantitative study of the conversion of a Lamb wave at the bevelled edge of a plate. A harmonic wave (successively the A1 and S0 Lamb modes) is generated using a wedge. The normal displacements at the surface of the plate are measured with a laser vibrometer and used to compute an energy evaluation. In order to determine a good mean value of incident and reflected wave amplitudes, the signals are isolated by a Fourier treatment. Then, the energy flow repartition among the converted modes is computed in both cases and for different values of the bevel angle.     

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...     

Three-Dimensional Scattering of an Incident Plane Shear Horizontal Guided Wave by a Partly through-Thickness Hole in a Plate

We investigate the three-dimensional(3D) scattering problem of an incident plane shear horizontal wave by a partly through-thickness hole in an isotropic plate,in which the Lamb wave modes are also included due to the mode conversions by the scattering obstacle in the 3D problem.An analytical model is presented such that the wave fields are expanded in all of propagating and evanescent SH modes and Lamb modes,and the scattered far-fields of three fundamental guided wave modes are analyzed numerically for different sizes of the holes and frequencies.The numerical results are verified by comparing with those obtained by using the approximate Poisson/Mindlin plate model for small hole radius and low frequency.It is also found that the scattering patterns are different from those of the SO wave incidence.Our work is useful for quantitative evaluation of the plate-like structure by ultrasonic guided waves.     

PVDF梳状换能器接收非线性兰姆波的实验研究*

该文基于PVDF压电薄膜对梳状换能器进行设计制作,并将该换能器应用于接收非线性兰姆波信号实验研究。首先通过输出矢量和方法分析PVDF梳状换能器的工作特性,然后将设计制作的PVDF梳状换能器应用于铝板中非线性兰姆波信号的接收,并与传统压电陶瓷换能器经斜劈接收的非线性兰姆波信号进行比较分析。实验结果表明,两种换能器所接收到的信号幅值随传播距离的变化趋势相近,线性增长的积累效应表征结果相似,且PVDF梳状换能器可以对基波和二次谐波信号同时响应。除此之外,PVDF梳状换能器用于接收非线性兰姆波信号更加稳定。因此,PVDF梳状换能器有望应用于复杂构件的在线检测与监测研究。     

Mode selection of Lamb waves for the evaluation of solid plates with liquid loading

This paper studies the mode selection of Lamb waves for evaluating solid plates with liquid loading. For this purpose, the Lamb wave selected should have the features such as zero normal displacement components at the plate surface in contact with liquid, small dispersion, and maximum group velocity. It is found that when the phase velocity of Lamb wave is equal to the longitudinal wave velocity of the plate material, its normal displacement at the plate surface is always zero. Through the numerical analyses, the specific S₂ Lamb wave that has zero normal displacement component at the plate surface, small dispersion and maximum group velocity compared with the other Lamb waves has been found. With respect to the specific S₂ Lamb wave, some experimental examinations have been carried out. It is found that the liquid loading on the plate surface has less influence on the specific S₂ Lamb wave signal but it can effectively eliminate the other signals. Moreover, the specific S₂ Lamb wave selected exhibits the capability of detecting multiple defects in the solid plate with the liquid loading. It can be concluded that the specific S₂ Lamb wave selected is suitable for the evaluation of solid plates with liquid loading.     

Lamb wave band gaps in locally resonant phononic crystal strip waveguides

Using finite element method, we have made a theoretically study of the band structure of Lamb wave in a locally resonant phononic crystal strip waveguide with periodic soft rubber attached on the two sides of epoxy main plate. The numerical results show that the Lamb wave band gap based on local resonant mechanism can be opened up in the stub strip waveguides, and the width of the local resonant band gap is narrower than that based on the Bragg scattering mechanism. The results also show that the stub shape and width have influence on the frequency and width of the Lamb wave band gap.     

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。     

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。     

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.