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.     

用于储罐底板缺陷检测的超声兰姆波模式研究

从超声兰姆波的声场方程出发,得到板材表面离面位移(法向位移)为零的条件,即当超声兰姆波的相速度等于板材介质的纵波声速时,在板材表面的离面位移为零。在给定适当频厚积的条件下,分别数值模拟了仅有切向位移而无离面位移的A1、S1、A2和S2兰姆波模式在有液体负载的单层钢板中的传播情形。结果表明:离面位移为零的S2模式频散较小且对板中缺陷更为敏感。     

Rayleigh-Lamb wave propagation on a fractional order viscoelastic plate

A previous study of the authors published in this journal focused on mechanical wave motion in a viscoelastic material representative of biological tissue [Meral et al., J. Acoust. Soc. Am. 126, 3278-3285 (2009)]. Compression, shear and surface wave motion in and on a viscoelastic halfspace excited by surface and sub-surface sources were considered. It was shown that a fractional order Voigt model, where the rate-dependent damping component that is dependent on the first derivative of time is replaced with a component that is dependent on a fractional derivative of time, resulted in closer agreement with experiment as compared with conventional (integer order) models, such as those of Voigt and Zener. In the present study, this analysis is extended to another configuration and wave type: out-of-plane response of a viscoelastic plate to harmonic anti-symmetric Lamb wave excitation. Theoretical solutions are compared with experimental measurements for a polymeric tissue mimicking phantom material. As in the previous configurations the fractional order modeling assumption improves the match between theory and experiment over a wider frequency range. Experimental complexities in the present study and the reliability of the different approaches for quantifying the shear viscoelastic properties of the material are discussed.     

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     

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.     

Piezoelectric transducer parameter selection for exciting a single mode from multiple modes of Lamb waves

Excitation and propagation of Lamb waves by using rectangular and circular piezoelectric transducers surface-bonded to an isotropic plate are investigated in this work. Analytical stain wave solutions are derived for the two transducer shapes, giving the responses of these transducers in Lamb wave fields. The analytical study is supported by a numerical simulation using the finite element method. Symmetric and antisymmetric components in the wave propagation responses are inspected in detail with respect to test parameters such as the transducer geometry, the length and the excitation frequency. By placing only one piezoelectric transducer on the top or the bottom surface of the plate and weakening the strength of one mode while enhancing the strength of the other modes to find the centre frequency, with which the peak wave amplitude ratio between the S0 and A0 modes is maximum, a single mode excitation from the multiple modes of the Lamb waves can be achieved approximately. Experimental data are presented to show the validity of the analyses. The results are used to optimize the Lamb wave detection system.     

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.     

Classification of flaw severity using pattern recognition for guided wave-based structural health monitoring

In this paper, the authors present a formal classification routine to characterize flaw severity in an aircraft-grade aluminum plate using Lamb waves. A rounded rectangle flat-bottom hole is incrementally introduced into the plate, and at each depth multi-mode Lamb wave signals are collected to study the changes in received signal due to mode conversion and scattering from the flaw. Lamb wave tomography reconstructions are used to locate and size the flaw at each depth, however information about the severity of the flaw is obscured when the flaw becomes severe enough that scattering effects dominate. The dynamic wavelet fingerprint is then used to extract features from the raw Lamb wave signals, and supervised pattern classification techniques are used to identify flaw severity with up to 80.7% accuracy for a training set and up to 51.7% accuracy on a series of validation data sets extracted from independent plate samples.     

Elastic constants determination by direct measurement of the beat wavelength between A0 and S0 Lamb modes with pulsed TV holography

A whole-field optical technique of high sensitivity, namely pulsed TV holography with phase evaluation by the Spatial Fourier Transform Method, is applied to the acquisition of instantaneous displacement fields of ultrasonic Lamb waves in aluminium plates a few millimetres thick. Two Lamb modes, the A0 and S0 ones, are simultaneously generated in the plate, producing a clear beating. Several values of the beat wavelength, corresponding to different excitation frequencies, are obtained by direct measurement of the distance between nodes in the wave field. The obtained values are fitted to the theoretical Rayleigh–Lamb frequency spectrum in order to determine the elastic constants of the plate material. We conclude that it is necessary to know the value of another parameter to univocally solve the problem, and so the bulk longitudinal wave velocity is measured by the pulse-echo method. Then the Poisson's ratio is obtained and, from these two parameters, the Young's modulus can also be determined.     

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.     

一种评价固体板材表面性质的非线性超声兰姆波方法

在基频与二倍频兰姆波相速度匹配但群速度失配的条件下, 通过选择适当的兰姆波二次谐波时域信号的测量起止时间, 可完全扣除换能器对二次谐波积分振幅测量所带来的影响。本文提出采用兰姆波二次谐波的积分振幅作为评价参量, 以实现对板材表面性质的准确评价。当板材表面性质发生改变时, 原本在理想表面条件下成立的基频与二倍频兰姆波相速度匹配的条件不再严格满足, 这将显著地影响到兰姆波的二次谐波发生效率, 相应的二次谐波积分振幅随表面性质的改变也将发生非常敏感的单调变化。实验结果表明,利用扣除换能器影响之后所测得的兰姆波二次谐波的积分振幅,可对板材表面性质的变化情况进行准确评价。     

Interaction of a bounded ultrasonic beam with a thin inclusion inside a plate

A theoretical study of the reflection of a two-dimensional Gaussian ultrasonic beam, incident at a Lamb angle of a plate containing a thin rectangular inclusion at an arbitrary position, is presented on the basis radiation mode theory. The inclusion is parallel to the plate surface and its thickness is assumed to be much smaller than the ultrasonic wavelength. It is shown that the amplitude and phase of the reflected beam profile can be used for accurate inclusion characterization. However, this only holds for certain internal positions of the inclusion and for material combinations that do not strongly perturb the excitation of Lamb waves in the plate. When these conditions are satisfied, it is possible to define the Lamb waves and the associated experimental conditions for which good estimates can be obtained of the position of the beginning point of the inclusion as well as of the length and the thickness of the inclusion.     

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.     

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.     

Experimental study of ultrasonic beam sectors for energy conversion into Lamb waves and Rayleigh waves

When a bounded beam is incident on an immersed plate Lamb waves or Rayleigh waves can be generated. Because the amplitude of a bounded beam is not constant along its wave front, a specific beam profile is formed that influences the local efficiency of energy conversion of incident sound into Lamb waves or Rayleigh waves. Understanding this phenomenon is important for ultrasonic immersion experiments of objects because the quality of such experiments highly depends on the amount of energy transmitted into the object. This paper shows by means of experiments based on monochromatic Schlieren photography that the area within the bounded beam responsible for Lamb wave generation differs from that responsible for Rayleigh wave generation. Furthermore it provides experimental verification of an earlier numerical study concerning Rayleigh wave generation.     

Laser-ultrasonic generation of Lamb waves in the reaction force range

The Laser-ultrasonic generation of Lamb waves in an elastic plate is investigated theoretically and experimentally for a laser source whose intensity is high enough to create reaction forces (normal tractions) on the illuminated surface of the specimen. The analytical solutions for transient waves are derived using the integral transform method first by considering an arbitrary source shape and time excitation function, and then specifically for circular and line source shapes. The simulation study allows us not only to predict the behavior of individual wave modes but also to construct the overall responses; thus it helps us better understand the wave excitation mechanisms. The dispersive and multi-modal nature of laser-generated Lamb waves is presented by showing the spatiotemporal Fourier transform of displacements obtained by the simulation study. The transform, displayed in the frequency-wave number domain, enunciates the characteristics of the propagating individual Lamb wave modes. The simulation results are then compared with the 2-D Fourier transform of a set of experimental data obtained by scanning an aluminum plate specimen.     

采用单个压电传感器的单模式兰姆波激发频率的选择

考虑了压电传感器(PZT)与板之间的耦合作用,从理论上研究了单个压电传感器激发时产生单模式兰姆波的频率调节方法,实验给出了模式选择在兰姆波结构健康监测中的应用. 在板材、板厚以及PZT尺寸一定的情况下,从理论上能够预测到作为频率函数的各兰姆波模式的幅值变化. 根据某特定兰姆波模式的幅值最大而其他模式幅值相对最小时所对应的频率,即可识别出该兰姆波模式优化的激发频率. 数值仿真验证了理论的有效性以及单模式兰姆波选择的可能性. 在不同的激发频率下,分别激发了优化的A0 模式,优化的S0模式以及共存的A0和S0模 关键词： 兰姆波 压电传感器 激发频率 结构健康监测     

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.     

Influence of adhesive layer properties on laser-generated ultrasonic waves in thin bonded plates

This paper studies quantitatively the generation of Lamb waves in thin bonded plates subjected to laser illumination, after considering the viscoelasticity of the adhesive layer. The displacements of such plates have been calculated in the frequency domain by using the finite element method, and the time domain response has been reconstructed by applying an inverse fast Fourier transform. Numerical results are presented showing the normal surface displacement for several configurations: a single aluminum plate, a three-layer bonded plate, and a two-layer plate. The characteristics of the laser-generated Lamb waves for each particular case have been investigated. In addition, the sensitivity of the transient responses to variations of material properties (elastic modulus, viscoelastic modulus, and thickness) of the adhesive layer has been studied in detail.     

Nonlinear lamb waves in a metal plate with defects

Experimental results on the propagation of finite-amplitude Lamb waves in a solid plate made of polycrystalline aluminum alloy with defects are presented. The Lamb waves are recorded and visualized using a scanning laser vibrometer. The dependences of the higher harmonic amplitudes, both averaged over the plate surface and measured at a point far from the defect and at the site of the defect, on the fundamental frequency amplitude are studied. A threshold character of the higher harmonic generation and a power-law behavior of their amplitudes are revealed, the latter feature being unconventional for the nonlinearity associated with the anharmonicity of the crystal lattice of the material. The possibility of locating the distribution of individual defects from the measured spatial distribution of structural nonlinearity in the material under study is experimentally demonstrated. The results of the experiments are explained in terms of the bilinear medium model.