金属板中Lamb波波速与应力关系的实验研究

本文给出了金属板中Lamb波波速对同向应力变化率测量的装置,探讨分析了测量原理及误差,并对Lamb波的波速与应力关系进行了实验研究。结果表明Lamb波的波速对应力有较好的线性关系,Lamb波相速度对应力的变化率的实验值与理论值符合很好。     

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...     

Importance of the near Lamb mode imaging of multilayered composite plates.

In recent years Lamb waves are being used for internal defect detection in multilayered composite plates. Different Lamb modes generate various stress levels in different layers. As a result, all Lamb modes are not equally sensitive to internal defects of various layers. A number of studies have been carried out to identify which Lamb mode is most effective for detecting defects in a specific layer. However, one shortcoming of the Lamb wave inspection technique is that in a symmetrically layered composite plate stress and displacement magnitudes and energy distribution profiles for all Lamb modes are symmetric about the central plane of the plate. As a result, the ability of a Lamb mode to detect defects in a specific layer of the plate is identical to its ability to detect defects in the corresponding layer of mirror symmetry. Hence, from the Lamb wave generated image one cannot distinguish between the defects in these two layers of mirror symmetry. In this paper it is investigated how by fine-tuning the frequency and the striking angle of the incident beam in the neighborhood of a Lamb mode one can separately detect internal defects in layers of mirror symmetry in the upper and lower halves of a plate.     

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。      

Study of the influence of thin layer loading on the propagation of Lamb waves using perturbation method

I.IntroductionSincethepublicationoftheclassicalpaper"Onthewavesinanelasticplate"byH.Lambin1917l1l,theterm"LaInbwave"hasbeenusedtorefertoanelasticdisturbancepropagatinginasolidplatewithfreeboundaries.Lambwavesarewidelyusedintheapplicationsofthedefectinspectionofthinwa.lledmaterial[2'8].InrecelltyearsLambwaveshavebeenwide1yusedinthefabricationofsensors.LamInwavesensorsdetectthechangesofenvironmentbymeasuringthechangeofphasevelocityofLambwaves.IncomparisonwithbuIkwavesandSAW's,Lambwavsprovi…     

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.     

Investigation of a silicon-based one-dimensional phononic crystal plate via the super-cell plane wave expansion method

The super-cell plane wave expansion method is employed to calculate band structures for the design of a silicon-based one-dimensional phononic crystal plate with large absolute forbidden bands. In this method, a low impedance medium is introduced to replace the free stress boundary, which largely reduces the computational complexity. The dependence of band gaps on structural parameters is investigated in detail. To prove the validity of the super-cell plane wave expansion, the transmitted power spectra of the Lamb wave are calculated by using a finite element method. With the detailed computation, the band-gap of a one-dimensional plate can be designed as required with appropriate structural parameters, which provides a guide to the fabrication of a Lamb wave phononic crystal.     

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.     

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.     

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。     

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.     

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.     

Lamb wave extraction of dispersion curves in micro/nano-plates using couple stress theories

In this paper, Lamb wave propagation in a homogeneous and isotropic non-classical micro/nano-plates is investigated. To consider the effect of material microstructure on the wave propagation, three size-dependent models namely indeterminate-, modified- and consistent couple stress theories are used to extract the dispersion equations. In the mentioned theories, a parameter called ‘characteristic length’ is used to consider the size of material microstructure in the governing equations. To generalize the parametric studies and examine the effect of thickness, propagation wavelength, and characteristic length on the behavior of miniature plate structures, the governing equations are nondimensionalized by defining appropriate dimensionless parameters. Then the dispersion curves for phase and group velocities are plotted in terms of a wide frequency-thickness range to study the lamb waves propagation considering microstructure effects in very high frequencies. According to the illustrated results, it was observed that the couple stress theories in the Cosserat type material predict more rigidity than the classical theory; so that in a plate with constant thickness, by increasing the thickness to characteristic length ratio, the results approach to the classical theory, and by reducing this ratio, wave propagation speed in the plate is significantly increased. In addition, it is demonstrated that for high-frequency Lamb waves, it converges to dispersive Rayleigh wave velocity.     

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     

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.     

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.     

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.     

A finite difference analysis of the field present behind an acoustically impenetrable two-layer barrier

The interaction of an incident sound wave with an acoustically impenetrable two-layer barrier is considered. Of particular interest is the presence of several acoustic wave components in the shadow region of this barrier. A finite difference model capable of simulating this geometry is validated by comparison to the analytical solution for an idealized, hard-soft barrier. A panel comprising a high air-content closed cell foam backed with an elastic (metal) back plate is then examined. The insertion loss of this panel was found to exceed the dynamic range of the measurement system and was thus acoustically impenetrable. Experimental results from such a panel are shown to contain artifacts not present in the diffraction solution, when acoustic waves are incident upon the soft surface. A finite difference analysis of this experimental configuration replicates the presence of the additional field components. Furthermore, the simulated results allow the additional components to be identified as arising from the S(0) and A(0) Lamb modes traveling in the elastic plate. These Lamb mode artifacts are not found to be present in the shadow region when the acoustic waves are incident upon the elastic surface.     

Lamb waves in anisotropic plates (review)

Propagation of Lamb waves in elastic anisotropic plates is studied in the framework of the six-dimensional Cauchy formalism. Closed-form secular equations for dispersion curves for Lamb waves propagating in a plate with arbitrary elastic anisotropy are obtained.     

Effect of misalignment of air-coupled probes on Ao Lamb mode propagating in a metal plate

Proper alignment of air-coupled ultrasonic transducers for generation and reception of Lamb waves is vital in order to acquire a high amplitude wave group. Any misalignment with either the transmitter or the receiver or both adversely influences the amplitude of a Lamb mode. This paper reports a systematic attempt to quantify the reduction in the amplitude of the fundamental anti-symmetric Lamb mode (A_o) in a metal plate caused by misalignments in air-coupled probes. Three different types of misalignments – linear, orientation and synchronised orientation were deliberately introduced in the transducers, and experiments were performed on a 6 mm thick aluminium plate. Amplitudes of A_o mode measured at various configurations were normalised with that of A_o mode, captured in a reference configuration. Suitable curves fitted over the experimental data points revealed that Gaussian curves represent appropriately the variations in normalised amplitudes of A_o mode. Moreover, analytical expressions were derived to predict the difference in arrival times of Lamb mode(s) due to orientation and synchronised orientation misalignments.