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     

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.     

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.     

Cumulative second-harmonic generation of Lamb waves propagating in a two-layered solid plate

The physical process of cumulative second-harmonic generation of Lamb waves propagating in a two-layered solid plate is presented by using the second-order perturbation and the technique of nonlinear reflection of acoustic waves at an interface. In general, the cumulative second-harmonic generation of a dispersive guided wave propagation does not occur. However, the present paper shows that the second-harmonic of Lamb wave propagation arising from the nonlinear interaction of the partial bulk acoustic waves and the restriction of the three boundaries of the solid plates does have a cumulative growth effect if some conditions are satisfied. Through boundary condition and initial condition of excitation, the analytical expression of cumulative second-harmonic of Lamb waves propagation is determined. Numerical results show the cumulative effect of Lamb waves on second-harmonic field patterns.     

Guided elastic waves in a pre-stressed compressible interlayer

The propagation of guided elastic waves in a pre-stressed elastic compressible layer embedded in a different compressible material is examined. The waves propagate parallel to the planar layer interfaces as a superposed dynamic stress state on the statically pre-stressed layer and host material. The underlying stress condition in the two materials is characterized by equibiaxial in-plane deformations with common principal axes of strain, one of the axes being perpendicular to the layering. Both materials have arbitrary strain energy functions. The dispersion equation is derived in explicit form. Analysis of the dispersion equation reveals the propagation characteristics and their dependence on frequency, material parameters and stress parameters. Combinations of these parameters are also defined for which guided waves cannot propagate.     

套管中模式波的响应特征*

在固井质量评价中主要利用套管中模式波的幅度或衰减变化反映水泥的胶结状况,不同测井仪器在套管中激发的模式波的类型不同,研究套管中各模式波的传播特征和影响因素可充分挖掘测量数据的潜在应用价值。CBL和SBT等测井仪器在套管中主要激发拉伸波,类同于平板中的零阶对称Lamb波,水泥环封隔测井仪器的斜入射模式在套管中主要激发套管弯曲波,类同于平板中的零阶反对称Lamb波,垂直入射模式激发套管共振波,类同于平板中的高阶对称Lamb波。该文重点分析了这些模式波的衰减特征及其对微环的响应,套管弯曲波在套后耦合轻质水泥时对微环不敏感,但在套后耦合常规水泥或重水泥时,其衰减明显高于胶结良好的状况;拉伸波对微环的存在最为敏感;套管共振波对微环不敏感。     

Propagation of time-reversed Lamb waves in acrylic cylindrical tubes as cortical-bone-mimicking phantoms

The present study aims to investigate the propagation of time-reversed Lamb waves in acrylic cylindrical tubes as cortical-bone-mimicking phantoms. Time-reversed Lamb waves could be successfully launched in 6 acrylic tubes with wall thicknesses from 2 to 12 mm by using a modified time reversal method. The group velocities of the time-reversed Lamb waves in the acrylic tubes were measured by using the axial transmission technique. They decreased very slightly with increasing wall thickness, showing good agreement with the theoretical group velocity of the A0 Lamb wave in the acrylic plate. These results suggest that the time-reversed Lamb waves in the acrylic tubes would essentially behave as the A0 Lamb wave, consistent with the behavior of the slow guided wave in long cortical bones. It is expected that the application of the time-reversed Lamb waves in long bones would enhance clinical potential of ultrasonic technologies for the diagnosis of osteoporosis.     

The measurement of A0 and S0 lamb wave attenuation to determine the normal and shear stiffnesses of a compressively loaded interface

Guided waves in an elastic plate surrounded by air propagate with very low attenuation. This paper describes the effect on this propagation of compressively loading an elastomer with high internal damping against one surface of the elastic plate. The propagation of both A0 and S0 Lamb modes is considered. The principal effect is shown to be increased attenuation of the guided waves. This attenuation is caused by leakage of energy from the plate into the elastomer, where it is dissipated due to high viscoelastic damping. It is shown that the increase in attenuation is strongly dependent on the compressive load applied across the solid-solid interface. This interface is represented as a spring layer in a continuum model of the system. Both normal and shear stiffnesses of the interface are quantified from the attenuation of A0 and S0 Lamb waves measured at each step of the compressive loading. The normal stiffness is also measured independently by normal incidence, bulk longitudinal wave ultrasound. The resulting predictions of wave propagation behavior, such as attenuation, obtained by the model are in excellent agreement with those measured experimentally.     

A study of time harmonic guided Lamb waves and their caustics in composite plates

Spatial steady-state Lamb wave propagation in an anisotropic composite plate excited by harmonic surface sources is modeled using a Green’s matrix representation in a frequency-wavenumber domain. An approach based on a residue integration technique for two dimensional wavenumber integrals for the computation of displacements outside an excitation source is presented in this paper. In the far-field zone of the excitation source, the method of stationary phase is used, which gives an asymptotic expansion of the displacement vector as a sum of cylindrical waves. Near caustic directions, a far-field solution is computed in terms of Airy functions. The results obtained applying residue integration technique and asymptotic expansion are found to be coinciding with the results of the computation by using the adaptive quadratures. Moreover, these approaches agree well with experimental data. Then, the advantages and disadvantages of the various methods applied for modeling of Lamb wave propagation are discussed in this paper. Focussing and other properties of Lamb waves are studied using numerical examples.     

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.     

Natural beam focusing of non-axisymmetric guided waves in large-diameter pipes

The propagation of non-axisymmetric guided waves in larger diameter pipes is studied in this paper by treating the guided waves as corresponding Lamb waves in an unwrapped plate. This approximation leads to a simpler method for calculating the phase velocities of hollow cylinder guided waves, which reveals a beam focusing nature of non-axisymmetric guided waves generated by a partial source loading. The acoustic fields in a pipe generated by a partial-loading source includes axisymmetric longitudinal modes as well as non-axisymmetric flexural modes. The circumferential distribution of the total acoustic field, also referred as an angular profile, diverges circumferentially while guided waves propagate with dependence on such factors as mode, frequency, cylinder size, propagation distance, etc. Exact prediction of the angular profile of the total field can only be realized by numerical calculations. In particular cases, however, when the wall thickness is far less than the cylinder diameter and the wavelength is smaller than or comparable to the pipe wall thickness, the acoustic field can be analyzed based on the characteristics of Lamb waves that travel along a periodic unwrapped plate. Based on this assumption, a simplified model is derived to calculate the phase velocities of non-axisymmetric flexural mode guided waves. The model is then applied to discussions on some particular characteristics of guided-wave angular profiles generated by a source loading. Some features of flexural modes, such as cutoff frequency values are predicted with the simpler model. The relationship between the angular profiles and other factors such as frequency, propagation distance, and cylinder size is obtained and presented in simple equations. The angular profile rate of change with respect to propagation distance is investigated. In particular, our simplified model for non-axisymmetric guided waves predicts that the wave beam will converge to its original circumferential shape after the wave propagates for a certain distance. A concept of "natural focal point" is introduced and a simple equation is derived to compute the 1st natural focal distance of non-axisymmetric guided waves. The applicable range of the simplified equation is provided. Industrial pipes meet the requirement of wall thickness being far less than the pipe diameter. The approximate analytical algorithms presented in this paper provides a convenient method enabling quick acoustic field analysis on large-diameter industrial pipes for NDE applications.     

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...     

Effect of the surface free energy on the behaviour of surface and guided waves

The aim of this paper is to evaluate the influence of the surface free energy upon the propagation of the eigenmodes of structures, by studying successively (a) the Rayleigh wave for an elastic half-space, (b) the Lamb waves for an elastic layer, and (c) the guided modes for a tri-layer structure (e.g., metal/adhesive/metal). The surface free energy is a parameter which appears in the jump conditions of stresses and displacements at each interface, and which consequently modifies the eigenmodes, solutions of the boundary conditions system. As expected, the Rayleigh wave is dispersive and its velocity increases when the surface free energy increases. In the same way, the velocity of Lamb waves also increases except at normal angle of propagation where the surface free energy does not arise. Moreover, near the Rayleigh angle, the behaviour of the A₀ and S₀ Lamb modes varies strongly according to the surface free energy. Similar results are observed for the tri-layer structure.     

不锈钢折弯板裂纹Lamb波检测技术*

金属弯板广泛应用于车辆、船舶、飞机等大型装备结构件中，折弯处易形成应力集中产生裂纹，直接影响构件的使用安全和寿命。本文开展了不锈钢弯板裂纹缺陷Lamb波检测技术研究，计算了钢板的频散曲线，优选三种不同频率的S0模态：0.25MHz、0.5MHz、1MHz。利用COMSOL软件建立频域仿真模型，模拟了Lamb波在3mm厚“L”形弯板内部的传播情况，开展折弯板裂纹缺陷检测实验，并使用小波包变换的方法对实验信号进行分析。结果表明，经小波变换后，0.25MHz、0.5MHz、1 MHz的S0模态Lamb波均可用于裂纹缺陷的识别检测.     

利用Taylor展开法研究Lamb波在功能梯度材料中的传播特性

超声技术可用于对功能梯度材料(FGMs)的性质进行评估. 由于FGMs性质的非均匀性,采用分布函数来描述FGMs弹性常数和密度沿厚度方向的变化趋势,并提出利用Taylor展开的方法来解决分布函数为任意函数时的FGMs中Lamb波的传播问题. 利用本征函数展开法得到了铁基氧化铝FGMs中Lamb波的相速度色散曲线,讨论了材料性质分布对铁基氧化铝FGMs中Lamb波传播特性的影响. 为FGMs性质(沿板厚方向变化)的反演提供了理论依据. 关键词： 功能梯度材料 Lamb波 Legendre多项式 分布函数     

Detection of cracks at rivet holes using guided waves

Guided Lamb waves can be used for a fast inspection of large areas, e.g. the detection of cracks at rivet holes in the fuselage of airplanes. When the guided wave hits a discontinuity like a hole, a typical scattered displacement field is obtained. A change of the scattered field indicates the development of a crack. In the experiments, the first anti-symmetric mode A0 of Lamb waves in plates is excited selectively by means of a piezoelectric transducer. The used frequency range is below the cut-off frequencies of higher wave modes. The scattered field around undamaged and damaged holes is measured on a grid around the hole with a heterodyne laser interferometer. Two types of damage are introduced: a notch cut with a very fine saw blade, and a fatigue grown crack. A significant change in the scattered field due to the defect is seen. Good agreement of the experimental results with theoretical calculations is obtained. The wave propagation is studied using Mindlin's theory of plates. The scattered field is calculated analytically and using finite difference methods (FDMs).     

Locating air leaks in manned spacecraft using structure-borne noise

All manned spacecraft are vulnerable to leaks generated by micrometeorite or debris impacts. Methods for locating such leaks using leak-generated, structure-borne ultrasonic noise are discussed and demonstrated. Cross-correlations of ultrasonic noise waveforms from a leak into vacuum are used to find the location of the leak. Four methods for sensing and processing leak noise have been developed and tested and each of these can be used to reveal the leak location. The methods, based on phased-array, distributed sensor, and dual sensor approaches, utilize the propagation patterns of guided ultrasonic Lamb waves in the spacecraft skin structure to find the source or direction of the leak noise. It is shown that each method can be used to successfully locate the leak to within a few millimeters on a 0.6-m2 aluminum plate. The relative merits of the four methods are discussed.     

In situ 2-D piezoelectric wafer active sensors arrays for guided wave damage detection

This paper presented development work of an in situ method for damage detection in thin-wall structures using embedded two-dimensional ultrasonic phased arrays. Piezoelectric wafer active sensors were used to generate and receive guided Lamb waves propagating in the plate-like structure. The development of a generic beamforming algorithm that does not require parallel ray assumption through using full wave propagation paths is described. A virtual beam steering method and device, the embedded ultrasonic structural radar, was implemented as a signal post-processing procedure. Several two-dimensional configurations were investigated and compared with beamforming simulation. Finally, rectangular shape arrays were developed for verifying the generic formulas and omnidirectionality. The rectangular arrays yield good directionality within the 360° full range and are able to detect damage anywhere in the entire plate.     

High-frequency guided ultrasonic waves for hidden defect detection in multi-layered aircraft structures

Aerospace structures often contain multi-layered metallic components where hidden defects such as fatigue cracks and localized disbonds can develop, necessitating non-destructive testing. Employing standard wedge transducers, high frequency guided ultrasonic waves that penetrate through the complete thickness were generated in a model structure consisting of two adhesively bonded aluminium plates. Interference occurs between the wave modes during propagation along the structure, resulting in a frequency dependent variation of the energy through the thickness with distance. The wave propagation along the specimen was measured experimentally using a laser interferometer. Good agreement with theoretical predictions and two-dimensional finite element simulations was found. Significant propagation distance with a strong, non-dispersive main wave pulse was achieved. The interaction of the high frequency guided ultrasonic waves with small notches in the aluminium layer facing the sealant and on the bottom surface of the multilayer structure was investigated. Standard pulse-echo measurements were conducted to verify the detection sensitivity and the influence of the stand-off distance predicted from the finite element simulations. The results demonstrated the potential of high frequency guided waves for hidden defect detection at critical and difficult to access locations in aerospace structures from a stand-off distance.     

A new multichannel time reversal focusing method for circumferential Lamb waves and its applications for defect detection in thick-walled pipe with large-diameter

This paper proposes a new multichannel time reversal focusing (MTRF) method for circumferential Lamb waves which is based on modified time reversal algorithm and applies this method for detecting different kinds of defects in thick-walled pipe with large-diameter. The principle of time reversal of circumferential Lamb waves in pipe is presented along with the influence from multiple guided wave modes and propagation paths. Experimental study is carried out in a thick-walled and large-diameter pipe with three artificial defects, namely two axial notches on its inner and outer surface respectively, and a corrosion-like defect on its outer surface. By using the proposed MTRF method, the multichannel signals focus at the defects, leading to the amplitude improvement of the defect scattered signal. Besides, another energy focus arises in the direct signal due to the partial compensation of dispersion and multimode of circumferential Lamb waves, alongside the multichannel focusing, during MTRF process. By taking the direct focus as a time base, accurate defect localization is implemented. Secondly, a new phenomenon is exhibited in this paper that defect scattered wave packet appears just before the right boundary of truncation window after time reversal, and to which two feasible explanations are given. Moreover, this phenomenon can be used as the theoretical basis in the determination of defect scattered waves in time reversal response signal. At last, in order to detect defects without prior knowing their exact position, a large-range truncation window is used in the proposed method. As a result, the experimental operation of MTRF method is simplified and defect detection and localization are well accomplished.