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.     

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.     

Lamb wave mode decomposition using concentric ring and circular piezoelectric transducers

Lamb waves using surface-bonded piezoelectric transducers (PZTs) have been widely used for nondestructive testing (NDT). However, the identification of individual Lamb wave modes and the subsequent data interpretation are often difficult due to the dispersive and multimodal natures of Lamb waves. To tackle the problem, a Lamb wave mode decomposition technique using concentric ring and circular PZTs is proposed. Its advantages over the conventional approaches are that (1) PZTs need to be placed only a single surface of a specimen and (2) mode decomposition can be performed at any desired frequency without changing the PZT size and/or spacing configuration. The proposed mode decomposition technique is formulated by solving 3D Lamb wave propagation equations considering the PZT size and shape, and this technique requires a specially designed dual PZT composed of concentric ring and circular PZTs. The effectiveness of the proposed technique for the Lamb wave mode decomposition is investigated through numerical simulation and experimental tests performed on an aluminum plate.     

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.     

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.     

基于Lamb波频散特性的薄板声发射源定位方法研究

声发射源时差定位方法中波速的确定是定位准确的关键问题,根据模态声发射理论,声发射信号在薄板内的传播过程中具有频散现象和多模态特性.不同频率不同模态的声波其传播速度不同.基于Lamb波频散特性和声发射检测技术,采取时频联合分析方法对铝薄板中声波模式进行识别;利用低频段频散不明显的扩展波的波速和同一频率同一模态波到达两传感器的时间差来实现声发射源的准确定位;通过铝薄板中AE源定位实验表明,采用S0模式,即扩展波的波速进行定位计算,可以比较准确地确定声发射源的位置,而且理论值与实际值相差很小.     

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.     

板背部缺陷的单侧非接触式超声无损检测方法

随着板状结构在石化、航空航天和电力等工业领域中的广泛应用,急需发展相应的无损检测技术,对其结构完整性进行定期评估,以保证结构的安全运行。基于空气耦合换能器的Lamb波技术,可以非接触快速地对板状结构进行扫描,在结构安全检测领域有广阔的应用前景。本文采用基于势函数法的空气耦合板状结构声传播模型,通过理论求解得到其Lamb波临界角随频厚积的变化规律。实验中采取空气耦合换能器激发和接收Lamb波,采用傅里叶变换和信号滤波技术识别S0和A0模式,并通过与理论结果比较进行确认。最后,分别采用S0和A0模式对板背部半通孔缺陷进行定位,结果显示该单侧非接触式超声无损检测方法可用于板状结构背部缺陷的检测。     

基于电磁声激励Lamb波的裂纹深度检测

本文采用电磁声传感器接收单一S₀模态激励,测量Lamb波在板中不同深度的槽形裂纹处的反射与透射,用于对已知扩展长度的表面裂纹进行深度测量。然后分析了Lamb波模态的频散与波动特性,由超声Lamb波的波结构,近似计算了S₀模态入射到裂纹时的反射系数。计算结果与实验结果一致。结果表明,Lamb波在有限长裂纹处的反射系数可采用二维模型中的反射系数求解公式近似求解。采用电磁超声传感器接收单一S₀模态激励,重复测量稳定性高,适用于Lamb波反射系数的测量。Lamb波的反射系数与裂纹深度有很好的对应关系,可用于板表面已知长度裂纹的深度测量。     

Effect of uniaxial stress on the propagation of higher-order Lamb wave modes

On the basis of the non-linear theory of elasticity and the invariant based formulation developed by Ogden, we analyse the effect of homogeneous stress on the propagation of Lamb waves. Using the theory of incremental deformations superimposed on large deformations, we derive the equations governing the propagation of small amplitude waves in a pre-stressed plate. By enforcing traction-free boundary conditions at the surfaces of the plate, we further obtain the characteristic equations for symmetric and anti-symmetric Lamb wave modes and investigate the effect of stress on the phase velocity, i.e. the acoustoelastic effect. A comparison with experimental data exhibits a better correlation than previously published results. The outcomes of this study can be utilised in the development of new techniques for the measurement of applied stresses based on the acoustoelastic effect. In particular, a strong sensitivity of the phase velocity to the applied stress near the cut-off frequencies of higher-order Lamb wave modes is a very promising option, which seems to have been overlooked in previous studies.     

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。     

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.     

板中正交静应力与任意方向兰姆波波速的关系

运用部分波分析法(或子波分析)理论推导了在正交静应力下,板中任意方向的Lamb波的频散方程,给出了任意方向Lamb波波速、正交静应力和频率之间的关系. 进行了数值计算并讨论了对称方向的Lamb波波速对单向静应力的依赖关系,为将Lamb波用于应力测量提供了理论依据.      

基于时间反转法的Lamb波检测技术的研究进展

Lamb波具有传播距离远、衰减小等特点,已被广泛应用于大型板类结构的损伤检测。时间反转是实现超声波聚焦的有效方法之一。本文回顾并总结了近20年来时间反转方法在Lamb波检测领域中的研究进展。针对Lamb波固有的频散和多模态等传播特性,详细论述了时间反转法在板结构Lamb波检测中的应用。最后对基于时间反转法的免基准信号Lamb波损伤检测方法进行了总结,分析其存在的问题并对其应用前景进行了展望。     

板壳结构中的非线性兰姆波

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,井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.     

Effect of a biasing electric field on the propagation of antisymmetric Lamb waves in piezoelectric plates

Based on the theories of anisotropic elasticity, piezoelectricity and elastic waves in solids, the propagation of antisymmetric Lamb waves in a biasing electric field is investigated in this paper. By solving the coupled differential equations of motion under a biasing electric field, the phase velocity equations of antisymmetric Lamb wave modes for electrically open and shorted cases are obtained, respectively. The beating effect arising from the difference between the phase velocity of the zero-order symmetric mode and antisymmetric mode exists in the plate when the plate has a thickness comparable to or slightly larger than the wavelength. The influence of the biasing electric field on the phase velocity, beat wavelength, mechanical displacement and stress fields for the lowest two antisymmetric modes of Lamb waves are discussed in detail. From the calculated results, it is seen that the phase velocity of the fundamental antisymmetric mode is especially sensitive to the applied biasing electric field.     

Lamb mode stresses as means of identifying voids in the adhesive zone of bilaminates

Lamb wave technique has emerged as a reliable tool in the nondestructive testing of laminated plates. Some current studies to identify the specific Lamb modes that can characterize different kinds of defects in layered plates using Lamb waves have shown that the modes for which high stresses and low displacements occur in the interface indicate the presence of defects like pores or voids whereas the modes for which the displacements are high show the presence of harder inclusions. In this context this paper tests an earlier analytical model developed to facilitate NDT of porosity in the adhesive zone of bilaminates.The model tested treats the pore infested thin adhesive region as a linear elastic material with voids (LEMV). For certain parametric values of the LEMV adhesive layer the influence of these voids on dispersion and stresses carried by the first few Lamb modes in glass/glue/glass (G/g/G) bilaminate is traced in the range 0–10 MHz. The frequency–phase velocity points experimentally obtained by Kundu and Maslov are seen to fall very close to the present dispersion. The stresses traced using the present model in G/g/G plate at these experimentally tallied points show an easily discernable rise in the central region of adhesive, as observed by Kundu and Maslov.The model appears to be useful as a good first approximation to detect voids in adhesive zone of composite structural elements.     

Propagation characteristics of thermoelastic waves in piezoelectric (6 mm class) rotating plate

The propagation of Lamb waves in a homogeneous, transversely isotropic (6 mm class), piezothermoelastic plate rotating with uniform angular velocity about normal to its boundary has been investigated. The generalized (non-classical) theories of thermoelasticity in contrast to Sharma and Pal [Sharma, J.N., Pal, M., 2004. Lamb wave propagation in transversely isotropic piezothermoelastic plate. J. Sound Vib. 270, 587–610] have been used to investigate the problem. The surfaces of the plate are subjected to stress free, thermally insulated/isothermal and electrically shorted boundary conditions. Secular equations for wave propagation modes in the plate are derived from a coupled system of governing partial differential equations of linear piezothermoelasticity. After obtaining the complex characteristic roots with the help of Descartes' algorithm, the transcendental secular equations have been solved by functional iteration numerical technique to compute phase velocity and attenuation coefficient. Finally, in order to illustrate the analytical development, numerical solution of secular equations is carried out for PZT-5A piezo-thermoelastic material. The corresponding simulated results of various physical quantities such as phase velocity, attenuation coefficients, specific loss factor of energy dissipation, thermo-mechanical coupling factor and relative frequency shifts have been presented graphically for both rotating and non-rotating plates for comparison purpose. There is a scope for extension of the present work to other classes of piezo/pyroelectric crystals. The study will be useful in design and construction of gyroscope, rotation sensors, temperature sensors and other pyro/piezoelectric surface acoustic wave (SAW) devices.     

偏压电场对压电板中Lamb波相速度的影响

本文研究了偏压电场作用下,Lamb波在压电板中的传播行为，首先给出了偏压电场作用时压电板中的应力场及电位移场，然后通过求解含初应力及初电位移的小幅波动问题的耦合方程，分别给出了Lamb波的对称模态和反对称模态的相速度方程，以典型的PZT－5H压电陶瓷板为例进行了数值计算,并讨论了偏压电场对Lamb波相速度及频散曲线的影响，结果表明，偏压电场可以显著地改变Lamb波的传播速度，借此可使声波器件获得延时效果。     

MEASUREMENT AND ANALYSIS OF LASER GENERATED RAYLEIGH AND LAMB WAVES CONSIDERING ITS PULSE DURATION

In this article, laser generated Rayleigh and Lamb waves are studied by taking into account its pulse duration. The physical model and theoretical solution are presented to predict the corresponding waveforms for aluminum samples under the ablation generation regime.The waveforms of the excited Rayleigh and Lamb waves by laser with selected pulse duration were measured by laser interferometer and analyzed theoretically, and the agreement between measurement and analysis is demonstrated for the validation of the theoretical model and solution.The broadening of the Rayleigh wave and the disappearing of high order Lamb wave modes can be found with the increase of the pulse duration by the laser ultrasonic technique.