Use of parabolic reflector to amplify in-air signals generated during impact-echo testing

The impact-echo method is a commonly used nondestructive testing technique for elastic plates in civil engineering. The impact-echo mode corresponds to the frequency at zero group velocity of S(1) Lamb mode. Recent development of the air-coupled impact-echo (ACIE) method introduces the possibility for rapid scanning of large structures and increases the practicality of in situ measurements. However, sensors used in ACIE are susceptible to ambient noise, which complicates in situ ACIE measurements. This letter presents the results of ACIE measurements taken using a parabolic reflector together with standard measurement microphones to increase the signal to noise ratio for ACIE measurements. The signal gain and effects of sensor location with respect to impact location are discussed.     

Elastic constants of a plate from impact-echo resonance and Rayleigh wave velocity

A new method is proposed for calculating the dynamic elastic constants of an isotropic plate from measurements of the impact-echo resonance and Rayleigh wave velocity. Poisson's ratio is shown to be a single-valued function of the ratio between thickness frequency and Rayleigh wave velocity. This dependence is derived theoretically from the condition of resonance at the minimum frequency of the first-order symmetric Lamb mode. A finite element model is developed to determine how this frequency varies with Poisson's ratio. The results obtained by modal analysis and the power-spectral density technique are in good agreement with those calculated as the solution of the S1 Lamb mode equation. The method is verified by impact-echo tests on concrete and methacrylate plates. A laser interferometer is used to detect the vibration. Thickness frequencies are accurately identified by applying the multicross-spectral density to the signals detected at several points close to the impact point. In a separate experiment, Rayleigh waves are generated by the mediator technique. The wave velocities are determined from the arrival times of the surface wave at several points. Finally, the main sources of uncertainty are evaluated.     

Edge resonance and zero group velocity Lamb modes in a free elastic plate

The local resonances of a free isotropic elastic plate are investigated using laser ultrasonic techniques. Experimental results are interpreted in terms of zero group velocity Lamb modes and edge mode. At a distance from the edge larger than the plate thickness a sharp resonance is observed at the frequency where the group velocity of the first symmetrical Lamb mode vanishes. Close to the edge of the plate, the resonance due to the edge mode dominates. Both zero group velocity and edge resonances appear at the theoretically predicted frequencies. These frequencies do not vary with the distance from the edge of the plate and the transition between the two modes of vibration, at about the plate thickness, is abrupt. Using a laser excitation on the edge, the amplitude profile of the normal displacement at the edge resonance frequency was determined.     

Three-dimensional hybrid model for predicting air-coupled generation of guided waves in composite material plates

For contact-less, non-destructive testing (NDT) purposes using air-coupled ultrasonic transducers, it is often required to numerically simulate the propagation of ultrasonic waves in solid media, and their coupling through air with specific transducers. At that point, one could simulate the propagation in the air and then in the solid component, using a Finite Element (FE) model. However, when three-dimensional (3D) modeling becomes necessary, such a solution reveals to be extremely demanding in terms of number of degrees of freedom and computational time. In this paper, to avoid such difficulties, the propagation in air from an ultrasonic transmitter to a tested solid plate is modeled in 3D using a closed-form solution. The knowledge of the transducer characteristics (diameter, frequency bandwidth, efficiency in Pa/V) allows the spatial distribution and actual pressure (in Pa) of the acoustic field produced in the air to be predicted, for a given input voltage. This pressure field is applied in turn as a boundary condition in a 3D FE model, to predict the plate response (displacement and stress guided beams) for a given distance between the transmitter and the plate, and for a given angle of orientation of the transmitter with respect to the plate. The FE model is so restricted to modeling of the solid structure only, thus reducing very significantly the number of degrees of freedom and computational time. The material constituting the plate is considered to be an anisotropic and viscoelastic medium. To validate the whole modeling process, an air-coupled ultrasonic transducer is used and oriented at a specific angle chosen for generating one specific Lamb mode guided along a composite plate sample, and a laser probe measures the normal velocity at different locations on the surface of the plate. In the field of NDT, it is generally suitable to excite a pure Lamb mode in order to ease the interpretation of received signals that would represent waves scattered by defects. After a validation step, the numerical model is then used to investigate the effect of the material anisotropy on the purity of the incident guided mode.     

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。     

Guided waves propagating in sandwich structures made of anisotropic,viscoelastic, composite materials

The propagation of Lamb-like waves in sandwich plates made of anisotropic and viscoelastic material layers is studied. A semi-analytical model is described and used for predicting the dispersion curves (phase velocity, energy velocity, and complex wave-number) and the through-thickness distribution fields (displacement, stress, and energy flow). Guided modes propagating along a test-sandwich plate are shown to be quite different than classical Lamb modes, because this structure does not have the mirror symmetry, contrary to most of composite material plates. Moreover, the viscoelastic material properties imply complex roots of the dispersion equation to be found that lead to connections between some of the dispersion curves, meaning that some of the modes get coupled together. Gradual variation from zero to nominal values of the imaginary parts of the viscoelastic moduli shows that the mode coupling depends on the level of material viscoelasticity, except for one particular case where this phenomenon exists whether the medium is viscoelastic or not. The model is used to quantify the sensitivity of both the dispersion curves and the through-thickness mode shapes to the level of material viscoelasticity, and to physically explain the mode-coupling phenomenon. Finite element software is also used to confirm results obtained for the purely elastic structure. Finally, experiments are made using ultrasonic, air-coupled transducers for generating and detecting guided modes in the test-sandwich structure. The mode-coupling phenomenon is then confirmed, and the potential of the air-coupled system for developing single-sided, contactless, NDT applications of such structures is discussed.     

First and second order phase transitions in gauge theories at finite temperature

We consider in general the nature of the phase transition which occurs in 4D gauge theories coupled to scalar and spinor fields at finite temperature. It is shown that the critical behavior can be isolated in an effective 3D theory of the zero frequency mode whose lagrangian may be calculated explicitly in weak coupling perturbation theory. This lagrangian, in turn, may be investigated by means of standard ?-expansion techniques. Theories with an asymptotically free gauge coupling constant possess no stable fixed point in the ?-expansion and are inferred to have weakly first-order phase transitions; theories not satisfying this condition may have second-order transitions.     

Mode spectrum of noncollinear electroacoustic boundary-guided waves in a ferroelectric with a moving strip domain

The mode spectrum of electroacoustic boundary waves guided by a strip domain uniformly moving in a 4-mm ferroelectric is considered in the quasi-static approximation. The motion of the strip domain is found to cause the wave vector of the electroacoustic wave to be noncollinear with the guiding boundaries. The frequency dependences of the phase velocity are presented for the symmetric and antisymmetric modes of the electroacoustic wave. These dependences are compared in the reference system fixed to the strip domain and in the laboratory reference system. It is shown that, at low and moderate frequencies, the symmetric mode of the electroacoustic wave is more efficiently localized by a moving strip domain than by a single domain wall.     

Lamb waves beam deviation due to small inclination of the test structure in air-coupled ultrasonic NDT

In Lamb waves inspection, an air-coupled transmitter transducer is oriented at a specific angle such that it generates a pure Lamb mode which propagates along the structure and interacts with any existing defects. For this inspection system, amplitude losses appears when small inclinations of the tested structure occurs. An important factor which affects directly these losses has been observed, it consists of the Lamb waves beam (LWB) deviation due to this bad alignment. In this work, a simple expression of LWB deviation has been deduced. This expression includes the test structure angle, phase velocity of generated Lamb mode, and the phase velocity of waves propagating in the coupled medium. A(0) Lamb mode is generated and detected in 1 mm thick aluminium plate sample using 1 MHz PZ27 piezoelectric transducers of 20 mm of diameter. Experimental LWB deviation angles are measured for different inclination angles of the test sample. A comparative study is released with theoretical results. For 1 degree of misalignment in the aluminium plate inclination, and transducers separation distance of 35 mm, LWB deviation angle is around 7 degrees and the amplitude is reduced by around 11%. Then, for a large separation distance, we must move the receiver transducer to detect the deviated LWB. It is shown that, for both theoretical and experimental studies, the LWB deviation and its measured amplitude are very sensitive to the alignment of the tested structure with respect to the transmitter-receiver transducers plane. In metal plates it is most satisfactory to use A(0) mode compared with S(0) mode since it is easy to excite and has a large amplitude and small deviation beam angles.     

The frequency width of symmetric modes of an aluminum plate: manifestation of a complex slowness on a frequency spectrum

The evolution of the experimental frequency width of symmetric modes of an aluminum plate is studied as a function of the angle of incidence below the first critical angle. It is found that the frequency width predicted by resonant scattering theory, corrected for the directivity of emitter and receiver, generally explains the experimental frequency width well. However, large discrepancies remain for the frequency width of the S1 mode at angles of incidence larger than 9 degrees. It is demonstrated that these are caused by not taking into account the complex nature of the slowness of the plate mode. This suggests that there is a need for a theory that models the interaction of a beam of ultrasound, bounded in space and time, with an elastic plate.     

Modulation instability of wave packets in the presence of linear and nonlinear mode coupling

Conditions for modulation instability of a wave packet consisting of two codirected linearly coupled waves propagating in a light guide with Kerr-type nonlinearity are formulated. The development of the instability with regard to light guide parameters, linear and nonlinear mode coupling, and input power is analyzed for symmetric and antisymmetric light guide excitations. Unlike in single-mode light guides, here modulation instability may arise in the frequency ranges of normal material dispersion and at the zero perturbation frequency.     

Application of the laser generated focused-Lamb wave for non-contact imaging of defects in plate

The laser generation method of focused-Lamb wave is expected to have high defect-detection ability with advantages of non-contact testing. In this method, the laser beam is illuminated on the surface of the object through an arrayed-arc slit, and then the energy of the generated Lamb wave is concentrated on the focus point of arc. This focusing effect enables the concentration of higher wave intensity on the focus with better S/N ratio of signal, and has better spatial resolution compared to the conventional line arrayed method. This paper describes a 2-D imaging system using this laser generated, focused-Lamb wave combined with its detection by the air-coupled transducer. This technique is fully non-contact so it can be easily applied for the automatic inspection. The effectiveness of the proposed method was verified by experiments on a 1-mm thick aluminum plate with artificial drill-hole defect with diameters of 1mm. The 2-D image of was constructed by scanning and the result showed that the location and size of defects were clearly detected.     

Negative group velocity Lamb waves on plates and applications to the scattering of sound by shells

Symmetric Lamb waves on plates exhibit anomalies for certain regions of frequency. The phase velocity appears to be double-valued [M. F. Werby and H. Uberall, J. Acoust. Soc. Am. 111, 2686-2691 (2002)] with one of the branches having a negative group velocity relative to the corresponding phase velocity. The classification of the symmetric plate modes for frequencies appearing to have a double-valued phase velocity is reviewed here. The complication of a double-valued velocity is avoided by examining mode orthogonality and the complex wave-number spectra. Various authors have noted an enhancement in the backscattering of sound by elastic shells in water that occurs for frequencies where symmetric leaky Lamb waves (generalized to case of a shell) have contra-directed group and phase velocities. The ray diagram for negative group velocity contributions to the scattering by shells [G. Kaduchak, D. H. Hughes, and P. L. Marston, J. Acoust. Soc. Am. 96, 3704-3714 (1994)] is unusual since for this type of mode the energy on the shell flows in the opposite direction of the wave vector. Circumnavigation of the shell is not required for the leaky ray to be backward directed.     

分层固体板中导波的激发与频散特性

针对无限大弹性分层固体板,研究了结构中导波的频散和激发特性。首先使用传递矩阵法推导分层板模型中导波的频散方程,然后用二分法求取导波各模式的频散曲线,进而分析结构中导波的频散特性。结果表明:在速度递增或递减的分层板中,基阶模式和高阶模式的高频极限分别等于低速层的瑞利波速和横波波速。对于含低速夹层的分层板,所有模式的高频极限都等于低速层的横波速度。在导波激发特性方面,研究了在具有一定宽度的法向力源作用下的分层板中导波各模式在结构中的法向位移谱。发现在速度递增的分层板结构中基阶模式是主导模式,而对于速度递减和含低速夹层模型,主导模式在不同的频段范围内对应不同的导波模式。      

Investigation of acoustic waves of higher order propagating in plates of lithium niobate

This paper presents theoretical investigation of higher order acoustic plate waves propagating in single crystals of lithium niobate. The dependencies of wave velocity and electromechanical coupling coefficient of antisymmetric, symmetric, and shear horizontal modes on the parameter hf (h=plate thickness, f=operating frequency) are calculated as a function of propagation direction on X-, Y-, and Z-cut lithium niobate plates. It is found that several modes can provide values of K2 that are much greater than can be obtained with surface acoustic waves (SAWs). For example, K2 as high as 0.26 and 0.38 can be obtained from SH1 and A2 modes, respectively. This compares with a maximum value of K2=0.055 for SAWs. It is further shown that there are several crystal cut and propagation directions that can allow efficient excitation and detection of a single mode with minimal interference due to other modes.     

Review of air-coupled ultrasonic materials characterization

This article presents a review of air-coupled ultrasonics employed in the characterization or nondestructive inspection of industrial materials. Developments in air-coupled transduction and electronics are briefly treated, although the emphasis here is on methods of characterization and inspection, and in overcoming limitations inherent in the use of such a tenuous sound coupling medium as air. The role of Lamb waves in plate characterization is covered, including the use of air-coupled acoustic beams to measure the elastic and/or viscoelastic properties of a material. Air-coupled acoustic detection, when other methods are employed to generate high-amplitude sound beams is also reviewed. Applications to civil engineering, acoustic tomography, and the characterization of both paper and wood are dealt with here. A brief summary of developments in air-coupled acoustic arrays and the application of air-coupled methods in nonlinear ultrasonics complete the review. In particular, the work of Professor Bernard Hosten and his collaborators at Bordeaux is carefully examined.     

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.     

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.     

基于空耦超声Lamb波的金属板状结构内部缺陷检测方法

针对接触式超声检测方法在金属板结构内部缺陷实际工程检测中存在的环境要求高、效率低、操作难度高等问题,提出了空耦超声Lamb波检测方法,该方法能更好地适应现场应用环境,提高检测效率,减少传感器数量。通过有限元仿真和实验分析比较了空耦超声检测与接触式超声检测两种方法接收到的信号和成像效果。结果表明:有限元仿真和实验中,空耦超声检测方法对缺陷位置的定位误差分别为2 mm和3.6 mm,接触式检测方法对缺陷位置的定位误差分别为2 mm和11.3 mm,空耦检测具有较高的定位精度;单侧激励条件下,适合采用A0模态Lamb波对板内缺陷进行检测;空耦超声检测可以通过调整信号接收角度接收单一模态Lamb波,避免伪像产生。该方法为后续金属板状结构内部缺陷的空耦超声检测提供参考。     

The interaction of the S0 Lamb mode with vertical cracks in an aluminium plate

This article presents the interaction of the first symmetric Lamb mode S0 with vertical cracks in an aluminium plate placed in vacuum. The cracks are symmetrical regarding to the median plane of the plate and their heights are increasing from 0% to 100% of the plate thickness, by steps of 25%. The frequency-thickness product is chosen to be lower than the S1 frequency cut-off. A modal decomposition method is used to solve the diffraction problem. The variation with the height of the crack of the reflection and transmission coefficients of modes propagating in the far field is predicted. The displacement fields at both sides of the cracks are also calculated, so that it is possible to quantify the crack-opening displacement. These results are compared to numerical predictions obtained using a finite element software. Measurements are also conducted and compared to the predictions.