Transmission analysis of ultrasonic Lamb mode conversion in a plate with partial-thickness notch

Mode conversions of Lamb waves can occur upon encountering damage or defect such as a notch, leading to newly-converted modes apart from wave reflection and transmission. In this paper, the transmission of the fundamental Lamb modes symmetrical S0 and anti-symmetrical A0 with anti-symmetrical notches were investigated in steel plates within the relatively short propagation distance. The group velocity and modal energy of the converted modes were analyzed using simulations and experiments. Two-dimensional finite difference time domain (2D-FDTD) method was employed to calculate the scattering field and extract numerical trends for simulation study and experimental confirmation. Both simulations and experiments revealed that the apparent group velocities of the converted modes in the transmitted signals subject to the notch positions. To describe the mode conversion degree and evaluate the notch severity, wave packets of the originally-transmitted modes and newly-converted modes were separated and corresponding mode energy percentages were analyzed at different notch severities. Frequency-sweeping measurements illustrated that the modal energy percentages varied monotonically over the notch-depth increase with a statistically consistency (R = 1.00, P < 0.0004).     

A laser beam deflection technique for the quantitative detection of ultrasonic Lamb waves

Ultrasonic Lamb waves have been measured with a quantitative optical beam deflection (OBD) technique. Calibration of the technique is derived for two cases of laser probe beam cross-section, one with a uniform beam and the other with a Gaussian beam intensity distribution. Expressions for angular beam deflection angle are derived for both cases in terms of the total light intensity falling on the photodetector, assumed to have a square-law voltage response. Using a Gaussian beam intensity distribution from a HeNe laser, the OBD measurements were compared with those from a Michelson interferometer to show that measurements were self-consistent.     

Experimental study of the A0 and S0 Lamb waves interaction with symmetrical notches

The aim of this work is to study the fundamental Lamb modes interaction with defects in isotropic plates. For these experimental investigations, symmetrical notches with various depths milled in aluminum plates are considered. Moreover, the incident Lamb wave of a specific mode is generated by means of two identical thin piezoceramic transducers placed at the opposite sides of the plate. The waves scattered by the notch are recorded with conventional transducers located on the plate surface in front and behind the defect. The selection of the A₀ or the S₀ modes is obtained by exciting the transducers with anti-phased or in-phased signals, respectively. Furthermore, a calibration process is investigated to correct errors caused by the presence of the receiver between the emitters and the defects. The power reflection and transmission coefficients are then obtained and the power balance is verified. Finally, these measurements are compared successfully with those obtained by a numerical method using the finite-element modeling described in a previous work.     

Liquid level sensor using ultrasonic Lamb waves

This paper describes a novel, noninvasive method for measurement of liquid level in closed metal tanks that are under high pressure. It is based on the use of ultrasonic Lamb waves propagating along the tank wall. Contact with liquid substantially changes the characteristics of these waves and this can be used as an indicator of liquid presence. Theoretical analysis shows that the symmetric and antisymmetric Lamb wave modes, both fundamental and higher order, are sensitive to presence of the liquid. The optimal wave frequency depends on the thickness of the tank wall and wall material. A prototype level sensor based on this principle has been developed. It uses two pairs of wedge transducers to generate and detect Lamb waves propagating along the circumference of the gas tank. An operating frequency of 100 kHz is found to be optimal for use with tanks having a wall thickness of 30-50 mm. Prototype sensors developed under this program have been used successfully in oil fields in the far northern region of Russia.     

Wideband low frequency generation and detection of Lamb and Rayleigh waves using electromagnetic acoustic transducers (EMATs)

This paper describes a new type of non-contact electromagnetic transducer (EMAT) that can be used to generate both Lamb and Rayleigh waves on metal samples. The generated waves are wideband and low frequency with a dominant frequency content centred at approximately 200 kHz extending to around 500 kHz. The transducers have been used on both aluminium and steel, but operate more efficiently on aluminium due to its lower electrical resistance and density when compared to steel.     

Cumulative second-harmonic analysis of ultrasonic Lamb waves for ageing behavior study of modified-HP austenite steel

The cumulative second-harmonic analysis of ultrasonic Lamb wave has been performed to study the precipitation kinetics and microvoid initiation of ferritic Cr–Ni alloy steel during the ageing process. Ageing of ferritic Cr–Ni alloy materials have been done at 1223 K and 1173 K for different degradation time intervals and air cooled. The results show that the normalized acoustic nonlinearity of Lamb wave increases with the formation of fine precipitates at the early stage of ageing till about 1000 h and keeps as a plateau with the precipitates dynamic balance for a long-term ageing, and then decreases gradually at the final holding time with the coarsening of precipitates and initiation of microvoids. The results also show that the variation of nonlinear Lamb wave follows the same trend as that of hardness in materials. Therefore, the cumulative second-harmonic of ultrasonic Lamb waves has been found to be strongly sensitive to the precipitates behavior and microstructure evolution during the thermal ageing of ferritic Cr–Ni alloy steel.     

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。     

A feasibility study of the use of bounded beams resembling the shape of evanescent and inhomogeneous waves

Plane waves are solutions of the visco-elastic wave equation. Their wave vector can be real for homogeneous plane waves or complex for inhomogeneous and evanescent plane waves. Although interesting from a theoretical point of view, complex wave vectors normally only emerge naturally when propagation or scattering is studied of sound under the appearance of damping effects. Because of the particular behavior of inhomogeneous and evanescent waves and their estimated efficiency for surface wave generation, bounded beams, experimentally mimicking their infinite counterparts similar to (wide) Gaussian beams imitating infinite harmonic plane waves, are of special interest in this report. The study describes the behavior of bounded inhomogeneous and bounded evanescent waves in terms of amplitude and phase distribution as well as energy flow direction. The outcome is of importance to the applicability of bounded inhomogeneous ultrasonic waves for nondestructive testing.     

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.     

The attenuation of Lamb waves in the presence of a fluid

When a plate bearing a Lamb wave is in contact with a fluid the wave is attenuated. This report presents a relatively simple model for calculating attention. The validity of the approach is established by comparison of calculated results and measurements.     

兰姆波在搭接焊缝上的反射和透射

采用数值模拟方法和实验研究了兰姆波在搭接焊缝上的反射和透射。数值模拟了频率500 kHz的兰姆波S0与.A0模态,分别在2 mm厚不锈钢板上的不同宽度搭接焊缝模型上的反射和透射,并计算了相应的反射系数和透射系数。发现:当搭接焊缝宽度小于4 mm时,S0模态的反射系数和焊缝宽度具有近似的线性关系,而焊缝余高和两板之间的间隙对S0模态反射系数的影响很小。基于兰姆波S0模态反射系数与焊缝宽度的线性关系。提出了通过测量S0模态反射系数快速测量搭接焊缝宽度的方法。实验测得的2 mm厚不锈钢板上不同宽度搭接焊缝对500 kHz的入射兰姆波S0模态的反射系数,验证了上述线性关系,说明了可用兰姆波反射回波测量搭接焊缝宽度。     

Time reversal technique for health monitoring of metallic structure using Lamb waves

Time reversal active sensing using Lamb waves is investigated for health monitoring of a metallic structure. Experiments were conducted on an aluminum plate to study the time reversal behavior of A₀ and S₀ Lamb wave modes under narrow band and broad band pulse excitation. Damage in the form of a notch was introduced in the plate to study the changes in the characteristics of the time reversed Lamb wave modes experimentally. Time–frequency analysis of the time reversed signal was carried out to extract the damage information. A measure of damage based on wavelet transform was derived to quantify the hidden damage information in the time reversed signal. It has been shown that time reversal can be used to achieve temporal recompression of Lamb waves under broadband signal excitation. Further, the broad band excitation can also improve the resolution of the technique in detecting closely located defects. This is demonstrated by picking up the reflection of waves from the edge of the plate, from a defect close to the edge of the plate and from defects located near to each other. This study shows the effectiveness of Lamb wave time reversal for temporal recompression of dispersive Lamb waves for damage detection in health monitoring applications.     

Interaction of Rayleigh waves with a rib attached to a plate

An analysis of the interaction of a pulse of Rayleigh waves on a plate with a rectangular flange or rib attached in the far field of its acoustic emission (AE) source is presented. A finite difference (FD) model is used to give numerical visualizations of the development of the complete wave-field propagating through the structure and also to give displacement data for selected points. An ‘energy partition model’, for Rayleigh wave propagation across the rib has been developed and is described. Ray theory wave arrival time calculations are given for the propagation of various mode-converted components transmitted across the flange. A series of experimental measurements of AE wave propagation across a T-butt welded rib on a plate were made and these are compared with the model predictions. The practical implications of these findings for acoustic emission monitoring of large structures of complex shape are discussed.     

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.     

Propagation of Lamb waves in an immersed periodically grooved plate: Experimental detection of the scattered converted backward waves

Guided waves propagation in immersed plates with irregular surfaces has potential application to detection and assessment of the extent, depth and pattern of the irregularity. The complexity of the problem, due to the large number of involved parameters, has limited the number of existing studies. The simplest case of irregularities of practical interest is the two-dimensional corrosion profile. Even this case is in general so complex, that one can extract several amplitude dominant periodic surfaces only by using a Fourier spectrum of the surface. Guided waves in plates, with one or both free surfaces having periodic perturbations of different shapes, have been presented in specialized literature.     

Active fiber composites for the generation of Lamb waves

Active fiber composites (AFC) are thin and conformable transducer elements with orthotropic material properties, since they are made of one layer of piezoelectric ceramic fibers. They are suitable for applications in structural health monitoring systems (SHM) with acoustic non-destructive testing methods (NDT). In the presented work the transfer behavior of an AFC as an emitter of transient elastic waves in plate-like structures is investigated. The wave field emitted by an AFC surface bonded on an isotropic plate was simulated with the finite-difference method. The model includes the piezoelectric element and the plate and allows the simulation of the elastic wave propagation. For comparison with the model experiments using a laser interferometer for non-contact measurements of particle velocities at different points around the AFC on the surface of the plate were performed. Transfer functions defined as the ratio of the electric voltage excitation signal and the resulting surface velocity at a specific point are separately determined for the two fundamental Lamb wave modes. In order to take the orthotropic behavior of the AFC into account the transfer functions are determined for several points around the AFC. Results show that the AFC is capable to excite the fundamental symmetric and antisymmetric Lamb wave mode. The antisymmetric mode is mainly radiated in the direction of the piezoelectric fibers, while the symmetric mode is spread over a larger angle. The amplitudes of the emitted waves depend on the frequency of the excitation as well as on the geometric dimensions of the transducer.     

Air-coupled detection of nonlinear Rayleigh surface waves to assess material nonlinearity

This research presents a new technique for nonlinear Rayleigh surface wave measurements that uses a non-contact, air-coupled ultrasonic transducer; this receiver is less dependent on surface conditions than laser-based detection, and is much more accurate and efficient than detection with a contact wedge transducer. A viable experimental setup is presented that enables the robust, non-contact measurement of nonlinear Rayleigh surface waves over a range of propagation distances. The relative nonlinearity parameter is obtained as the slope of the normalized second harmonic amplitudes plotted versus propagation distance. This experimental setup is then used to assess the relative nonlinearity parameters of two aluminum alloy specimens (Al 2024-T351 and Al 7075-T651). These results demonstrate the effectiveness of the proposed technique – the average standard deviation of the normalized second harmonic amplitudes, measured at locations along the propagation path, is below 2%. Experimental validation is provided by a comparison of the ratio of the measured nonlinearity parameters of these specimens with ratios from the absolute nonlinearity parameters for the same materials measured by capacitive detection of nonlinear longitudinal waves.     

Lamb waves in phononic crystal slabs: truncated plane parallels to the axis of periodicity

A theoretical study is presented on the propagation properties of Lamb wave modes in phononic crystal slabs consisting of a row or more of parallel square cylinders placed periodically in the host material. The surfaces of the slabs are parallel to the axis of periodicity. The dispersion curves of Lamb wave modes are calculated based on the supercell method. The finite element method is employed to calculate the band structures and the transmission power spectra, which are in good agreement with the results by the supercell method. We also have found that the dispersion curves of Lamb waves are strongly dependent on the crystal termination, which is the position of the cut plane through the square cylinders. There exist complete or incomplete (truncated) layers of square cylinders with the change of the crystal termination. The influence of the crystal termination on the band gaps of Lamb wave modes is analyzed by numerical simulations. The variation of the crystal termination leads to obvious changes in the dispersion curves of the Lamb waves and the widths of the band gaps.     

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.     

Analysis of multiple wavelengths of Lamb waves generated by meander-line coil EMATs

The electromagnetic acoustic transducers (EMATs) with a meander-line coil possess the capability of generating Lamb waves carrying multiple wavelengths, and the characteristics of multiple wavelengths is analyzed by developing a spatial transversal filter model for the EMAT. It is shown that the characteristics is due to the wavelength spectrum of the EMATs, which is a wavelength-domain representation of information about the wavelength components, and the magnitude of each components is modulated by an envelope which depends on the geometric pattern of the meander-line coil. The characteristics of multiple wavelengths might cause the multi-modes phenomenon, therefore a method for removing the effect of multiple wavelengths is proposed. It is shown that the effect can be removed by designing an EMAT which can produce a special envelop to suppress the harmonic wavelengths. Experiments are set up to study the characteristics of multiple wavelengths and verify the validity of the proposed method.