A0 Lamb Wave Research Articles

Investigation of Lamb wave modes recognition and acoustic emission source localization for steel plate based on golden jackal optimization VMD parameters and CWT

Accurate identification of Lamb wave modes in acoustic emission(AE) signals propagating on steel plates is crucial for precise source localization. In this paper, we propose a novel method that optimizes variational mode decomposition(VMD) parameters using golden jackal optimization(GJO) and identifies Lamb wave modes on steel plates through continuous wavelet transform(CWT). The Hsu-Nielsen source(HNS) is employed as the AE source. The minimum permutation entropy of the AE signal is used as the optimization objective, with GJO adaptively determining the optimal mode number (K) and penalty factor (α) for VMD. The maximum correlation coefficient method is applied to reconstruct the AE waveform, and both A0 and S0 Lamb wave modes are identified in the wavelet time–frequency domain using CWT. Furthermore, an AE source localization algorithm based on the time difference of arrival and the geometric relationship between two sensors is developed, utilizing the group velocity of the S0 mode. The proposed method effectively identifies acoustic wave modes, achieving an average relative localization error of approximately 0.48% for HNS.

Anomalous wavefront control of Lamb wave with metasurfaces via superposed prism resonance

As a special branch of metamaterials characterized by phase discontinuity, elastic metasurfaces have presented extraordinary capacity for elastic wave manipulation. This class of metamaterials has received extensive attention in recent years. In this paper, a subwavelength elastic metasurface with locally resonant prisms is employed to steer the propagation of the A0 Lamb wave. Based on the dispersion curve and transmission ratio, we establish that the resonant feature of prisms is influenced by the diagonal ratio of cross section. By gradually tuning the diagonal ratio of prism cross section, the pattern of resonance modes and the mechanism of resonance superposition are clarified. In this regard, two different resonant modes can be superimposed at a certain frequency. A complete 2 π phase shift that is crucial for redirecting wave propagation can therefore be realized. To have a broader working frequency range, the influence of prism height on the resonance superposed frequency and the effect of plate thickness on the incident flexural wave are explored. Based on the generalized Snell’s law, negative refraction is verified numerically through a metasurface assembled from unit cells with constant phase change. In addition, other wavefront modulations such as eccentric focusing, nonparaxial propagation are also demonstrated. This novel design introduces new degrees of freedom in many engineering applications such as seismic wave protection, structural health monitoring and energy harvesting.

A frequency steerable electromagnetic acoustic transducer

Abstract Electromagnetic acoustic transducers (EMATs) are convenient for non-destructive evaluation of plate-like structures since they can generate, without the need for contact with the medium under test, different types of ultrasonic guided waves. Guided-wave EMATs usually generate waves omnidirectionally or in a principal propagation direction. Beam steering is desirable in several applications, such as in inspections of large-area structures. This is usually achieved with several independently controlled elements forming a phased array. Alternatively, mono-element transducers with directional-dependent spectral content can steer the generated wave beam by altering the frequency of the excitation signal. A piezoelectric transducer with this characteristic, namely a frequency steerable acoustic transducer, was previously proposed. Its design was addressed in the wavenumber domain, leading to unconventional transducer shapes, but still reproducible with a piezoelectric patch, albeit unfeasible to implement as an EMAT. Here, we propose a new kind of EMAT, namely, frequency steerable EMAT (FSEMAT), whose design is addressed in the spatial domain in order to ensure its physical realization with a coil-magnet arrangement whilst still effectively presenting steering capability. The novel EMAT was designed to generate the A 0 Lamb wave mode in a frequency range from approximately 100 to 600 kHz. The FSEMAT was fabricated and experimentally evaluated in an aluminium plate at different frequencies within the designed frequency range, where each frequency corresponded to a specific propagating direction with high directivity, assessed by half-power beam widths of approximately 10 degrees. Furthermore, its theoretical directivity was computed by means of a wavenumber spectrum-based model, and showed good agreement with experimental results. The new transducer allows great flexibility effectively providing beam steering with a single EMAT.

On the cutoff, reappearance, and persistence of subsonic leaky A0 Lamb waves

Abstract Subsonic leaky A0 Lamb waves, whose phase speeds are lower than the fluid’s sound speed, exhibit several peculiar behaviours. In this work, we investigate three such behaviours: Cutoff, where the A0 branch cuts off at some point in the subsonic domain, reappearance, where the cut-off A0 branch reappears at lower frequencies, and persistence, where the A0 branch is never cut off at all. From the literature, we take the case of a 1 mm thick aluminium plate immersed in air of varying density. We then analyse its exact leaky A0 wave solutions by means of a sound radiation model that takes energy conservation into account. This analysis explains these peculiar behaviours by connecting them with the conditions that allow sound-radiating subsonic leaky A0 Lamb waves.

Guided Ultrasonic Wave Monitoring of Damage in Anisotropic Composites

Lightweight, carbon fibre reinforced composites are often employed for the manufacture of aerospace components due to their good strength to weight ratio. However, due to poor interlaminar strength, composite components are prone to barely visible impact damage, caused by low velocity impacts, during aircraft operation. Guided-wave-based structural health monitoring (SHM) techniques, using a network of distributed sensors, is an important Structural Health Monitoring (SHM) tool for the detection and localization of in-service impact damage in composite structures. However, the material anisotropy of composite laminates influences guided wave propagation and scattering. These anisotropic effects, if unaccounted for, could lead to inaccurate localization of damage, and potential regions of the structure where guided waves cannot propagate with sufficient amplitude, reducing damage sensitivity. Defect characterization can be improved by considering the scattering characteristics of various damage types for the sparse array signal processing. Guided wave scattering (A0 Lamb wave mode) was investigated around an artificial insert delamination in a quasi-isotropic CFRP panel. Permanent magnets, mounted on an undamaged region of the plate, were also used as scattering targets and compared to the delamination case. Full 3D Finite Element (FE) simulations were performed for both the delamination and magnet cases and compared to wavefield data obtained from non-contact laser Doppler vibrometer (LDV) measurements. Individual ply layers were modelled using unidirectional composite material properties to accurately capture the anisotropy effects. Good agreement was found between the experimental measurements and simulations. Scattered guided wave amplitudes around each damage type show strong directional dependency with energy focusing along the fiber directions of the outer ply layers of the laminate. Distinct scattering behavior was observed for each damage type. Implications of anisotropy and angular scattering on sparse array SHM of different defect types are discussed.

A guided wave propagation method for delamination detection in fiber-metal laminates

This study aimed to assess the delamination detection in FMLs via the finite element (FE) simulations of Lamb wave propagation. An FE model of an FML specimen with [Al/902/Al/902/Al] layup was developed. Delamination damage of 10 and 25 mm diameters was induced between different layers of the FML specimen. The fundamental antisymmetric Lamb wave mode (A0) at 60 kHz and the fundamental symmetric Lamb wave mode (S0) at the frequency of 206 kHz were propagated on the developed FE models. The Lamb wave phase velocity was obtained from the FE models and compared with those obtained from the Lamb wave propagation tests. The sensitivity of the A0 and S0 Lamb wave modes to the delamination and its diameter were examined. The inverse Lamb wave propagation problem was then solved, and the elastic modulus of the FML specimen was estimated in the intact and delamination regions. It was observed that the phase velocity of the S0 Lamb wave mode had a higher sensitivity to the delamination damage compared to that of the A0 Lamb wave mode. The phase velocity of the A0 Lamb wave mode was more sensitive to the delamination diameter. The capability of the proposed simulated Lamb wave propagation method as a virtual lab for detecting delamination in the FMLs was confirmed.

Thermal stress estimation of a constrained metallic plate using symmetric and antisymmetric Lamb wave group velocities

This paper presents a technique for estimating thermal-induced stress in constrained metallic plates using the group velocity of Lamb waves, the accuracy of which is crucial for assessing the structural integrity and serviceability of metallic structures. However, without the ability to gauge the current stress levels, obtaining such measurements is technically challenging. To overcome this, we propose a thermal stress estimation technique that uses changes in the group velocities of the fundamental symmetric (S0) and antisymmetric (A0) Lamb wave modes caused by thermal and stress variations. First, this study introduces a theoretical-based zero-crossing algorithm to measure the group velocities of S0 and A0 Lamb wave modes. Next, leveraging the acoustoelastic coefficients corresponding to the S0 and A0 modes, which are determined before the plate’s installation, this study generates the lines depicting the changes in group velocity induced by temperature variations (CT) for both the S0 and A0 modes. These CT lines are derived from the lines illustrating changes in group velocity due to thermal stress variations (CTS), which are obtained after plate installation. Ultimately, the generated CT lines can be used to estimate thermal stress throughout the entirety of the plate’s operational life span by isolating the distinct stress variation effects from the CTS lines. The numerical validation results show favorable accuracy in thermal stress estimation in a constrained plate subjected to temperature variation using both S0 and A0 Lamb wave modes, with average errors of 0.63 % and 0.91 %, respectively.

In-situ sparse-array imaging for through-thickness cracks in plates with [formula omitted] Lamb waves and an efficient waveform inversion algorithm

Structural health monitoring (SHM) requires efficient online crack detection and characterization to prevent structural failures, which mainly arise from fatigue cracks. Existing solutions for crack characterization involve analyzing sensed wave signals directly, but these approaches usually require onerous steps or many sensors to obtain sufficient and clear wave packets. An alternative strategy is a model-based inversion, which takes the full waveform into consideration and does not require analysis on a single wave packet. This approach can achieve accurate characterization with fewer sensors and simpler implementation. We propose an efficient model based on the Huygens’ principle and the no-mode-conversion property of the A0 mode Lamb waves to meet the requirements of online monitoring. We then verify the proposed model-based crack imaging method through simulation and experiments on smooth and rough cracks. The proposed method is easy, cheap, and efficient, making it a desirable option for SHM tasks.

Directional Multi-Frequency Guided Waves Communications Using Discrete Frequency-Steerable Acoustic Transducers.

A novel directional transducer based on Guided Waves (GW) is introduced in this paper, designed for use in structural health monitoring (SHM) and acoustic data communication applications, i.e., systems in which the elastic medium serves as a transmission channel and information is conveyed through the medium via elastic waves. Such systems can overcome difficulties associated with traditional communication methods like wire-based or radio frequency (RF), which can be complex and have limitations in harsh environments or hard-to-reach places. However, the development of these techniques is hampered by GW dispersive and multi-modal propagation and by multi-path interference. The shortcomings can be effectively addressed by employing Frequency Steerable Acoustic Transducers (FSATs), which leverage their inherent directional capabilities. This can be achieved through the exploitation of a frequency-dependent spatial filtering effect, yielding to a direct correlation between the frequency content of the transmitted or received signals and the direction of propagation. The proposed transducer is designed to actuate or sense the A0 Lamb wave propagating in three orientations using varying frequencies, and has three channels with distinct frequencies for each direction, ranging from 50 kHz to 450 kHz. The transducer performance was verified through Finite Element (FE) simulations, accompanied by experimental testing using a Scanning Laser Doppler Vibrometer (SLDV). The unique frequency-steering capability of FSATs is combined with the On-Off Keying (OOK) modulation scheme to achieve frequency directivity in hardware, similar to ongoing research in 5G communications. The MIMO capabilities of the transducer were finally tested over a thin aluminum plate, showing excellent agreement with the FE simulation results.

Modelling acoustic radiation from vibrating surfaces around coincidence: Radiation into fluids

It is well-known that vibrating surfaces generate sound waves in adjacent fluids. According to the classical radiation model, the nature of these waves depends on whether the vibration’s phase speed cv is above (supersonic) or below (subsonic) the fluid sound speed cf. The transition between these two domains is known as coincidence. In the supersonic domain, the sound wave radiates into the fluid. In the subsonic domain, the classical model states that the wave becomes evanescent and clings to the surface. In the last 30 years, however, several articles on leaky guided waves have reported radiating waves in the subsonic domain, which is at odds with the classical model. In this article, we investigate an enhanced model for sound radiation near and below coincidence. Unlike the classical model, this model fully respects conservation of energy by balancing the radiated power with power lost from the guided wave underlying the vibration. The model takes into account that this power loss and the consequent attenuation of the surface vibration result in an inhomogeneous radiated sound wave — an effect that cannot be neglected near coincidence. We successfully validate the model against exact solutions for leaky A0 Lamb waves around coincidence. The model can also be used as a perturbation method to predict the attenuation of leaky A0 waves from the properties of free A0 waves, giving more accurate estimates than existing perturbation methods. We further investigate subsonic leaky A0 waves using the enhanced model. Thereby we, for example, explain the peculiar reappearance or persistence of the leaky A0 wave at lower frequencies, an effect brought to attention by previous theoretical studies.

A Lorentz Force EMAT Design with Racetrack Coil and Periodic Permanent Magnets for Selective Enhancement of Ultrasonic Lamb Wave Generation

This article proposes an electromagnetic acoustic transducer (EMAT) for selectively improving the purity and amplitude of ultrasonic Lamb waves in non-ferromagnetic plates. The developed EMAT consists of a racetrack coil and a group of periodic permanent magnets (PPMs). Two-dimensional finite element simulations and experiments are implemented to analyze the working mechanism and performance of the PPM EMAT. Thanks to the specific design, the eddy currents increase with increasing wire density and the directions of the magnetic fields and Lorentz forces alternate according to the polarities of the magnet units. Wires laid uniformly beneath the magnets, and the gaps between adjacent magnets generate tangential and normal Lorentz forces, resulting in-plane (IP) and out-of-plane (OP) displacements, respectively. The constructive interference occurs when the wavelength of the generated Lamb wave is twice the spacing of the magnets, leading to large amplitudes of the targeted ultrasonic Lamb waves. Therefore, the PPM EMAT is capable of generating pure symmetric or antisymmetric mode Lamb waves at respective frequencies. The results prove that the developed PPM EMAT can generate pure either S0 or A0 mode Lamb waves at respective frequencies. The increase in wire width and wire density further increases the signal amplitudes. Compared with the case of conventional meander-line-coil (MLC) EMAT, the amplitudes of the A0 and S0 mode Lamb waves of our PPM EMAT are increased to 880% and 328%, respectively.

FEM-based analysis on sensing out-of-plane displacements of low-order Lamb wave modes by CMUTs

It is well known that acoustic emission (AE) signals, generated by external impacts or damages such as crack initiation, mainly propagate in the form of Lamb waves in plate-like structures. In this work, MEMS-based resonant capacitive micro-machined ultrasonic transducers (CMUTs), which are designed for sensing out-of-plane displacements, have been verified by finite element method (FEM) modeling and theoretical analysis for their feasibility of detecting low-order Lamb waves (A0 and S0). First, combining the propagation theory of Lamb waves and the “spring-mass-damper” model of CMUTs, the out-of-plane sensing mechanism has been explained, together with the analytical expression of sensitivity. Then, simulations based on FEM have been carried out to show that the designed CMUTs are sensitive to out-of-plane displacements, while extremely insensitive to in-plane displacements. Meanwhile, a transient analysis has found the potential abilities of CMUTs for sensing A0 and S0 lamb waves. Besides, the sensing characteristics of CMUTs have also been investigated, including the influence of squeezed-film damping, the amplitude of the input signal, the cell number, and cell space. Finally, the ball drop impact is simulated to show the potential of identifying the location of the AE source by CMUTs. Our studies reveal the out-of-plane sensing behaviors of CMUTs for Lamb waves and may have the potential in promoting the miniaturization and integration of AE sensors.

Error-Index-Based Algorithm for Low-Velocity Impact Localization

Flat plates and cylindrical shells are commonly used in large equipment. To locate the low-velocity impact points in these structures, this study proposes an error-index-based algorithm for impact localization. The time of arrival of an impact-generated A0 Lamb waves was first estimated based on the energy of the signal. Equations for calculating the error indices were proposed for flat-plate and cylindrical shell structures, and the probability distribution functions of the impact points are constructed for visual localization. The impact test results on a flat plate and cylindrical shell indicated that, compared to the Morlet wavelet method, the proposed algorithm improved the mean relative error of impact point localization on the flat plate by 0.22%, 15.64%, and 15.26% under three different noise conditions, respectively (i.e., no noise, and SNR = 5 and 0 dB). For the cylindrical shell, the mean relative error of impact localization improved by 1.8%, 3.97%, and 28.12% under the three conditions, respectively. The results indicated that the proposed localization algorithm can accurately locate the impact points on a flat plate and cylindrical shell, even under strong background noise conditions, providing a reference for future research on locating low-velocity impact points in large equipment.

A New Focused EMAT Design With Narrow Magnet to Achieve Both A0-Lamb Signal Enhancement and Waveform Distortion Correction

Due to the high magnetic flux density at the edge of the magnet, the narrow-magnet Electromagnetic Acoustic Transducer can excite the ultrasonic wave with a larger amplitude than the conventional EMAT, but the waveform of the former is distorted. This paper presents a new focused EMAT design with a narrow magnet, which can both enhance the ultrasonic A0-Lamb signal and correct the distorted waveform. A synthesis equation of the ultrasonic signals based on the contribution of the in-plane (IP) and out-of-plane (OP) components of the magnet field is proposed to analyze the mechanism of the waveform distortion. The distorted wave is corrected by an uneven split-wires arrangement strategy. The EMAT employs a sector-shaped narrow magnet and a set of focused meander-line coils containing uneven split wires, for generating a 1MHz focused A0-Lamb wave in an aluminum plate. A three-dimensional finite element model of the EMAT is established using COMSOL Multiphysics to perform numerical simulations, and the effectiveness of the EMAT design is verified. The experimental results show that the EMAT not only corrects the signal distortion due to the narrow magnet and suppresses its side lobes, but also enlarges the amplitude of the A0-Lamb wave by 55.6% under the same magnetic flux density when compared with conventional EMAT.

Tangential bond stiffness evaluation of adhesive lap joints by spectral interference of the low-frequency A0 lamb wave

Transmission spectra of the lowest-order antisymmetric (A0) Lamb wave for adhesively bonded single lap joints are experimentally investigated in a frequency range below 0.4 MHz. Based on the theoretical results of the wave interference, a tangential bond stiffness evaluation method is proposed for the lap joints. Aluminum alloy plates bonded with epoxy adhesive on different conditions were prepared as bonded specimens. An air-coupled ultrasonic transducer was used to generate the A0 mode in the specimens, and the signals of the transmitted waves across the joints were measured with a pin-type piezoelectric transducer. Spectral analysis was performed for the measured waveforms, and the transmission coefficient was calculated for each specimen as a function of frequency. The experimental results showed that the transmission coefficient has local maxima and minima at multiple frequencies, called peak and notch frequencies, respectively. The sets of the peak and notch frequencies were different among the bonded specimens. Based on the peak and notch frequencies, the tangential bond stiffness was estimated for each bonded specimen. As a result, the bond stiffnesses obtained for the specimens with the same nominal bond thickness and adherend pretreatment were almost equal even if the bond lengths were different. Furthermore, the evaluation results showed that pretreatments such as sanding and contamination of adherend surfaces affect the bond stiffness due to the change in the interfacial stiffness.

Study on Nonlinear Lamb Wave Test for Invisible Impact Damage on CFRP Laminates

The impact damage imposed on carbon fiber–reinforced polymer (CFRP) materials used in aircraft fuselage may seriously affect flight safety. An ultrasonic testing method can be used to inspect for damage; however, in some cases of invisible or barely visible impact damage, linear ultrasound may not provide a clear indication of the underlying damage. Accordingly, a nonlinear Lamb wave technique was developed in this study to detect invisible impact damage (IID). First, a nonlinear Lamb wave testing platform was set, as well as damage areas with different impact energies. Second, the anisotropic propagation of Lamb waves was studied to determine the wave mode and the distribution of the transducers, and the linear parameters of the Lamb waves were determined. Last, three types of characteristic parameters of nonlinear Lamb waves were obtained for damage detection. As revealed from the results, the linear ultrasonic parameters of A0 mode Lamb waves can be applied to the detection of macro surface cracks, and the frequency shift, relative nonlinearity coefficient (RNC), and fluctuation coefficient of RNCs are highly sensitive to the detection of IID. Thus, a combination of nonlinear S0 Lamb waves and linear A0 Lamb waves can be used for IID and macro surface crack detection, respectively.

Microcrack localization based on static component induced by a primary A0 Lamb wave in a thin plate.

A microcrack localization method based on a static component (SC) induced by a primary A0 Lamb wave is proposed. Based on the bilinear stress-strain constitutive model, a two-dimensional finite element model is built to investigate the interaction between microcracks and Lamb waves. The A0 Lamb wave at low frequency is selected to be the primary Lamb wave, which is beneficial to microcracks localization. Based on the time of flight of the generated SC pulse, an indicator named normalized amplitude index is defined for finding the location and number of microcracks. Simulation results show that one or multiple microcracks can be effectively located.

Numerical Investigation of Excitation of Various Lamb Waves Modes in Thin Plastic Films

Ultrasonic-guided waves are widely used for the non-destructive testing and material characterization of plates and thin films. In the case of thin plastic polyvinyl chloride (PVC), films up to 3.2 MHz with only two Lamb wave modes, antisymmetrical A0 and symmetrical S0, may propagate. At frequencies lower that 240 kHz, the velocity of the A0 mode becomes slower than the ultrasonic velocity in air which makes excitation and reception of such mode complicated. For excitation of both modes, we propose instead a single air-coupled ultrasonic transducer to use linear air-coupled arrays, which can be electronically readjusted to optimally excite and receive the A0 and S0 guided wave modes. The objective of this article was the numerical investigation of feasibility to excite different types of ultrasonic-guided waves, such as S0 and A0 modes in thin plastic films with the same electronically readjusted linear phased array. Three-dimensional and two-dimensional simulations of A0 and S0 Lamb wave modes using a single ultrasonic transducer and a linear phased array were performed. The obtained results clearly demonstrate feasibility to excite efficiently different guided wave modes in thin plastic films with readjusted phased array.

Double defects-induced elastic wave coupling and energy localization in a phononic crystal

This study aims to investigate elastic wave localization that leverages defect band splitting in a phononic crystal with double defects through in-depth analysis of comparison of numerical and experimental results. When more than one defect is created inside a phononic crystal, these defects can interact with each other, resulting in a distinctive physical phenomenon from a single defect case: defect band splitting. For a phononic crystal consisting of circular-hole type unit cells in a thin aluminum plate, under A0 (the lowest antisymmetric) Lamb waves, both numerical simulations and experiments successfully confirm the defect band splitting phenomenon via frequency response functions for the out-of-plane displacement calculated/measured at the double defects within a finite distance. Furthermore, experimental visualization of in-phase and out-of-phase defect mode shapes at each frequency of the split defect bands is achieved and found to be in excellent agreement with the simulated results. Different inter-distance combinations of the double defects reveal that the degree of the defect band splitting decreases with the increasing distance due to weaker coupling between the defects. This work may shed light on engineering applications of a multiple-defect-introduced phononic crystal, including broadband energy harvesting, frequency detectors, and elastic wireless power transfer.

Two-dimensional scattering features of the mixed second harmonic A0 mode Lamb waves for incipient damage localization

Inspection of incipient structural damage is of great significance. Existing techniques based on nonlinear guided waves have shown great promise for the detection of incipient damage due to material microstructure changes, but with only limited success for damage localization, which is technically more challenging. Our previous work uncovered the existence of the second harmonic A0 mode Lamb waves in a PZT-driven system, as a result of the mixing of the primary A0 and S0 mode Lamb waves, thus pointing at the possibility of performing damage localization through tuning the size of the wave mixing zone. In the present study, a two-dimensional incipient damage localization method is proposed based on this newly discovered wave phenomenon. By visualizing the nonlinear wave field, damage-induced nonlinear wave scattering features are first investigated. A dedicated localization algorithm is then proposed and evaluated. Numerical results show that the energy of the scattered nonlinear wave is mainly confined to a narrow region along the actuator-damage path, the spatial variation of which can be approximated by a simple Gaussian function. Embedding this information into the proposed localization strategy, damage localization can be achieved using a simple physical system. Experiments are finally carried out to validate the 2nd A0 wave scattering features and the proposed damage localization method.