Search

• Contact surface boundary conditions between the two surfaces of the vertical crack were considered to study contact acoustic nonlinearity (CAN) from the breathing contact crack in conjunction with the modal decomposition method, Fourier transform, and variational principle-based algorithm. • The clapping effects when the crack closed due to the different ratios of incident wave amplitude to crack width with the contact boundary conditions between the crack surfaces were studied and analyzed to get the quantitative correlation between analytical calculations and FE simulation. • When the crack state was modulated at a low frequency (much lower than the one of the probing ultrasonic waves), the related mode conversion coefficients were modulated accordingly both in the fundamental frequency and harmonic frequency. To characterize fatigue crack, an analytical calculation and finite element (FE) simulation of Lamb wave propagating through the region of a breathing crack in a two-dimensional(2D) isotropic plate were studied. Contact surface boundary conditions between the two surfaces of the vertical crack were considered to study contact acoustic nonlinearity (CAN) from the breathing contact crack in conjunction with the modal decomposition method, Fourier transform, and variational principle-based algorithm. Reflection and transmission coefficients in the fundamental frequency and second harmonic frequency were calculated and analyzed quantitatively. Different ratios of incident wave amplitude to crack width were studied to calculate CAN results related to micro-crack width. In addition, a low-frequency (LF) vibration(10 Hz) excitation was introduced to perturb the free surface vertical crack to close, and an interrogating Lamb wave(1 MHz) was used to study crack-related CAN in different conditions for interpreting the modulation mechanism. The contact boundary conditions between two surfaces of vertical crack were set which were dynamically changed due to the low frequency modulation. The clapping effects when the crack closed due to the modulation of the contact boundary conditions between the crack surfaces were studied and analyzed to get the quantitative correlation between CAN and LF modulation. The results obtained from the analytical model were compared with those from the FE simulation, showing good consistency. Knowledge of these effects is essential to correctly gauge the severity of surface cracks in the plate, which can be spotlighted in its application to quantitative evaluation of micro fatigue cracks in structural health monitoring(SHM). [ABSTRACT FROM AUTHOR]

• A passive sensor for ultrasound based on thermochromic liquid crystals (TLCs) is introduced. • Its use for characterising ultrasound sensors and for visualising wavefields in plates is presented and explained. • The sensor offers the potential for immediate visualisation without the need for scanning, and can be applied directly onto a sample or in air. • Ultrasound is visualised via local heating of the TLC and an absorbing backing layer. Acoustic field and vibration visualisation is important in a wide range of applications. Laser vibrometry is often used for such visualisation, however, the equipment has a high cost and requires significant user expertise, and the method can be slow, as it requires scanning point by point. Here we suggest a different approach to visualisation of acoustic fields in the kHz – MHz range, using paint-on or removable film sensors, which produce a direct visual map of ultrasound displacement. The sensors are based on a film containing thermochromic liquid crystals (TLC), along with a backing/underlay layer which improves absorption of ultrasound. The absorption generates heat, which can be seen by a change in colour of the TLC film. A removable sensor is used to visualise the resonant modes of an air-coupled flexural transducer operated from 410 kHz to 7.23 MHz, and to visualise 40 kHz standing waves in a Perspex plate. The thermal basis of the visualisation is confirmed using thermal imaging. The speed and cost of visualisation makes the new sensor attractive for use in condition monitoring, for fast assessment of transducer quality, or for analysis of acoustic field distribution in power ultrasonic systems. [ABSTRACT FROM AUTHOR]

• The improved VMD and DWT are combined to denoise and reconstruct the signal under strong noise without a reference. • The selection of wavelet function and transform level in DWT is optimized by Shannon entropy to denoise the signal without a reference. • The RAPID and the CNN are used to achieve spatial localization and visualization of the composite delamination. In this paper, a damage spatial imaging approach based on novel signal extraction is suggested to reconstruct the Lamb wave response signal under strong noise and realize the spatial localization of damage. First, the Variable Mode Decomposition (VMD) parameters are optimized by the improved Grey Wolf optimization method (IGWO) to decompose the response signal. To rebuild the response signal, the correlation coefficient is used to choose the optimal modal component and the residual. To give the best wavelet function and transform level for adaptive denoising of the reconstructed signal without a reference signal, an enhanced Discrete Wavelet Transform (DWT) based on Shannon entropy is proposed. To achieve damage localization imaging, a damage spatial localization model is built utilizing a reconstruction algorithm for probabilistic inspection of damage (RAPID) approach and a convolutional neural network (CNN). The suggested method may successfully increase the signal-to-noise ratio (SNR) of the reconstructed response signal and lower the error of spatial localization under strong noise through experiments. The spatial localization of composite damage using Lamb wave under strong noise is expanded in this paper. [ABSTRACT FROM AUTHOR]

• Cumulative second harmonic S0 Lamb waves are enhanced using a topologically optimized metamaterial structure. • The metamaterial-structure-aided monitoring system presents improved sensitivity to material microstructural changes. • The mode conversion efficiency is evaluated in simulations and experiments. Cumulative second harmonic Lamb waves in nonlinear media feature increasing amplitudes with propagation distance, conducive to the monitoring of material microstructural changes in structures. The phenomenon can be readily generated by zero-order symmetric (S0) mode waves in the low-frequency range. However, in a practical piezoelectric-transducer-activated system, both S0 and A0 (zero-order antisymmetric) mode Lamb waves are inevitably excited, while only the former is responsible for cumulative effects. The generation efficiency of the cumulative second harmonics is then affected by the presence of the A0 waves. To tackle the problem, this study develops a metamaterial structure, referred to as a meta-structure, to tactically enhance the cumulative second harmonic S0 Lamb waves by converting the A0 mode components into S0 mode waves. Topology optimization is conducted to design the meta-structure, which is surface-mounted onto the structure under inspection, to achieve high-efficiency A0-to-S0 wave mode conversion. Through tuning the parameters and constraints of the optimization, the designed single-sided meta-structure breaks the structural symmetry in the thickness direction, while facilitating its practical implementation. Typical scenarios with different meta-structure materials are discussed. Numerical simulations demonstrate that the strain amplitudes of the fundamental S0 mode waves can be increased by 60% with the deployment of the meta-structure, alongside an enhancement of the second harmonic S0 mode waves at different sensing distances. Finally, the designed meta-structure is fabricated via 3D printing technique and tested experimentally on an aluminum plate subjected to thermal aging treatment for monitoring the heating-induced microstructural changes inside the structure. Experimental results confirm an increase in the wave amplitudes of the linear S0 mode waves with the assistance of the meta-structure. The developed system improves the sensitivity of nonlinear Lamb wave-based monitoring methods in characterizing material microstructural changes, which shows great promise for detecting incipient damage in practical structural health monitoring applications. [ABSTRACT FROM AUTHOR]

• An energy focusing method of broadband Lamb wave by metamaterial is proposed. • All frequencies waves can reach the focus simultaneously by designing excitation. • The focusing energy is improved in proposed method compared to traditional method. • The method is effective for different transmitter/receiver position. In the field of structure health monitoring (SHM), the use of Lamb wave to locate damage is a common method. Energy focusing is beneficial for damage localization because of higher SNR and higher resolution. Optimization design of elastic metamaterials is promising for energy focusing based on speed modulation. However, current design scheme is effective only for narrowband Lamb waves. Compared to narrowband waves, broadband Lamb waves with a larger frequency range carry richer structural information. In this study, an energy focusing method based on broadband Lamb waves by simultaneous designing excitation waveforms and elastic metamaterials is proposed. Firstly, COMSOL finite element simulation software is used to calculate the relationship between the metamaterial structure and the excitation wave. Subsequently, the metamaterial structure and the excitation signal form are designed according to the relationship. Finally, the metamaterial structure is bonded with the aluminum plate using 3D printing PA2200 nylon to verify the effectiveness of the method. [ABSTRACT FROM AUTHOR]

• The Lamb wave dispersion curves have a significant rising stage before convergence. • Modal displacement in couple stress theory is different from classical theory. • Displacement components vanish for specific modes and frequencies. • The modal displacements are verified by mathematical derivations and calculations. In micro-scale structures, the influence of scale effects on the mechanical properties cannot be ignored, and the continuum mechanics theory cannot effectively describe guided wave propagation. This paper studies modal displacements in an isotropic micro/nano-scale plate — an essential factor for the mode selection of Lamb waves in non-destructive testing technology. To achieve this, the consistent couple stress theory, which additionally accounts for the impact of scale effects on wave propagation, has to be employed. A mathematical derivation method with singular value decomposition is proposed, and the excitation amplitude is computed by applying a normal stress source to evaluate the in-plane and out-of-plane displacements. The results indicate that the in-plane displacement vanishes on the plate surface for anti-symmetric modes when the phase velocity equals the velocity of shear waves. Moreover, the intersections of symmetric and anti-symmetric dispersion curves identify specific frequencies at which the out-of-plane displacement vanishes on the free surface. These findings highlight the difference in modal displacement characteristics between micro-scale and macro-scale structures. The results from this study may furnish theoretical guidance for ultrasonic non-destructive testing of microstructures. [ABSTRACT FROM AUTHOR]

• A new non-destructive testing technique is proposed for Directed Energy Deposition. • A wave model describes wave propagation in both the substrate and the thin wall. • A laser vibrometer scans the thin wall fabricated by additive manufacturing. • A 0 mode Lamb wave in the thin wall is enhanced by frequency tuning. • A small defect caused by inconsistent powder delivery is detected and localized. Thin-walled metallic structures produced by the Directed Energy Deposition (DED) Additive Manufacturing (AM) process are prone to various fabrication defects, which hinder the wider applications of the technique in practice. In-situ inspection and monitoring methodologies are in high demand for improved quality control of printed parts. This paper presents an ultrasonic guided-wave-based method and a prototype that can potentially be used for in-situ inspection of thin-walled structures produced by DED. Lamb waves are excited by a Lead zirconate titanate (PZT) piezoelectric transducer bonded on the DED substrate remotely from the thin wall. The substrate works as a waveguide to transmit the waves which then propagate along the thin wall. A non-contact laser vibrometer is applied to measure the guide wave signals by scanning the surface of the thin wall. The mechanisms of guided wave generation and propagation along the substrate and printed part are theoretically studied. It allows for choosing proper inspection parameters to enhance the measurement sensitivity of guided waves and help interpret the signals for defect detection. Experiments were conducted with DED-produced stainless steel (316L) thin-walled structure. The new method is demonstrated in one example to detect and localize a small defect caused by inconsistent powder delivery of a fabricated thin wall sample, via analysing the B-scan ultrasonic guided wave signals. The new technique provides strong potential for in-situ online monitoring of the DED process. [ABSTRACT FROM AUTHOR]

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 A 0 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. • Enabled in-situ crack imaging with a sparse array of Lamb wave transducers. • Capable of characterizing through-thickness, linear, and smooth cracks in plates. • Employed waveform inversion to exploit adequate data despite sensor shortages. • Adapted the method for in-situ imaging with an efficient forward model. • Leveraged the non-mode-conversion property of the A0 mode in the model. [ABSTRACT FROM AUTHOR]

• A multimodal Lamb wave baseline-free method for corrosion detection. • It applies the diversity of mode types and mode sensitivities to replace the baseline signal. • It demonstrates a great robustness and effectiveness to damage detection. The multi-mode and dispersion nature of Lamb waves means that a variety of modes with individual mode structures and distinct dispersion behaviors would propagate in the structures simultaneously. The existence of a corrosion would result in thickness reduction, which means the frequency-thickness product under a specific excitation would also decrease. Due to dispersion diversity, the interaction of each individual Lamb mode at the corrosion may be distinct, i.e., the velocity varies in different extent and even in opposite trends. In this paper, the combination of multiple modes, rather than a single sensitive mode, is used for structure diagnosis. Specifically, two Lamb modes both sensitive to corrosion but with opposite variation trends are taken and the corrosion index is defined on the ratio of their time-of-flight, so as to enhance the sensitivity to corrosion and eliminate the influence of difference path lengths in the sensor network. On this basis, a probabilistic reconstruction algorithm is introduced for corrosion detection and localization. Since the two modes are extracted from the same wideband Lamb wave response, the proposed method is baseline-free. The influence of mode conversion on the effectiveness of the proposed method is discussed. Ultimately, the performance of the proposed method is demonstrated by an experimental example. The results show that the defect could be correctly identified and accurately localized. [ABSTRACT FROM AUTHOR]

• A method for predicting the cumulative characteristics of second harmonic Lamb waves in damped plates is proposed. • The influence of material damping and wave beam divergence on the cumulative effect of the second harmonic Lamb waves is analyzed. • The proposed method is validated numerically and experimentally. The second harmonic Lamb waves have high sensitivity to microstructural defects in materials and are therefore promising for incipient damage detection and monitoring of thin-walled structures. Existing studies have shown that the second harmonic Lamb waves can be cumulative with increasing propagation distance under the internal resonance conditions, which is conducive to nonlinear wave measurements in view of structural health monitoring. However, when propagating in a lossy structure with damping, the cumulative properties of the second harmonic Lamb waves are affected by energy dissipation and thus need to be re-examined. In this paper, a method for predicting the cumulative characteristics of second harmonic Lamb waves in damped plates is proposed. Instead of using material damping parameters which are difficult to obtain in practice, the proposed method relies on the attenuation patterns of Lamb waves at fundamental and double frequencies while taking into account the influence of the wave beam divergence. The proposed methodology is validated by finite element simulations and experiments. The results show that the cumulative second harmonic Lamb waves in the damped plate tend to increase and then decrease, and a "sweet" zone of relatively large amplitude can be predicted using the proposed method. The elucidation of the cumulative characteristics of the second harmonic Lamb waves provides guidance for effective system design for structural damage detection and monitoring applications. [ABSTRACT FROM AUTHOR]

We present an ultrasonic method of detecting cracks in pipelines based on using normally incident transducers in a pitch-catch setup, which can only excite Lamb modes of higher order than the fundamental modes A 0 and S 0 commonly used in crack detection applications. By excitation and measurements of the Lamb modes S 1 , S 2 , and A 3 , in a steel plate immersed in fluid with and without a notch (to emulate a crack), the performance of the modes towards crack detection is quantified by assessing whether it returns a high leaky component and whether the notch has a large impact on the leaky component. In order to narrow the scope of measurements necessary to investigate notch sensitivity for different system parameters, and to potentially optimize the system setup, we present a computationally efficient theoretical model based on angular spectrum method (ASM) and the theoretical sensitivity kernel formulation from the field of seismology that accounts for a scatterer in the wave path between the transmitter and receiver. The model is compared against measurements, which show that the frequency components of the S 2 mode has both the largest leaky frequency component in the given setup and the largest sensitivity at a frequency close to the maximum leaky frequency such that a difference caused by the notch is easily measured. By using the measurements and the validation calculation as baseline reference, we calculate the expected S 2 mode sensitivity and leaky components for larger plate thicknesses and larger standoffs, which exemplifies how the model can be applied in measurement system design and optimization. • Crack detection using normally incident transducers to excite Lamb waves is proposed. • Measurements show that frequencies near the S2 mode are highly sensitive to a notch. • A model of notch sensitivity is compared against measurements. • Examples of theoretical notch sensitivity with parameter changes are shown. [ABSTRACT FROM AUTHOR]

• Nonlinear Lamb wave imaging of micro-damage is achieved based on wavefield data. • A new approach is proposed for weak nonlinear feature enhancement. • Demonstrated capability of accurately imaging the fatigue crack tip. • Visualize the wave field of the harmonics. The traditional nonlinear ultrasonic technique, as typified by the second-harmonic generation and the frequency mixing response, can be employed to identify and characterize the micro-damage. However, the research on micro-damage characterization using nonlinear Lamb wave imaging technique remains an ongoing challenge and is rarely reported. A method called standardized amplitude difference is proposed for nonlinear feature enhancement, and further for fatigue crack imaging based on the wavefield data. Wavefield data contain abundant information on the spatial and temporal variation of propagating waves in the damaged structure. The nonlinearity index β ′ of the signal difference under the high and low incident wave amplitudes is calculated for fatigue crack imaging. Two scanning methods, including local scanning and global scanning, are introduced to image the fatigue crack tip and visualize the wave field of the harmonics respectively. The experimental validation, based on the imaging results of an aluminum alloy plate specimen with a barely visible fatigue crack and a steel plate with a blind hole, manifests that the proposed method can be used to enhance and extract the nonlinear features and suppress the fundamental frequency, so as to improve the signal-to-noise ratio (SNR) of the micro-damage imaging results. [ABSTRACT FROM AUTHOR]

• Resonance verification ensures energy concentration within the feature region of the welded joint, preventing leakage. • The 3D time-step FE method allows for unambiguous identification of ZGV propagation modes. • The presence of ZGV-FGWs in the welded joint is confirmed. Extensive research has been conducted on zero-group-velocity (ZGV) Lamb waves in elastic plates, demonstrating significant progress in the field of nondestructive testing. However, there is a scarcity of studies focusing on ZGV modes in complex structures. In this paper, we present our research investigating the presence of ZGV feature guided waves (FGWs) in a welded joint. Our approach follows a similar methodology used to study ZGV Lamb waves in elastic plates. By employing two-dimensional (2D) finite element (FE) modeling, we analyze the response spectra of the welded joint when subjected to a force source, revealing the occurrence of resonance in the response spectra. To investigate resonance modes in the welded joint, we employ the three-dimensional (3D) time-step FE method. By applying spatial 2D and short-time Fourier transforms to the received time-domain signals, we analyze the frequency content and spatial distribution of the signals. This analysis allows us to verify the existence of non-propagation and propagation modes in the welded joint. The non-propagation mode refers to the presence of signals with a zero wavenumber, indicating that they do not propagate or travel along the welded joint. These signals are typically associated with local resonances or vibrations within the welded joint itself. On the other hand, the propagation mode corresponds to signals with nonzero wavenumbers, suggesting that they propagate or travel along the welded joint. Furthermore, by further analyzing the propagation mode in the welded joint, similar to the analysis of ZGV modes in solid plates, we have observed that it also exhibits ZGV characteristics based on the wavenumber-frequency spectra. To further analyze acoustic field distributions at resonance frequencies, we utilize the semi-analytical finite element method in conjunction with the perfectly matched layer method. The results obtained from this analysis are consistent with those obtained from the 2D FE method and 3D time-step FE method, thereby confirming that propagation modes with ZGV characteristics at resonance frequencies correspond to FGWs, which we refer to as ZGV-FGWs. Through this step-by-step analysis, we ultimately establish the existence of ZGV-FGWs in the welded joint. This study introduces fresh ideas and serves as a point of reference for future research on ZGV-FGWs in complex structures. [ABSTRACT FROM AUTHOR]

Rodent models of behavior used in the fields of neuroscience and psychology generate a wealth of multimodal data. For instance, as a rodent moves and behaves in its environment, muscle contractions apply subtle forces to any surface the animal contacts. These forces generate acoustic waves that propagate through the waveguide as Lamb and shear horizontal (SH) waves and contain information about the rodent's physiology, behavior, and underlying psychological state. If the information in these waves were to be tapped, it would provide a novel, non-invasive way to study rodent behavior. This article lays the foundations for using guided ultrasonic waves generated by a mouse's movement on an aluminum plate for detecting behavior and drawing inferences about acoustic startle responses. The experimental setup involves piezoelectric sensors capturing the waves generated by the rodent's movement, which are then stored as discrete acoustic emission (AE) hits using an amplitude threshold-based data acquisition system. This method of data acquisition ensures that data collection occurs only when the animal moves or behaves, and each movement/behavior is represented by values of features within the generated wavepackets (AE hits). Through open field tests with C57BL/6J mice, utilizing piezoelectric sensors and the DAQ system, it was observed that every movement/behavior of the animal generated Lamb wavepackets within the frequency range of 20 kHz to 100 kHz. Furthermore, rearing behavior in the animals also led to the generation of SH wavepackets in the frequency range of 75 kHz to 230 kHz. This criterion was subsequently employed to detect rearing behavior. In the acoustic startle response test, where the animals' responses to intense sound pulse were recorded, AE hits' features proved useful in quantifying the response. These experimental findings validate the proposed technology's practicality and demonstrate its capability to enhance studies of rodent behavior. • An open-field arena is designed to capture the guided ultrasonic waves generated by the movement/behavior of mice. The arena features an aluminum base plate equipped with ultrasonic sensors. • In this setup, we treat the mouse as an acoustic source, and the resulting guided waves are regarded as acoustic emissions (AE). • As the mice freely explore the open-field arena, every movement/behavior gives rise to Lamb waves with frequency content spanning from 20 kHz to 100 kHz. • Notably, specific motions, such as rearing and occasionally sniffing, correlate with the generation of shear horizontal waves, with frequencies ranging from 75 kHz to 230 kHz. • Another novel aspect of this research lies in conducting the acoustic startle response (ASR) in an unconstrained environment, facilitating the quantification of the "intensity" of the response through the absolute energy of the AE hits. Additionally, this study marks the first observation of variations in the physical motions associated with ASR. [ABSTRACT FROM AUTHOR]

The interactions between ultrasonic waves and damage provide crucial information for developing effective damage detection techniques in various fields, including non-destructive testing and structural health monitoring, and they can be investigated through wave propagation. Then, this article presents an approach to investigate the longitudinal wave in thin plates with symmetric damage considering oblique incidence. The approach includes a strategy to determine the plate thickness reduction due to the damage presence by considering an oblique incidence of waves generated by the actuator. Modeling is developed to compute each wave packet of reflected and transmitted waves separately, which allows one to describe the wave scattering. Numerical simulations are carried out and the results show that the sensor size can be adjusted to improve the existence of damage detection and the determination of the damage depth. Results from experimental tests are presented to demonstrate the approach considering a circular actuator. The findings contribute to improving the comprehension of the interaction between guided waves and discontinuities, potentially encouraging the use of waves for damage sizing purposes rather than only for detection and improve the current state of the art in wave propagation by investigating the effects of different excitation frequencies and the influence of the damage parameters and sensor sizing on the resulting waves. • Analysis of the scattering of longitudinal waves in plates with symmetric damage. • A model that describes each wave packet is presented. • Optimal frequencies to detect symmetric damage are presented. • The optimal frequencies depend on the incidence angle. • The sensor size can be adjusted to improve the damage detection process. [ABSTRACT FROM AUTHOR]

• Proposing a CSBL method for dispersion curve estimation of Lamb waves obtained by random sensor network. • Sparsity and consistency of wavenumber in complex frequency response are considered in CSBL. • Employing hierarchical Laplace prior in CSBL for sparsity promotion. • Performance of recognition slightly declines as number of signals reduces. • Providing critical information for Lamb-wave-based defect detection. This paper proposes a new dispersion curve estimation method that employs the complex sparse Bayesian learning (CSBL). It is well accepted that guided wave packets are distorted because of the differences in propagation velocities at different frequencies; thus, the preceding velocity–frequency curve estimation is beneficial for wave packet recovery, feature recognition and defect localization. Conventional dispersion curve estimation methods, such as two-dimensional Fourier transform and multiple signal classification, are suitable for array signal and are restricted by the transducer aperture, leading to a small application scope. According to the frequency–response model of the guided wave, for each frequency, the responses obtained by the transducers can be sparsely represented based on an overcomplete dictionary matrix constructed using multiple discretized wavenumbers and known distances. A CSBL algorithm was developed to infer the posterior probability density function of the weight vector in the sparse representation. The non-zero elements in the sparse weight vector mean that the corresponding dictionary atoms indicated wavenumbers are contained in the frequency response, and the velocity–frequency curve can be finally derived from the wavenumber–frequency curve. The proposed CSBL method has a satisfactory capability to solve this sparse representation of the complex frequency response because a hierarchical form of the Laplace prior is employed to achieve a high degree of sparsity of the weight vector. This method effectively incorporates the real and imaginary parts of the complex frequency response by employing the same hyperparameter to integrate the known information. This method requires only a few randomly placed transducers; thus, it has a wide range of applications. The effectiveness of the proposed approach was validated using multiple guided-wave signals obtained through numerical simulations and an experimental study on a plate structure. [ABSTRACT FROM AUTHOR]

• Damage imaging is achieved under an excitation with a small amplitude. • Long-duration excitation is used to improve transmitting energy. • Pulse compression and dispersion compensation is used to improve resolution. Considering a trade-off between temporal-spatial resolution and multi-mode nature of Lamb waves, tone bursts with short durations are usually used as excitations in Lamb wave based damage detection. A short-duration excitation usually requires a large amplitude to carry sufficient energy so as to obtain response signals with enough signal-to-noise ratio and cover a large inspection area. In this paper, an alternative Lamb wave damage imaging method using nonlinear chirp (nonlinear frequency modulation, NLFM) excitation with a long duration and a small amplitude is proposed. The signal processing techniques of pulse compression and dispersion compensation are adopted to compress the long-duration wave packets of response signals into short ones. Compared with conventional tone burst excitations with short durations and small amplitudes, due to the long duration of the nonlinear chirp excitation and the use of pulse compression, sufficient energy can be applied to transducers under small amplitude excitations so the image contrast in imaging will not degrade. Furthermore, as large amplitude excitations are no longer required, high voltage amplifiers are not necessary so the hardware of the Lamb wave testing system is simplified. Experiments on a carbon steel plate with an artificial crack are carried out and Lamb wave signals are collected using a linear array consisting of nine PZTs. Experimental results under the NLFM signal and conventional tone bursts are provided. Experimental results show that under the condition of the same excitation amplitude, the proposed method under the NLFM excitation can achieve better imaging quality compared with methods under conventional tone bursts. [ABSTRACT FROM AUTHOR]

• A tunable bidirectional SH wave transducer was proposed. • The transducer was based on antiparallel d 15 piezoelectric strips (APS) • Simulations and experiments validated the proposed SH wave transducer. • The transducer can selectively suppress SH 0 wave and excited SH 1 wave. • The transducer can also excite circumferential SH wave in pipelines. Guided wave based defects inspection is very promising in the field of structural health monitoring (SHM) and nondestructive testing (NDT) due to its less dissipation and thus long distance coverage. In comparison with the widely used Lamb waves, shear horizontal (SH) waves are relatively simple but less investigated probably due to the traditional notion that SH waves were usually excited by electromagnetic acoustic transducers (EMAT). In this work, we proposed a tunable method to excite single-mode bidirectional SH waves in plates using antiparallel thickness-shear (d 15) piezoelectric strips (APS). The proposed SH wave driving mechanism here is similar to that by using the periodic permanent magnetics (PPM) based EMAT with the period of strips equal to half of the wavelength. Both finite element simulations and experiments were conducted to validate this transducer in excitation of bidirectional SH waves. Results show that the Lamb waves excited by single piezoelectric strip can be suppressed very well. The radiation angle of the excited bidirectional SH wave can be reduced by extending the strip length, increasing the driving frequency or using more strips. Moreover, the APS transducer can selectively excite SH 1 wave and suppress the SH 0 wave at 174 kHz and 273 kHz in a 10 mm-thick aluminum plate. Considering its simple structure, flexible design and low excitation energy, the APS SH wave transducer is expected to be widely used in near future. [ABSTRACT FROM AUTHOR]

• Waves guided by the edge of a thick elastic plate with facets are studied. • 8 edge modes are experimentally observed via the wavenumber-frequency analysis. • The existence of the predicted edge waves spectrum is confirmed experimentally. • The attenuation of higher order edge waves is strongly affected by the facets. • Edge waves are predominant in the wave-field excited by a piezoelectric transducer. The existence of the edge waves spectrum predicted in a series of recent theoretical studies is investigated and confirmed experimentally. Wave motion in 20 mm thickness aluminium rectangular plate with two facets is generated by a circular piezoelectric transducer and measured by laser Doppler vibrometry. Eight edge modes (four symmetric and four antisymmetric) are clearly observed by means of wavenumber-frequency analysis applied to out-of-plane velocities measured at the edge. The semi-analytical method used by the authors in previous theoretical studies is modified to take into account the facets. By the numerical investigations of edge waves in the plate with facets, the sensitivity of attenuation of higher order edge waves to the form of edge profile is revealed. A good agreement between experimental data and theoretical predictions is demonstrated for dispersion curves and the waveforms of individual modes extracted by means of 2D bandpass filters. [ABSTRACT FROM AUTHOR]

• A SH wave phased array system was proposed for monitoring of plate-like structures. • The system can detect both surface defects and inside defects without baseline. • The system can detect a through-thickness hole as small as 2 mm. • The system can detect multi defects simultaneously. Guided wave based structural health monitoring (SHM) has been regarded as an effective tool to detect the early damage in large structures and thus avoid possible catastrophic failure. In recent years, Lamb wave phased array SHM technology had been intensively investigated while the inherent multi-mode and dispersive characteristic of Lamb waves limits its further applications. In comparison, the fundamental shear horizontal (SH 0) wave is non-dispersive with uncoupled displacements and thus more promising for defect detection. In this work, we proposed an SH 0 wave linear phased array SHM system based on our recently proposed omni-directional SH wave piezoelectric transducer (OSH-PT). Firstly, the working principle of the phased array system was presented and the total focusing method (TFM) was employed for imaging. Then the SH 0 wave mode generated by the OSH-PT was confirmed in a defect-free plate. Finally, experiments were carried out to examine the performances of this SHM system. Results showed that the proposed system can detect a through-thickness hole as small as 2 mm in diameter with the location error only about 6.3 mm. Moreover, the proposed phased array system can also detect multi-defects. Due to its low working frequency and thus low attenuation, the proposed phased array system is capable of monitoring large structures. This work will lay the foundations of SH wave based phased array SHM. [ABSTRACT FROM AUTHOR]

A nonlinear ultrasonic method is proposed based on a group of newly discovered wave triplets where two primary codirectional shear-horizontal SH0 waves mix in a weakly nonlinear plate and generate a cumulative S0 Lamb wave at the sum frequency. Theoretical analyses show that any combination of two primary SH0 waves whose frequencies sum to the frequency at which the SH0 mode intersects the S0 Lamb wave mode results in an internally resonant secondary S0 Lamb wave. Moreover, the relationship between the frequency combination and the nonlinear Lamb wave generation efficiency is revealed, which guides further engineering applications. Finite element validations are carried out with the aid of a subtraction method for the nonlinear feature extraction. The cumulative effect of the generated S0 Lamb wave at the sum frequency as well as the influence of the frequency combinations on the nonlinear Lamb wave generation efficiency is confirmed. Experiments are performed to validate the proposed method as well as demonstrate its use for material characterization. The experiments require a gel filter to mitigate the influence of the undesired nonlinear sources. With the gel filter, the cumulative effect of the secondary S0 Lamb wave is verified and the corresponding slope is extracted and further used to characterize the material status of the fatigue samples. Results demonstrate the proposed method provides high sensitivity to early fatigue damage, which makes it promising for the further early damage detection applications. [ABSTRACT FROM AUTHOR]

• Stress-relaxation in composites is characterized using nonlinear Lamb waves. • Stress-relaxation in is coupled with the second-order nonlinear Lamb wave modes. • Rate and degree of relaxation: functions of number and frequency of loading cycles. • Rate and degree of relaxation: inherently correlated to the remaining strength. Experimentally observed dissipated nonlinearity in Lamb wave propagation in composites due to stress-relaxation is reported herein. It was found that the stress relaxation in composite is inherently coupled with the second order nonlinear parameter derived from the Lamb wave modes. Due to the combined effect of internal stresses and damage accumulation in composites, the second harmonic frequency was found to be shifted towards the lower frequency with increasing amplitude, which was partially recovered and shifted back during the stress relaxation. A comprehensive fatigue experiment was conducted on ASTM standard composite specimens with fatigue loading sequences and relaxation, while the guided Lamb wave signals were collected using piezoelectric sensors integrated with the specimens. A remarkable ∼27% reduction of acoustic nonlinearity was observed during relaxation. Rate and degree of relaxation were found to be the function of number and frequency of loading cycles and inherently correlated with the remaining strength of the composites. [ABSTRACT FROM AUTHOR]

• Wave-propagation characteristics are depicted between Lamb waves and various orientation crack. • A propagation distance calculation method considering dispersion effects was achieved using Sparse Decomposition. • A novel algorithm to quantify various orientation and length crack without baseline signals has been developed. Crack damage is one of the significant factors that may accumulate at the stress concentration area of engineering structures and cause catastrophic accidents. In this paper, we proposed a novel approach to identify the crack location and size by exploiting the reflections and diffractions of Lamb waves. The interaction mechanism between the crack and Lamb wave has been analyzed thoroughly, our analysis of the interaction between the crack and Lamb wave revealed that both reflections and diffractions carry valuable damage information that reflects the size and orientation of the crack. As the interaction coefficients between these two components and the crack are different, there are supposed to exist differences between them in the amplitude value. We implemented a threshold to classify the signals received from all paths into two groups: reflections and diffractions. Then we constructed an overcomplete dictionary of waveforms corresponding to different propagation distances to extract the damage information. Using sparse decomposition, the received signals were mapped to their corresponding propagation distances without the use of baseline signals. The diffractions allow us to determine the crack's tip points, while the reflections provide information about the edge points. The kinked crack's size and orientation were visualized based on the time-domain signals acquired in our experiment. We provided a comprehensive description of our algorithm and verified it through numerical simulation and experimental data. Our results show high agreement with actual cracks, demonstrating the efficacy of our proposed method. [ABSTRACT FROM AUTHOR]

• A new multi-GPU-based spectral element formulation for ultrasonic wave propagation. • Novel direct GPU-to-GPU message exchange strategies enabled by CUDA-aware MPI. • Significant accelerations over a multi-CPU core-based counterpart formulation. • Achievable accelerations and model sizes scalable with the number of GPUs. • Practicality shown through simulating real-life ultrasonic inspection scenarios. In this paper, we introduce a new multi-GPU-based spectral element (SE) formulation for simulating ultrasonic wave propagation in solids. To maximize communication efficiency, we purposely developed, based on CUDA-aware MPI, two novel message exchange strategies which allow the common nodal forces of different subdomains to be shared between different GPUs in a direct manner, as opposed to via CPU hosts, during central difference-based time integration steps. The new multi-GPU and CUDA-aware MPI-based formulation is benchmarked against a multi-CPU core and classical MPI-based counterpart, demonstrating a remarkable acceleration in each and every stage of the computation of ultrasonic wave propagation, namely matrix assembly, time integration and message exchange. More importantly, both the computational efficiency and the degree-of-freedom limit of the new formulation are actually scalable with the number of GPUs used, potentially allowing larger structures to be computed and higher computational speeds to be realized. Finally, the new formulation was used to simulate the interaction between Lamb waves and randomly shaped thickness loss defects on plates, showing its potential to become an efficient, accurate and robust technique for addressing the propagation of ultrasonic waves in realistic engineering structures. [ABSTRACT FROM AUTHOR]

• Anisotropic wave skew effects can cause an apparent offset in guided wave velocities. • Difference from theory of UD CFRP plate experiments and FE simulations. • Reduced accuracy for damage detection and localization in composite structures. • Skew angle correction for point source excitation, implemented experimentally. Guided ultrasonic wave propagation in anisotropic structures results in directional dependency of velocity and wave skewing effects that can impact the accuracy of damage detection. Phase and group velocities of the A 0 guided wave mode, propagating in a unidirectional carbon fiber reinforced laminate, were investigated experimentally and through finite element analysis. A correction for the significant offset in phase and group velocities due to wave skewing effects is illustrated for both point and short line sources, achieving good agreement with theoretical calculations assuming planar wave fronts. The influence of the line excitation length on velocity measurements is discussed. [ABSTRACT FROM AUTHOR]

• A real time-reversal operation based on the Lamb wave to detect the damage rather than virtual. • A multi-modal superposition finite difference time domain method is proposed to simulate the Lamb waves propagation with little calculation cost, which facilitates damage imaging output quickly. • A maximum energy frame method is presented to automatically determine the focusing time from wavefield animation, and enabling the detection of multiple damage points. • A detailed comparison between the proposed method and other four Lamb wave-based damage detection methods is evaluated. This study proposes a wavefield reconstruction method with a time-reversal operation (W R -TR) based on the Lamb wave to detect the damage in the plate. Currently, it is challenging to implement the wavefield reconstruction method for damage detection because of two issues. One is how to quickly simulate the Lamb wavefield. The other is how to determine the focusing time for searching the desired frame from wavefield animation, which can show the location and size of damage. In response, this study introduces a multi-modal superposition finite difference time domain method (MS-FDTD) to simulate the Lamb waves propagation with little calculation cost, which facilitates damage imaging output quickly. In addition, a maximum energy frame method (MEF) is presented to automatically determine the focusing time from wavefield animation, enabling the detection of multiple damage points. The simulations and experiments have demonstrated good noise robustness, anti-distortion ability, and broad applicability with dense or sparse array layouts. Moreover, a detailed comparison between the proposed method and other four Lamb wave-based damage detection methods is evaluated in this paper. [ABSTRACT FROM AUTHOR]

• Legendre Orthogonal Polynomial Expansion (LOPE) method mapping the relationship between the wave velocity and initial stresses was developed to generate the input characteristics of linear and non-linear variation for deep neural network. • A Deep Neural Network (DNN) was combined with LOPE for the inverse of initial stress based on Lamb wave dispersion date rather than objective function obtained from wave equations. • The performances of ReLU activation function and Sigmoid activation function were illustrated in detail for current inverse work. The prediction of the initial stress in composites is essential for the non-destructive testing (NDT) and structural health monitoring (SHM) of carbon fibre reinforced polymer (CFRP). This paper examines the potential of Lamb waves in the inverse of initial stress by calculating the influence of initial stress on the dispersion characteristics of Lamb waves propagating in multilayered CFRP laminates. By introducing the mechanics of incremental deformation into the linear three-dimensional elasticity theory, the Legendre orthogonal polynomial expansion (LOPE) method is used to mathematically model the Lamb wave propagating in multilayered CFRP laminates subjected to horizontal and vertical homogeneous initial stresses. Then, a three-hidden-layers Feed Forward Deep Neural Network (DNN) with Back Propagation (BP) algorithm is constructed to invert the magnitude and direction of the initial stresses. The input features are the phase velocities of fundamental Lamb wave A 0 mode at five different frequencies. Both training and testing samples are obtained by LOPE forward calculation. An ablation experiment is presented to compare the two different activation functions. Finally, the accuracy of the inverse is verified by comparing with the available outcomes of LOPE forward calculation. [ABSTRACT FROM AUTHOR]

• Measurement of the reflective function of highly attenuative material by using a pair of ultrasound transducers. • Transducer-pair method is proposed to acquire V(z) by using conventional ultrasound transducers with a high f-number and small aperture. • By comparing the results obtained from both the single transducer and the transducer-pair approach, the feasibility is demonstrated. Ultrasonic reflectivity using a V(z) technique is a powerful characterization method in acoustic microscopy to measure the elastic properties of materials. Conventional techniques generally use a low f-number with high frequency; however, to measure the reflectance function of the highly attenuative material, a low frequency is essential. In this study, the transducer-pair method based on Lamb waves is used to measure the reflectance function of a highly attenuative material. The results demonstrate the feasibility of the proposed method using a commercial ultrasound transducer with high f-number. [ABSTRACT FROM AUTHOR]

• A new method for computing RIs from Lamb waves with extended data length to accommodate extra indirect waves. • The damage missed by the direct wave may be exposed by the extra indirect waves. • The modified RIs demonstrate excellent sensitivity to damages and ensure a low threshold for the healthy condition. The Lamb wave reciprocity-based method is an effective candidate for the health monitoring of composite plates. However, if the damage is located symmetrically between the transmitter–receiver pair, the reciprocity still holds true and the method misjudges its presence. In the present work, a new method for computing the reciprocity index (RI) from Lamb wave signals with extended data length is proposed. This method exploits extra indirect waves that bounce one or more times between the damage and other reflectors. These waves probe the damage through different paths and from different directions. Thus, the damage missed by the direct wave may be exposed by the indirect waves. Benefiting from that, two modified RIs are defined and their performance is validated by two experimental examples. As expected, both indices demonstrate excellent sensitivity to damage even in the middle of the transmitter–receiver pair and ensure a low threshold for the pristine condition, illustrating an excellent ability to distinguish between health and illness. [ABSTRACT FROM AUTHOR]

• The increase of volumic fraction d of bonded Aluminum/Adhesive/Aluminum plate caused the occurring of double/simple ZGV-mode in S 0 /S 2 modes. • In viscous plate, and at the frequencies of ZGV-modes, the dispersion curves are connected. This phenomenon gives rise to a coupling mode. • The effects of d on these guided modes, in viscoelastic bonded plate, are investigated. These studies are of great importance for NDT applications since they play a critical role in the selection of the optimal inspection modes and frequencies. Before a nondestructive testing process gets set up, the sensitivity of the Lamb waves to the bonded plate's properties must be well understood. The dispersion and attenuation curves in thin bonded Aluminum/Adhesive/Aluminum plate are calculated by the Stiffness matrix method. The increase in the volumic fraction d caused the appearance of backward mode in the S 0 and S 2 dispersion curves. The effect of d on forward waves, and on backward waves and associated ZGV-modes, are studied. The frequencies of ZGV-modes decrease when d increases. The effects of d on dispersion and attenuation curves of the damped symmetric modes are shown. From certain values of d, and at the frequencies of the ZGV-modes, the dispersion curves of the symmetric modes are connected. This phenomenon gives rise to a C coupling mode. The attenuation levels of the ZGV-modes for different d values are calculated. The increase in d caused the shift of C-dispersion and C-attenuation curves toward the decreasing direction of the frequency axis, without significant change in the values of the phase velocity, and with slight decreases in the attenuation level of the C coupling mode. [ABSTRACT FROM AUTHOR]

• A theoretical model of nonlinear lamb wave in a linearly varying plate was proposed. • Its properties in linearly varying plate are discussed and verified. • The application of nonlinear Lamb wave technique may be extended from the uniform-thickness plate to the varying-thickness plate. The aim of this paper is to investigate propagation characteristics and the generation mechanism of the nonlinear lowest-order symmetric Lamb mode (S 0) which propagates downslope in free elastic plates with slowly linearly varying-thickness. From theoretical analyses, in a low frequency-thickness product (fd) range, the S 0 mode is slightly dispersive, it is easy to generate, and it approximately satisfies the principle of the phase velocity matching. Therefore, if a S 0 mode is excited at a proper frequency in the low fd range, the amplitude of the second harmonic wave is linearly increasing in a certain propagating-distance, which is valuable for the practical NDE application of the second harmonic wave. Moreover, numerical simulations and experiments have been carried out to validate theoretical results. Our investigation of properties of the second harmonic wave can be applied to characterize and evaluate micro-structural damages in varying-thickness waveguides. [ABSTRACT FROM AUTHOR]

• The ABH is introduced to attenuate AE reflection waves. • The parameter optimization method of the ABH is presented. • Simulations and tests show the ABH has a good prospect on reducing the AE boundary reflection. • The proposed method could improve the accuracy of the acoustic emission tests. Due to the difference between the characteristic impedance of air and plate structure, the acoustic emission (AE) wave propagating in a plate structure is reflected when reaching the boundary. It leads to the fact that the obtained signal contains not only direct AE components but also reflected components. The existence of the reflected AE wave brings error and difficulty to accurate AE source analysis. This paper attempts to introduce the acoustic black hole (ABH) into an experimental plate structure (a disc structure in this paper) to attenuate the reflected AE wave from the structure boundary and obtain the high Signal-Noise Ratio (SNR) direct AE wave. Firstly, the finite element model of a disc with an ABH is established to verify the attenuation of the reflected AE wave. Then, the orthogonal test is conducted to reveal the influence of geometric parameters of the ABH on reflection attenuation. And a method based on the optimal parameter combination of the ABH is proposed to attenuate boundary reflection. Finally, the broken-lead and friction experiments are performed on the processed disc with the ABH to verify the ability of the ABH to attenuate the boundary reflection of AE wave. Both analytical and experimental results show that the ABH is a candidate tool to reduce the reflected AE wave on the boundary. [ABSTRACT FROM AUTHOR]

• The aim of the present work is to develop a multi-mode imaging technique that will allow for identification of damage size and location using ultrasonic guided waves. • The proposed technique combines a reverse-time migration (RTM) imaging algorithm with a 3D wave propagation simulator using different wave modes. • This combination enables the separation of multiple modes using the wavefield filtering techniques, potentially providing more information to damage types. • Without the limitation of generating single dominant mode waves, wide frequency ranges are accessible, enabling optimal frequencies for a variety of ultrasonic data acquisition systems. The sensitivity of Lamb wave modes to a particular defect or instance of damage is dependent on various factors (e.g., the local strain energy density due to that wave mode). As a result, different modes will be more useful than others for damage detection and quantification, dependent on damage type and location. For example, prior work in the field has shown that out-of-plane modes may have a higher sensitivity than in-plane modes to surface defects in plates. The excitability of a certain data acquisition system and the corresponding resolution for damage imaging also varies with frequency. The aim of the present work was to develop a multi-mode damage imaging technique that enables characterization of damage type and size, general sensitivity to unknown damage types, higher resolution imaging, and detectability regardless of the data acquisition system used. A reverse-time migration (RTM) imaging algorithm was combined with a numerical simulator—the three-dimensional (3D) elastodynamic finite integration technique (EFIT)—to provide multi-mode damage imaging. The approach was applied to two simulated case studies featuring damaged isotropic plates. Sensitivities of damage type to wave mode were investigated by separating the A 0 and S 0 Lamb wave modes obtained from the resultant RTM wavefields. [ABSTRACT FROM AUTHOR]

This work aims to demonstrate the ability to evaluate bulk thermal aging of aeronautical composite materials using Lamb waves. These composite materials are bi-dimensional woven composite structures with polymers matrix. More than 20 different thermal aging profiles are obtained by modulating the temperature and curing duration. The impact on material properties is evaluated using normalized destructive characterization and x-ray computed tomography. Lamb waves are generated and detected using a single 3 MHz phased array transducer in contact with the composite structure. In that way, a spatio-temporal image of elastic wave propagation in the composite material is obtained. The dispersion curves are calculated by using a bi-dimensional discrete Fourier transform or singular value decomposition to project the experimental data into the wavenumber-frequency domain. Both methods allow for accurate estimation of the Lamb wave dispersion curves. Thermal aging is then evaluated by comparing experimental data with a set of dispersion curves that correspond to different controlled thermal aging profiles. Our promising results open the door toward quantitative evaluation of composite material thermal aging on the runway. [ABSTRACT FROM AUTHOR]

• Lamb waves in piezoelectric two layered structures show a wide range of properties. • Wave properties depend on mode order, layers thickness and transducer configuration. • Further improvements are expected for piezoelectric three layered structures. Using Bi 12 GeO 20 plate coated by AlN film, the main characteristics of the A 0 , S 0 , A 1 , and S 1 Lamb waves are numerically calculated and compared with those of SAW in the same structure. It is shown that (i) there exist only one SAW mode for this material combination, (ii) the mode exist in a narrow range of AlN thickness, (iii) it can be excited using four different transducer configurations, (iv) the velocity and coupling constants of the mode are, respectively, higher and lower as compared with the values for the uncoated Bi 12 GeO 20 substrate. On the other hand, for Lamb waves (i) there are several modes of different orders, (ii) the modes exist in a wide range of the AlN thickness, (iii) they may be excited using twelve IDT configurations, (iv) the velocities and coupling constants of the waves may be larger and smaller as compared with the values for the uncoated plate, (v) both characteristics of the modes depend on the mode order, film thickness, plate thickness, and transducer configuration, and (vi) the depth profiles of the modes are neither symmetrical nor anti-symmetrical. These properties make Lamb waves more attractive than SAW. Application of the waves and the structure for some applications are suggested. [ABSTRACT FROM AUTHOR]

• An efficient approach to the investigation of nonlinear scattering of guided waves. • The GPU implementation and the small-size model profile make the model highly efficient. • The wave damage interaction coefficients concept is extended for nonlinear scattering problems. • Super harmonic generation and selective mode conversion phenomena are observed. • The rough crack surfaces are considered. This article presents an efficient numerical approach to the investigation of nonlinear scattering and mode conversion phenomena of Lamb waves as they interact with breathing cracks. A Local Interaction Simulation Approach (LISA) is adopted, which possesses the versatility to capture arbitrary damage profiles. The stick-slip contact dynamics is implemented in the LISA model via the penalty method, which captures the nonlinear interactions between Lamb waves and breathing cracks. The LISA framework achieves remarkable computational efficiency with its parallel implementation using Compute Unified Device Architecture (CUDA) executed on powerful GPUs. A small-size LISA model with absorbing boundaries is tailored for the purpose of extracting the Lamb wave scattering and mode conversion features. Due to the explicit parallel CUDA implementation and the small-size model setup, the computation is highly efficient. Numerical case studies on nonlinear scattering of Lamb waves from breathing cracks are given. Distinctive higher harmonic generation and selective mode conversion phenomena are presented using the complex-valued Wave Damage Interaction Coefficients (WDICs) containing both amplitude and phase information of the scattered wave field. The effect of oblique incident angle on nonlinear scattering phenomenon is investigated. The rough crack surface feature with initial openings and closures is also considered to better approximate fatigue cracks in practical engineering scenarios. In addition, the wave amplitude effect on the nonlinear scattering and mode conversion is studied. This research may provide guidelines for the effective design of sensor arrays utilizing nonlinear Lamb waves for fatigue crack detection. [ABSTRACT FROM AUTHOR]

• Representations for waves of all types generated in the coupled structure. • Insight into the resonance transmission and backward mode phenomena. • Wave energy streamlines and guided wave profiles. • Source energy partition among the excited waves. Explicit integral representations for the wave fields generated by air-coupled or underwater transducers in an acoustic medium with a submerged elastic (metallic or laminate composite) plate are obtained in the form of path Fourier integrals. Together with the far-field asymptotics for the incident, reflected, transmitted and guided waves that were derived from those integrals, they proved to be a convenient tool for the in-depth study of wave phenomena inherent in such acoustic-elastic structures. The present paper is focused on the non-conventional properties of backward leaky waves such as the increased wave energy transfer through the plate due to the increasing occurrence of energy vortices impeding lateral outflow of wave energy. The transformation of classical Lamb waves into leaky guided waves due to a fluid loading, especially in the backward wave range, the energy properties of those waves and the appearing traveling Scholter-Stoneley waves as well as source energy partition among the reflected, transmitted and guided waves are also numerically illustrated and discussed. [ABSTRACT FROM AUTHOR]

• Besides dispersion, comprehensive amplitude modulation can also change the appearance of Lamb wave signals. • A dictionary reconstruction strategy is established with considerations of phase and amplitude information. • The performance of sparse imaging method relies on the denoising parameters and numbers of sources. Composite structure is increasingly used in civil and aerospace applications due to its high mechanical performance. Lamb wave based sparse reconstruction imaging for damage localization is promising for structural health monitoring (SHM) and nondestructive evaluation (NDE) by using few measurements. However, this dictionary based method requires accurate atoms to represent Lamb wave propagating features in structure very well. Besides dispersion, signal changes caused by amplitude modulation should be considered for waveform distortion when constructing the dictionary for sparse imaging method. In this paper, a non-contact laser is used for Lamb wave excitation which exhibits a strong amplitude modulation in low frequency. Additionally, the strong attenuation resulting from material damping would also presents a distance-dependent amplitude modulation. To reconstruct an amplitude model of Lamb wave, the decomposition method of system response and attenuation is proposed. Then, the influence of amplitude modulation on signal representation is analyzed, which shows the restriction of dictionary without considering amplitude modulation. On this basis, the amplitude considered dictionary is built together with the phase considered dictionary for sparse imaging in terms of damage detection. Furthermore, according to Lamb wave reflection model, the solution for sparse reconstruction imaging is given. Finally, the performance of sparse imaging method is discussed by experimental investigation with different parameters. The results show the efficiency of the proposed method with improved imaging performance and give comparisons for better parameter choice. [ABSTRACT FROM AUTHOR]

• Coupled models of EMATs are built via a mid-level method. • Approaches to solve the amplitudes of the S0 and A0 modes are compared. • The single frequency approach is used in characterizing excitability of Lamb waves. Electromagnetic acoustic transducers (EMATs) are versatile non-contact ultrasonic transducers with relatively low transduction efficiency. A fundamental problem not answered completely yet is how the structure of an EMAT influences the generation of various Lamb wave modes. We tackle this problem with fully coupled frequency domain EMAT models where the underlying integro-differential equations are solved directly and the magnitudes of the phasors of the displacement components at a point in the middle plane of a plate are used to represent the strength of the S0 and A0 mode waves. Idealized single-wire, two-wire and wire bundle EMATs with uniform bias magnetic field and practical meander line and tightly wound EMATs with distributed bias field are studied. Polar plots of the idealized EMATs with swept angle of the bias field show that the vertical component of the bias field decides the strength of the S0 mode waves. Sweeping of the width of the magnet for the practical EMATs generates S0 mode curves that could be explained from the distribution of the vertical component of the bias field. This work represents the first attempt to solve the proposed problem of characterizing excitability of Lamb waves with EMATs quantitatively, via the model-based approach. [ABSTRACT FROM AUTHOR]

Highlights • Transmission ratios of the S0 and A0 Lamb waves across a closed crack are analyzed. • Spring-type interface model is applied to model a partially closed crack. • S0 and A0 modes show remarkably different interaction with a closed crack. • Experimental results are presented for a fatigue crack under variable tensile loading. Abstract The transmission characteristics of Lamb waves across a partially closed through-thickness crack in a plate are investigated numerically and experimentally. In the numerical analysis, the spectral element method is used to simulate the transmission of the lowest-order symmetric (S0) and antisymmetric (A0) Lamb modes across a crack in a low-frequency range. The analysis is carried out for an open crack with traction-free surfaces as well as for a partially closed crack modeled as a spring-type interface characterized by normal and tangential stiffnesses. The transmission ratios of both modes are obtained from the spectral amplitude of the simulated transmission waveforms for different crack lengths and interfacial stiffnesses. The numerical results show that the transmission ratio of the S0 mode increases monotonically with the interfacial stiffness, but that of the A0 mode depends on the interfacial stiffness in a non-monotonic manner depending on the frequency. The Lamb wave transmission measurements are carried out for aluminum alloy plates with artificial slits or a fatigue crack. The experimental results for the plates with slits show reasonable agreement with the numerical results for open cracks. The measured transmission ratio of the S0 mode is shown to decrease with the tensile load applied to the plate, but that of the A0 mode shows different load dependence for different frequencies. The qualitative features of the experimental results for the fatigue crack are discussed based on the numerical simulation for closed cracks. [ABSTRACT FROM AUTHOR]

Highlights • A novel-joint damage detection algorithm based on Lamb waves and electro-mechanical impedance methods is developed. • A mobile transducer set contains PZT patches is designed. • A baseline-free damage characterizing algorithm is presented. Abstract Lamb waves and electro-mechanical impedance (EMI) based methods are increasingly used in damage detection owing to their high sensitivity to small structural defects. Lamb wave based methods are effective in detecting damages in a large area and electro-impedance based methods are suitable for characterizing the identified damage. Based on these two methods, a novel combined damage detection method is presented in this research. To achieve this, first, a mobile transducer set is developed, which can be used for both the Lamb waves and EMI based methods. Then, a baseline-free damage detection strategy that combines the Lamb waves and EMI methods is presented. Finally, a laboratory-sized test piece is used to validate the effectiveness of the proposed approach. The results achieved with the application of the presented combined method for characterizing an L-shape crack in an aluminum plate show better location accuracy and detection efficiency than those obtained by applying only one method. [ABSTRACT FROM AUTHOR]

Highlights • Damage localization method by the time-reversed Lamb waves is proposed for plates. • Mode conversion behavior of Lamb waves is considered in the time reversal process. • Localization of a notch-type defect in plates is numerically simulated. • Focused spots appear at the damage location by the proposed time reversal method. Abstract A damage localization method based on the time reversal focusing of the mode-converted scattered Lamb wave is proposed for plate structures with a non-symmetric defect in the thickness direction. Dual transducers are attached symmetrically on the upper and lower surfaces of the plate to selectively emit and receive the lowest-order symmetric (S0) and antisymmetric (A0) modes. The localization of damage is achieved by the numerical time-reversed (TR) simulation of the mode-converted Lamb wave generated at the defect. To investigate the validity of the proposed method, the signals of the Lamb waves in a plate with a partial-thickness notch are numerically simulated by the three-dimensional elastodynamic finite integration technique (EFIT). When the S0 mode is emitted in the damaged plate, not only the S0 mode is scattered but also the A0 mode is generated due to mode conversion at the notch. Similar mode conversion behavior is confirmed when the A0 mode is emitted. The time reversal of the mode-converted scattered Lamb waves creates focused spots at the damage location without using baseline data for the undamaged plate. The proposed method reduces the magnitude of the artifacts compared to the time reversal of the non-mode-converted Lamb wave, and yields the focused spot whose size is associated with the size of the notch and the half wavelength of the time-reversed wave mode. Furthermore, the proposed method is applied to a plate with a notch-type defect adjacent to an a priori known through-thickness hole, demonstrating the damage localization in a relatively complicated structure. [ABSTRACT FROM AUTHOR]

Highlights • Incremental Lamb wave scattering from a notch emanating from a through-hole is analyzed. • Multiple frequencies and hole diameters are considered as well as a notch with no hole. • Numerical results are validated with experimentally measured scattering patterns. • The presence of even a small hole significantly affects notch incremental scattering. • Incremental scattering from off-angle incident waves is a strong function of frequency. Abstract Lamb wave scattering from a crack originating at a through-hole is of practical importance because of the abundance of fastener holes used in engineering structures. Notches are often used to simulate cracks so that Lamb wave methods can be more conveniently investigated in the laboratory. A linear, three-dimensional finite element model is employed in this paper to study incremental scattering of the fundamental anti-symmetric (A 0 ) Lamb wave mode from notches emanating from through-holes. The term “incremental scattering” refers to the change in scattering caused by introduction of the notch and is motivated by structural health monitoring for which transducers are fixed and signal changes are interpreted to detect damage. Far-field angular scattering patterns are generated for multiple incident angles and frequencies, and such patterns are experimentally validated at one frequency by laser vibrometry measurements. Comparisons are made between a vertical notch alone (no hole) and notches located above and below the through-hole. Additionally, holes of different sizes are considered to investigate the effect of hole diameter on incremental scattering patterns. Results show that the presence, location and size of the through-hole affect both the shape and strength of notch incremental scattering patterns. [ABSTRACT FROM AUTHOR]

Highlights • The effect of ablation on the shape of laser-induced elastic waves is studied. • The elastic waves were generated and observed by projecting laser pulses. • Two numerical simulations were performed using heat flux and normal stress input. • The effects of thermal expansion and radiation pressure depend on energy intensity. Abstract In this paper, the effect of ablation on the shape of elastic waves generated by laser excitation is studied numerically and experimentally. Laser-induced ultrasound has been widely used in the nondestructive testing (NDT) field because it has the advantage that the sensor does not have to be directly attached to the target structure. In the safety assessment process, low energy excitation is used, and thus the structure is not damaged. Most studies related to laser ultrasound have focused on the method of detecting cracks within the elastic range, and there have been few studies on the effect of ablation. This research consists of experiments and numerical analyses. In experiments, elastic waves were generated in an aluminum plate by projecting laser pulses with different energy intensities. The velocities in the thickness direction were measured using a Laser Doppler Velocimeter (LDV) at a point 135 mm away from the excitation point. In the numerical study, two numerical simulations were carried out using heat flux and normal stress input to mimic laser pulse excitation. A thermo-mechanical simulation by heat flux was conducted to simulate thermal expansion by the laser pulse, and the normal stress was applied to reflect the effect of radiation pressure by ablation, respectively. Waveforms were synthesized by using different magnitude ratios of the obtained numerical responses and were compared with the experiment results. It is found that the effect of radiation pressure should not be neglected if the energy intensity is large although the effect of radiation pressure decreases as the energy intensity decreases. At the energy intensity with which ablation occurs, the effects of thermal expansion and radiation pressure exist simultaneously, and the contribution to the response depends on the energy intensity. [ABSTRACT FROM AUTHOR]

The feasibility of fatigue damage evaluation has been investigated using nonlinear Lamb waves with group-velocity mismatching. To choose an efficient mode pair, a parameter is proposed to quantify the efficiency of cumulative second-harmonic generation (SHG) of Lamb waves based on the normal modal analysis. Experiments and simulations are performed to verify the proposed parameter, which demonstrates that whether the matching condition of group velocity is satisfied or not, the efficiency of cumulative SHG increases with the order of Lamb mode for the five low-order Lamb waves investigated. Then, S3-s6 mode pair with group-velocity mismatching is chosen to characterize the fatigue damage of an aluminium alloy for the high efficiency of cumulative SHG. Results show that S3-s6 mode pair is sensitive to fatigue damage evolution and the integrated amplitude of second harmonics increases by nearly 300% with fatigue cycles. Nonlinear Lamb waves with group-velocity mismatching are validated to be a candidate to efficiently evaluate the fatigue damage. [ABSTRACT FROM AUTHOR]

For an elastic medium containing a homogeneous distribution of micro-cracks, an effective one-dimensional stress-strain relation has been determined with finite element simulations. In addition to flat micro-cracks, voids were considered that contain a Hertzian contact, which represents an example for micro-cracks with internal structure. The orientation of both types of micro-cracks was fully aligned or, for flat micro-cracks, totally random. For micro-cracks with Hertzian contacts, the case of random orientation was treated in an approximate way. The two types of defects were found to give rise to different degrees of non-analytic behavior of the effective stress-strain relation, which governs the nonlinear propagation of symmetric (S0) Lamb waves in the long-wavelength limit. The presence of flat micro-cracks causes even harmonics to grow linearly with propagation distance with amplitudes proportional to the amplitude of the fundamental wave, and gives rise to a static strain. The presence of the second type of defects leads to a linear growth of all harmonics with amplitudes proportional to the power 3/2 of the fundamental amplitude, and to a strain-dependent velocity shift. Simple expressions are given for the growth rates of higher harmonics of S0 Lamb waves in terms of the parameters occurring in the effective stress-strain relation. They have partly been determined quantitatively with the help of the FEM results for different micro-crack concentrations. [ABSTRACT FROM AUTHOR]

This paper studies the interaction of the fundamental symmetric Lamb wave mode S0 with delaminations in 8-layered glass fibre reinforced polymer (GFRP) laminated composites, using numerical models validated against experiments. The validation is performed using experiments on the eight layer quasi-isotropic GFRP composite laminate [0/90/45/−45] S . Further numerical studies were performed on the laminates [0/45/−45/90] S, [0/45/90/−45] S, [90/45/−45/0] S, [90/−45/0/45] S, [45/−45/0/90] S, and [45/90/−45/0] S to study the effect of ply layups on the reflection of S0 Lamb waves. The reflection coefficients calculated for these laminates followed a similar trend as the laminate [0/90/45/−45] S . Physical insight was obtained into the reflection behaviour, based on an analysis of wave dispersion in the sub-laminates. It was difficult to detect the delamination situated at the mid plane of the laminate, where the shear stress was found to be zero for all ply layups. The delaminations present at a depth greater than DL 12 (>0.42 mm) from the source of excitation, were found to be accessible for the laminates [0/90/45/−45] S, [0/45/−45/90] S and [0/45/90/−45] S . The sensitivity of the S0 mode reflection depends upon the position of the delamination along the thickness direction and ply layup orientation of the composite laminate. The S0 mode showed higher sensitivity to DL 23 and DL 34 (0.42 mm to 1.26 mm) in all the laminates that were inspected. [ABSTRACT FROM AUTHOR]

Numerous Lamb wave dispersion curve estimation methods have been developed to support damage detection and localization strategies in non-destructive evaluation/structural health monitoring (NDE/SHM) applications. In this paper, the covariance matrix is used to extract features from an ultrasonic wavefield imaging (UWI) scan in order to estimate the phase and group velocities of S0 and A0 modes. A laser ultrasonic interrogation method based on a Q-switched laser scanning system was used to interrogate full-field ultrasonic signals in a 2-mm aluminum plate at five different frequencies. These full-field ultrasonic signals were processed in three-dimensional space-time domain. Then, the time-dependent covariance matrices of the UWI were obtained based on the vector variables in Cartesian and polar coordinate spaces for all time samples. A spatial covariance map was constructed to show spatial correlations within the full wavefield. It was observed that the variances may be used as a feature for S0 and A0 mode properties. The phase velocity and the group velocity were found using a variance map and an enveloped variance map, respectively, at five different frequencies. This facilitated the estimation of Lamb wave dispersion curves. The estimated dispersion curves of the S0 and A0 modes showed good agreement with the theoretical dispersion curves. [ABSTRACT FROM AUTHOR]

This paper describes a completely non-contact ultrasonic method of gas flow metering using air-coupled leaky Lamb waves. To show proof of principle, a simplified representation of gas flow in a duct, comprising two separated thin isotropic plates with a gas flowing between them, has been modelled and investigated experimentally. An airborne compression wave emitted from an air-coupled capacitive ultrasonic transducer excited a leaky Lamb wave in the first plate in a non-contact manner. The leakage of this Lamb wave crossed the gas flow at an angle between the two plates as a compression wave, and excited a leaky Lamb wave in the second plate. An air-coupled capacitive ultrasonic transducer on the opposite side of this second plate then detected the airborne compression wave leakage from the second Lamb wave. As the gas flow shifted the wave field between the two plates, the point of Lamb wave excitation in the second plate was displaced in proportion to the gas flow rate. Two such measurements, in opposite directions, formed a completely non-contact contra-propagating Lamb wave flow meter, allowing measurement of the flow velocity between the plates. A COMSOL Multiphysics® model was used to visualize the wave fields, and accurately predicted the time differences that were then measured experimentally. Experiments using different Lamb wave frequencies and plate materials were also similarly verified. This entirely non-contact airborne approach to Lamb wave flow metering could be applied in place of clamp-on techniques in thin-walled ducts or pipes. [ABSTRACT FROM AUTHOR]

This paper investigates the propagation of Lamb waves in thin plates with quadratic nonlinearity by one-way mixing method using numerical simulations. It is shown that an A 0 -mode wave can be generated by a pair of S 0 and A 0 mode waves only when mixing condition is satisfied, and mixing wave signals are capable of locating the damage zone. Additionally, it is manifested that the acoustic nonlinear parameter increases linearly with quadratic nonlinearity but monotonously with the size of mixing zone. Furthermore, because of frequency deviation, the waveform of the mixing wave changes significantly from a regular diamond shape to toneburst trains. [ABSTRACT FROM AUTHOR]