S0 Lamb Wave Mode Research Articles

Measurements of S0 mode Lamb waves using a high-speed polarization camera to detect damage in transparent materials during non-contact excitation based on a laser-induced plasma shock wave

The demand for transparent materials has been expanding due to their ubiquity in products such as solar panels, tablet terminals, and smartphones. To mass produce high-quality products, quickly detecting damage on the µm scale and evaluating the quality are critical. Herein an Nd:YAG pulsed laser with a nanosecond order is used to generate a shock wave by laser induced plasma, which is subsequently used as a non-contact, non-destructive excitation force for transparent materials. Then, a high-speed polarization camera measures the generated Lamb wave. In this experiment, an impulse input is generated via a laser-induced plasma shock wave and the phase velocity of the generated Lamb wave in the polycarbonate plate is measured by a high-speed polarization camera. We found that this Lamb wave was in the S0 mode. Observing its propagation can detect scratches on the order of several hundred µm on the surface of a transparent plate in a non-contact, non-destructive manner.

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.

Closed-crack characterization using sparse decomposition based on nonlinear Lamb waves: a numerical study

It is known that the nonlinear interaction between closed cracks and primary elastic waves can lead to the generation of a second-harmonic component. In this work, the temporal S0-mode Lamb wave and closed-crack-interaction-induced second harmonic (abbr. closed-crack-induced second harmonic, CCISH) Lamb waves that were extracted for closed-crack characterization through a weighted and structured sparse decomposition (WSSD) algorithm. A 3D finite-element model of a thin aluminum plate based on the bilinear stiffness model is established to numerically study the nonlinear interaction between closed cracks and primary Lamb waves. Under S0-mode Lamb wave excitation, the temporal S0-mode CCISH signals are extracted from the original response using the pulse-inversion technique and a band-pass filter. A dictionary, whose columns are the normalized predicted CCISH waveforms generated by the proposed analytical CCISH generation and propagation model, is built to sparsely decompose the extracted array CCISH signals using adaptive weights. Images are generated using sparse coefficients to define the pixel values after solving the WSSD problem. Closed cracks with different locations and orientations are simulated, and imaging results show that the proposed method can characterize their location and orientation but not their length from the generated images.

Experimental investigation of the surface corrosion damage in plates based on nonlinear Lamb wave methods

This paper experimentally investigates the early stage damage caused by the surface corrosion in thin plates based on two nonlinear Lamb wave methods, which are the low-frequency S0 mode Lamb wave method and one-way S0-A0 Lamb mixing wave method. The experimental results show that the significant second/third harmonics and the resonant waves from these methods can be caused by the surface corrosion damage. Meanwhile, it is found that the normalized acoustic nonlinearity parameters in these methods increase monotonically with the number of corrosion times before the generation of the distinct cavities. Moreover, the position and the length of the surface corrosion region can be characterized by the resonant waves from one-way S0-A0 Lamb mixing wave method. This study reveals that the low-frequency S0 mode Lamb wave method and one-way S0-A0 Lamb mixing wave method are feasible to evaluate early stage damage caused by the surface corrosion.

An improved design of lamb wave EMAT for A0 wave generation and enhancement

A new structure of Lamb wave electromagnetic ultrasonic transducer (EMAT) is proposed in this work to suppress S0 mode Lamb wave (S0 wave) and enhance A0 mode lamb wave (A0 wave). The new EMAT consists of periodic magnet and meander-coil. Finite element models are established to analyze the static magnetic field and the excited ultrasonic signal. As a result, the local static magnetic field of the new EMAT is increased. S0 wave is suppressed obviously by new EMAT while A0 wave is enhanced significantly. Besides, the new EMAT structure is optimized. Finally, experiment has been performed on 2 mm thick aluminum. The experiment has verified that the amplitude of the A0 wave signal obtained by using new EMAT is increased by a factor of about 9.33. Besides, the experiment results have shown that the S0 wave obtained by using new EMAT is suppressed to be almost submerged in noise.

Analytical and Experimental Study of Fatigue-Crack-Growth AE Signals in Thin Sheet Metals.

The acoustic emission (AE) method is a very popular and well-developed method for passive structural health monitoring of metallic and composite structures. AE method has been efficiently used for damage source detection and damage characterization in a large variety of structures over the years, such as thin sheet metals. Piezoelectric wafer active sensors (PWASs) are lightweight and inexpensive transducers, which recently drew the attention of the AE research community for AE sensing. The focus of this paper is on understanding the fatigue crack growth AE signals in thin sheet metals recorded using PWAS sensors on the basis of the Lamb wave theory and using this understanding for predictive modeling of AE signals. After a brief introduction, the paper discusses the principles of sensing acoustic signals by using PWAS. The derivation of a closed-form expression for PWAS response due to a stress wave is presented. The transformations happening to the AE signal according to the instrumentations we used for the fatigue crack AE experiment is also discussed. It is followed by a summary of the in situ AE experiments performed for recording fatigue crack growth AE and the results. Then, we present an analytical model of fatigue crack growth AE and a comparison with experimental results. The fatigue crack growth AE source was modeled analytically using the dipole moment concept. By using the source modeling concept, the analytical predictive modeling and simulation of the AE were performed using normal mode expansion (NME). The simulation results showed good agreement with experimental results. A strong presence of nondispersive S0 Lamb wave mode due to the fatigue crack growth event was observed in the simulation and experiment. Finally, the analytical method was verified using the finite element method. The paper ends with a summary and conclusions; suggestions for further work are also presented.

Third harmonic shear horizontal waves for material degradation monitoring

Early detection of incipient damage in structures through material degradation monitoring is a challenging and important topic. Nonlinear guided waves, through their interaction with material micro-defects, allow possible detection of structural damage at its early stage of initiations. This issue is investigated using both the second harmonic Lamb waves and the third harmonic shear horizontal waves in this article. A brief analysis first highlights the selection of the primary–secondary S0 Lamb wave mode pair and primary–tertiary SH0 mode pair from the perspective of cumulative high-order harmonic wave generation. Through a tactic design, an experiment is then conducted to compare the sensitivity of the third harmonic shear horizontal waves and the second harmonic Lamb waves to microstructural changes on the same plate subjected to a dedicated thermal heating treatment. The third harmonic shear horizontal waves are finally applied to monitor the microstructural changes and material degradation in a plate subjected to a thermal aging sequence, cross-checked by Vickers hardness tests. The experiment results demonstrate that the third harmonic shear horizontal waves indeed exhibit higher sensitivity to microstructural changes than the commonly used second harmonic Lamb waves. In addition, results demonstrate that the designed third harmonic shear horizontal wave–based system entails effective characterization of thermal aging–induced microstructural changes in metallic plates.

Low frequency ultrasonic guided waves excitated by Galfenol Rod Ultrasonic Transducer in plate inspection

Lower frequency ultrasonic guided wave (20 kHz–200 kHz) has obvious advantages in large area plate monitoring. It enables longer propagation distances because of low attenuation and simple modes. The present study utilized a Galfenol Rod Ultrasonic Transducer (GRUT) excite low-frequency ultrasonic guided waves in plate inspection. It was verified by finite element simulation and experiment that GRUT can excite S0 mode Lamb wave, A0 mode Lamb wave and SH0 wave. A defects detection method based on A0 mode and S0 mode Lamb wave is proposed that “A0 mode Lamb wave is used for defect determination by its amplitude variation in time domain, and utilized S0 mode Lamb wave to locate the defect”. In this paper, utilize GRUT to detect a via hole with a radius of 2 cm, the experimental results show that the proposed method is convenient and fast with less signal processing, and the experimental error is 10.22 %.

Mode-mixing-induced second harmonic A0 mode Lamb wave for local incipient damage inspection

This paper reports the discovery of a special type of second harmonic A0 mode Lamb wave, which is generated through the mixing of primary S0 and A0 mode Lamb waves in a PZT-activated weakly nonlinear plate. Owing to the different propagating velocities of the S0 and A0 waves and the finite duration of their corresponding tone-burst wave packets, wave mixing takes place within a confined area which can be precisely controlled by tuning the wave excitation durations. When local incipient damage falls into the mixing zone, this second harmonic A0 mode wave provides higher damage detectability than the commonly used second harmonic S0 mode wave resulting from the global material nonlinearity. Moreover, through a tactic tuning of the mixing zone size, damage detection can be carried out zone by zone along the transmitter–receiver path to achieve damage localization. Finite element (FE) simulations are first carried out to ascertain the theoretically predicted phenomenon and the underlying generation mechanism of the second harmonic A0 mode Lamb waves. Capitalizing on its mode mixing feature between the primary A0 and S0 mode Lamb waves, a dedicated damage localization strategy alongside the corresponding algorithm is then proposed. Experiments are finally carried out with a dedicatedly designed inspection system with mitigated non-damage-related nonlinear interference. Both FE and experimental results demonstrate the appealing characteristics and the potential of the second harmonic A0 mode Lamb waves for local incipient damage detection and localization.

Location of micro-cracks in plates using time reversed nonlinear Lamb waves**Project supported by the National Key Research and Development Program of China (Grant No. 2016YFF0203000), the State Key Program of the National Natural Science Foundation of China (Grant No. 11834008), the National Natural Science Foundation of China (Grant No. 11774167), the Fund from the State Key Laboratory of Acoustics, Chinese

A promising tool to detect micro-cracks in plate-like structures is used for generating higher harmonic Lamb waves. In this paper, a method combining nonlinear S0 mode Lamb waves with time reversal to locate micro-cracks is presented and verified by numerical simulations. Two different models, the contact acoustic nonlinearity (CAN) model and the Preisach–Mayergoyz (PM) model, are used to simulate a localized damage in a thin plate. Pulse inversion method is employed to extract the second and fourth harmonics from the received signal. Time reversal is performed to compensate the dispersion of S0 mode Lamb waves. Consequently, the higher harmonics generated from the damaged area can be refocused on their source. By investigating the spatial distribution of harmonic wave packets, the location of micro-cracks will be revealed. The numerical simulations indicate that this method gives accurate locations of the damaged area in a plate. Furthermore, the PM model is proved to be a suitable model to simulate the micro-cracks in plates for generation of higher harmonics.

A Preliminary Numerical Study on the Interactions Between Nonlinear Ultrasonic Guided Waves and a Single Crack in Bone Materials With Motivation to the Evaluation of Micro Cracks in Long Bones

Fatigue damage in a bone occurs in the form of micro-scale cracks with the lengths as small as to a few microns. The evaluation of cracks in bones has recently been a hot topic. However, the current most frequently used method is based on traditional linear ultrasound, which is just sensitive to gross damages rather than micro cracks. Nonlinear ultrasonic technique, which is capable of detecting micro-scale damages, has been widely used in metallic structures. However, few study has been directed to employing second harmonic generation of nonlinear ultrasound to evaluate fatigue damages in bones. In this study, a preliminary study is conducted on the interactions between nonlinear guided waves and a single crack in bone materials motivating to the evaluation of micro cracks in long bones. Considering the symmetry, asymmetry, location, orientation, length and width of the crack in bone materials, their influences on second harmonic responses are discussed in detail. Our results are presented as follows. Firstly, not only the primary S0 but also A0 mode Lamb wave generates the second harmonic component of S0 mode after interacting with a symmetric crack. Secondly, along the thickness direction, the primary S0 mode Lamb wave possesses almost the same detection sensitivity, no matter where the crack is located. Thirdly, the amplitudes of S0 mode second harmonic component are increased slightly when the oblique angle of the crack is set from 0°to 45°, while the amplitudes increase dramatically when the oblique angle changes to 67.5° and 90°. Lastly, the second harmonic amplitude and the relative acoustical nonlinear parameter are increased with the length of the crack, while they possess a monotonically decreasing relationship with the width of the crack. Our preliminary studies will provide priori knowledge when using nonlinear ultrasonic guided waves for detecting micro-scale cracks in long bones in future clinical inspections.

Micro-crack detection of nonlinear Lamb wave propagation in three-dimensional plates with mixed-frequency excitationyg**Project supported by the National Natural Science Foundation of China (Grant Nos. 61571222, 61602235, and 11474160) and the Six Talent Peaks Project of Jiangsu Province, China.

We propose a nonlinear ultrasonic technique by using the mixed-frequency signals excited Lamb waves to conduct micro-crack detection in thin plate structures. Simulation models of three-dimensional (3D) aluminum plates and composite laminates are established by ABAQUS software, where the aluminum plate contains buried crack and composite laminates comprises cohesive element whose thickness is zero to simulate delamination damage. The interactions between the S0 mode Lamb wave and the buried micro-cracks of various dimensions are simulated by using the finite element method. Fourier frequency spectrum analysis is applied to the received time domain signal and fundamental frequency amplitudes, and sum and difference frequencies are extracted and simulated. Simulation results indicate that nonlinear Lamb waves have different sensitivities to various crack sizes. There is a positive correlation among crack length, height, and sum and difference frequency amplitudes for an aluminum plate, with both amplitudes decreasing as crack thickness increased, i.e., nonlinear effect weakens as the micro-crack becomes thicker. The amplitudes of sum and difference frequency are positively correlated with the length and width of the zero-thickness cohesive element in the composite laminates. Furthermore, amplitude ratio change is investigated and it can be used as an effective tool to detect inner defects in thin 3D plates.

A Microcrack Location Method Based on Nonlinear S0 Mode Lamb Wave and Probability Scan Positioning Imaging Matrix

Early damage, such as microcrack, occupies most of the fatigue life of materials, and timely detection of early damage and positioning has great engineering and economic value. In this paper, a matrix scanning and positioning imaging method based on a probabilistic algorithm is proposed. Cooperating with the single-mode (S0) lamb wave, the microcrack in the thin plate material can be efficiently positioned. Taking the S0 mode lamb wave as the fundamental wave can effectively reduce the influence of the dispersion effect on the signal analysis. Meanwhile, in order to reduce the noise interference, the signal is reconstructed by empirical mode decomposition (EMD) to achieve the filtering effect. Then, the ABAQUS finite element simulation software is used to compare the positioning results under different locations of microcrack and different arrangements of probe. Finally, the feasibility of the localization algorithm is verified by the RAM-5000 SNAP nonlinear ultrasound system. The experimental results are consistent with the simulation theory, and the microcrack is effectively positioned. This facilitates our timely remedial action or further assessment of the remaining value of the material.

New nonlinear ultrasonic method for material characterization: Codirectional shear horizontal guided wave mixing in plate

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.

Early monitoring of gas influx of drilling fluid in risers during deepwater drilling using Lamb waves

Early warning of gas in deepwater drilling risers is critical to the timely detection of seepage and consequently blowout reduction. We numerically simulate the acoustic field in water-based drilling fluids from a sound source outside the riser by using a 3D cylindrical coordinates finite-difference method. By changing the gas content of the drilling fluid, the relation between the amplitude and attenuation of the A0- and the S0-mode Lamb waves in the riser, the fluid properties in the pipe, and the position of the top and bottom interfaces of the slug flow were assessed. The simulation results suggests that the amplitude and attenuation of the Lamb waves reflect the gas content in the riser and are sensitive to low gas content. Moreover, the Lamb waves amplitude and attenuation reflect the position of the top and bottom interface of the slug flow.

Clamping Resonators for Low-Frequency S0 Lamb Wave Reflection

A recent elastic metamaterial study found that resonators that “clamp” a plate waveguide can be used to create a frequency stop-band gap. The result was that the resonator array can prohibit the propagation of an A0 Lamb wave mode. This study investigates whether the concept can be extended to S0 Lamb wave modes by designing resonators that can prohibit the propagation of S0 Lamb wave modes in a 1-mm aluminum plate waveguide at 50 kHz. The frequency-matched resonators did not reduce the transmitted signal, leading to the conclusion that the design concept of frequency-matched resonators is not always effective. On the other hand, the resonators designed to clamp the upper surface of the plate were very effective and reduced the transmitted signal by approximately 75%.

Damage Localization in Composite Laminates by Building in PZT Wafer Transducers: A Comparative Study with Surface‐Bonded PZT Strategy

Lamb waves provide sensitive and effective approach for nondestructive inspection of large‐scale composite structures. Traditionally in Lamb wave‐based damage detection systems, the piezoelectric (PZT) wafer transducers are attached on the surface of composite components. However, surface‐bonded PZT wafers are fragile, and they may lose serviceability when external load happens. In this paper, numerical and theoretical investigations are firstly carried out to analyze the Lamb wave features generated by PZT wafers that are located in the mid‐thickness of a thin‐walled plate. Subsequently, the authors integrate the PZT wafer arrays in woven glass fiber reinforced epoxy (WGF/epoxy) laminates with stacking sequence of [90°/0°]4. It is found that the approximate single S0 Lamb wave mode is generated by the built‐in PZT wafers. This makes the received signals very simple and easy to be interpreted. Utilizing the signals obtained by the built‐in and surface‐bonded PZT wafer transmitter‐receiver arrays, damage localization algorithms that considered the slowness profiles are compiled to help locating the defects. The compared results demonstrate that the built‐in PZT strategy has great potential for quantitative non‐destructive evaluation of composite structures.

Constrained optimization of a meander line EMAT generating S0 mode Lamb waves with genetic algorithms

In this work a multiphysics model of a meander line electromagnetic acoustic transducer (EMAT) to generate S0 mode Lamb waves in an aluminum plate is built and the structural parameters of the transducer are optimized based on the model. Three approa

Experimental and Numerical Study of Nonlinear Lamb Waves of a Low-Frequency S₀ Mode in Plates with Quadratic Nonlinearity.

This paper investigates the propagation of low-frequency S0 mode Lamb waves in plates with quadratic nonlinearity through numerical simulations and experimental measurements. Both numerical and experimental results manifest distinct ultrasonic nonlinear behavior which is mainly presented by the second harmonics. Meanwhile, we find that both the acoustic nonlinearity parameter and dispersion distance show the exponential decay trend with the increase of frequency-thickness. Moreover, the results reveal that the frequency is key to affect the acoustic nonlinearity parameter and dispersion distance with the same frequency-thickness. This study theoretically and experimentally reveals that nonlinear Lamb waves of the low-frequency S0 mode are feasible to quantitatively identify material weak nonlinearity in plates.

Design of nonlinear-Lamb-wave-based structural health monitoring systems with mitigated adhesive nonlinearity

Structural health monitoring (SHM) techniques with nonlinear Lamb waves offer the possibility of detecting incipient damages through the second harmonic generation. Particularly, the primary S0-secondary S0 Lamb wave mode pair in a weakly nonlinear plate is promising for SHM due to its appealing characteristics such as the cumulative second harmonic generation and flexible frequency selection. In a practical PZT-actuated SHM system, apart from the damage-related material nonlinearity of the plate (MNP), the adhesive nonlinearity (AN) is also proven to be a non-negligible nonlinear source, which may jeopardize damage diagnosis if not properly apprehended. By combining a nonlinear shear-lag model and the normal mode expansion method, a theoretical model is proposed in this work, which allows the investigation and the comparison of these two types of important nonlinearities in the system (AN and MNP). With the developed model, optimized nonlinear Lamb wave-based SHM systems can be designed with the mitigated influence of the undesired AN on the system. Finite element (FE) simulations are carried out to validate the proposed model and the effectiveness of the optimized systems through a tactical adjustment of the different nonlinear sources. The designed optimized system is verified by experiments, in comparison with an arbitrarily chosen one. The dominance level of the nonlinear sources in the two systems is evaluated through changing the MNP, which is realized by a thermal aging treatment. Both FE and experimental results demonstrate that the proposed model can effectively guide the design of SHM systems to mitigate AN so that the MNP can be well measured and further used as an indicator of the incipient structural damage.