Mixing of ultrasonic Lamb waves in thin plates with quadratic nonlinearity

Eliminating undesired high order harmonics in guided ultrasonic waves using local anti-resonance

A method utilizing the previously unexplored local anti-resonance phenomenon in a Flat Bottom Hole (FBH) is developed to eliminate the interference nonlinearity from undesired sources and enable the precise measurement of ultrasonic nonlinearity from material defects. The local anti-resonance phenomenon in an FBH is investigated using finite element method, on which basis the method to suppress the high order harmonics in incident waves is developed. The effectiveness of the method is validated through the experimental detection of a nonlinear scatterer and comparison with results from traditional configurations. The proposed method demonstrates the capability to precisely and reliably measure defect-specific ultrasonic nonlinearity, thereby advancing the application of the material characterization methods utilizing ultrasonic nonlinearity.

Meta-structure enhanced second harmonic S0 waves for material microstructural changes monitoring

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.

Second Harmonic Modulation for Ultrasonic Signals Based on the Design of the Phononic Crystal Filter

Nonlinear ultrasonic non-destructive testing (NDT) is a widely used method for detecting micro-damages in various materials and structures due to its high sensitivity and directional capability. However, the extraction and modulation of extremely weak nonlinear ultrasonic signals is quite a challenge in practical applications. Therefore, this paper focuses on the second harmonic modulation signal method in nonlinear ultrasonic NDT and proposes the design of the phononic crystal filter (PC filter) to achieve this filtering function. Through finite element simulations, it is demonstrated that the filtering frequency of the filter is influenced by the structural configuration, material wave speed, and geometric characteristics. Then, the design method for cubic PC filters is established. Furthermore, a time-domain finite element method is introduced to verify the filtering ability of the filter and further validate the rationality of this design approach.

Evaluating Structural Details' Influence on Elastic Wave Propagation for Composite Structures via Ray Tracing

This study presents a novel method based on ray tracing for analyzing wave propagation in composites specifically tailored for structural health monitoring applications. This method offers distinct advantages over the commonly used finite element method mainly in computational resource utilization, which has become a limiting factor for these kinds of analyses. The ray tracing method is evaluated against a number of example cases representing structural details such as thickness changes, stringers, or simulated damage, and the significance of ray tracing to study wave propagation under these conditions and how it can serve as a valuable tool for structural health monitoring are highlighted. This model has been developed as part of a complete SHM framework with the intention of being an efficient and simple way to calculate wave propagation and therefore it could be used as a way to determine relevant damage indicators or train an artificial intelligence model.

A multi-GPU and CUDA-aware MPI-based spectral element formulation for ultrasonic wave propagation in solid media

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.

One-way Lamb and SH mixing method in thin plates with quadratic nonlinearity: Numerical and experimental studies

This paper numerically and experimentally investigates the resonant behavior of one-way Lamb and SH (shear horizontal) mixing method in thin plates with quadratic nonlinearity. When the primary S₀-mode Lamb waves and SH₀ waves mix in the region with quadratic nonlinearity, both numerical and experimental results verify the generation of the resonant SH₀ waves if the resonance condition [Formula: see text] is satisfied. Meanwhile, we find that the acoustic nonlinear parameter (ANP) increases monotonously with material quadratic nonlinearity, the length of the damage region and the frequency of the resonant wave. Furthermore, the damage region can be located by the time-domain signal of the resonant wave based on one-way S₀-SH₀ mixing method. This study numerically and experimentally reveals that one-way Lamb and SH mixing method is feasible to quantitatively evaluate and locate the damage region of quadratic nonlinearity in thin plates.

A Feasibility Study for a Nonlinear Guided Wave Mixing Technique

Ultrasonic non-destructive testing is an effective means of examining objects without destroying them. Among such testing, ultrasonic nonlinear evaluation is used to detect micro-damage, such as corrosion or plastic deformation. In terms of micro-damage evaluation, the data that comes from amplitude comparison in the frequency domain plays a significant role. Its technique and parameter are called ultrasonic nonlinear technique and nonlinearity. A certain portion of nonlinearity comes from the equipment system, while the other portion of nonlinearity comes from the material. The former is system nonlinearity, while the latter is material nonlinearity. System nonlinearity interferes with interpretation, because its source is not from the material. In this study, in order to minimize system effects, a mixing technique is implemented. To use the large area inspection ability of the guided wave, the main research issue in this paper is focused on the guided wave mixing technique. Moreover, several bulk wave mixing theory equations become good concepts for guided wave mixing theoretical study, and the conventional nonlinear technique and guided wave mixing experimental results are compared in this study to confirm the reliability. This technique can play an important role in quantitatively discriminating fine damage by minimizing the nonlinearity of the equipment system.

Experimental and Numerical Investigation of the Micro-Crack Damage in Elastic Solids by Two-Way Collinear Mixing Method

This study experimentally and numerically investigated the nonlinear behavior of the resonant bulk waves generated by the two-way collinear mixing method in 5052 aluminum alloy with micro-crack damage. When the primary longitudinal and transverse waves mixed in the micro-crack damage region, numerical and experimental results both verified the generation of resonant waves if the resonant condition ωL/ωT=2κ/(κ−1) was satisfied. Meanwhile, we found that the acoustic nonlinearity parameter (ANP) increases monotonously with increases in micro-crack density, the size of the micro-crack region, the frequency of resonant waves and friction coefficient of micro-crack surfaces. Furthermore, the micro-crack damage in a specimen generated by low-temperature fatigue experiment was employed. It was found that the micro-crack damage region can be located by scanning the specimen based on the two-way collinear mixing method.

Impact Damage Detection in Patch-Repaired CFRP Laminates Using Nonlinear Lamb Waves

Carbon fiber-reinforced polymer (CFRP) laminates, a key composite material, are widely used in aircraft structures and are susceptible to low-velocity impact (LVI) damage from bird strikes, lightning strikes, hail impacts and other situations. Therefore, finding a method that repairs the damaged structure and detects the effect of these repairs under LVI is a very important goal. In this work, the repair effect of LVI damage in CFRP laminates repaired with patches of various sizes is investigated via experimental and numerical nonlinear Lamb wave analyses. An integrated numerical procedure that combines LVI with nonlinear Lamb wave detection is developed to predict the nonlinear Lamb wave behavior in LVI-damaged patch-repaired CFRP laminates. The CFRP laminate damage in the nonlinear Lamb wave simulation is evaluated based on relative acoustic nonlinearity parameters (RANPs). As a result, the integrated numerical procedure is validated with drop-weight impact tests and RAM-5000 SNAP nonlinear ultrasonic detection system. An optimal patch design is established via interpolation to optimize the absorbed energy, delamination surface area, second RANP and third RANP with different patch repair sizes. These parameters exhibit consistent curve fitting trends, indicating that they can be used as important indicators of impact damage. The optimal circular patch design with a radius of 2.5 r has better impact resistance behavior and repair performance.

Analytical and numerical investigations of one-way mixing of Lamb waves in a thin plate

This paper derives the resonance conditions for one-way resonant mixing of nonlinear Lamb waves. Two mode triplets are identified that satisfy such resonance conditions. It is also found that, when the primary waves are pulses of finite duration, the signal envelope of the corresponding resonant mixed wave is either a diamond or an elongated hexagon. The dimensions of these shapes are obtained explicitly in terms of the pulse lengths and group velocities of the Lamb modes in the mode triplet. These analytical results are verified by numerical simulations using the finite element method. Finally, a nondestructive evaluation method based on one-way mixing of Lamb waves is proposed for the inspection of a large area of a plate for damage distribution via a single access point. Numerical simulations of this nondestructive evaluation technique are conducted. It is found that using shorter pulses gives better spatial resolution, thus better suited for locating and sizing the damage zone, while using longer pulses gives a higher signal to noise ratio, thus better suited for quantifying the degree of damage in the damage zone. Results of this paper clarify some of the confusion in the existing literature regarding the resonance conditions for one-way mixing of nonlinear Lamb waves. They also provide a better understanding of the physical characteristics of the resonant mixed wave. Such understanding enables the design of optimal measurement systems for one-way mixing of Lamb waves for the purpose of conducting large area nondestructive evaluation of plate-like structures from a single access point. This proposed one-way mixing nondestructive evaluation technique can be extended to pipes.

The research on propagation characteristics of acoustic emission signals in stiffened plates based on the multipath propagation model

Mechanical equipment with the stiffener has a strong interference with the propagation of acoustic emission (AE) signals from faults, reducing the accuracy of fault detection. This paper conducts an in-depth study of the interaction between AE signals and the stiffener. The installation constraints, that can separate the direct signal, signals scattered from the stiffener and signals reflected from the boundary in the time domain, for sensors are deduced based on the multipath propagation model of AE signals in the stiffened plate. On this basis, the scattering characteristics of AE signals with different frequencies in different height stiffened plates are predicted by simulations. Moreover, the reflection and transmission coefficients are calculated to quantify the scattering characteristics. The results show that the signal, undergoing a "T-shaped" transformation at the stiffener, generates various modes, among which the transmission signal accounted for the largest proportion. In addition, experiments are performed to verify the numerical simulations, and the results are in good agreement with the numerical simulations. This work clarifies the propagation characteristics of AE signals in stiffened plates, and the research can optimize the spatial arrangement for sensors.

Characterization of Microcrack Orientation Using the Directivity of Secondary Sound Source Induced by an Incident Ultrasonic Transverse Wave

In this paper, characterization of the orientation of a microcrack is quantitatively investigated using the directivity of second harmonic radiated by the secondary sound source (SSS) induced by the nonlinear interaction between an incident ultrasonic transverse wave (UTW) and a microcrack. To this end, a two-dimensional finite element (FE) model is established based on the bilinear stress–strain constitutive relation. Under the modulation of contact acoustic nonlinearity (CAN) to the incident UTW impinging on the microcrack examined, the microcrack itself is treated as a SSS radiating the second harmonic. Thus, the directivity of the second harmonic radiated by the SSS is inherently related to the microcrack itself, including its orientation. Furthermore, the effects of the stiffness difference between the compressive and tensile phases in the bilinear stress–strain model, and the UTW driving frequency, as well as the radius of the sensing circle on the SSS directivity are discussed. The FE results show that the directivity pattern of the second harmonic radiated by the SSS is closely associated with the microcrack orientation, through which the microcrack orientation can be characterized without requiring a baseline signal. It is also found that the SSS directivity varies sensitively with the driving frequency of the incident UTW, while it is insensitive to the stiffness difference between the compressive and tensile phases in the bilinear stress–strain model and the radius of the sensing circle. The results obtained here demonstrate that the orientation of a microcrack can be characterized using the directivity of the SSS induced by the interaction between the incident UTW and the microcrack.

Nonlinear Lamb Wave Micro-Crack Direction Identification in Plates with Mixed-Frequency Technique

This paper investigates the direction identification of micro-cracks with nonlinear components generated by Lamb wave with frequency-mixing technique. Three-dimensional finite element simulations were carried out to investigate the interaction mechanism between Lamb wave signals and micro-cracks. Upon re-visiting the conventional Lamb wave excitation signal with two kinds of fundamental frequencies (f1 and f2), it was found to be possible to generate new types of frequencies (f1 ± f2) at the sideband if nonlinear sources existed in the plate. A pulse inversion method was used to extract the sideband frequency for nonlinear ultrasonic detection. By arranging piezoelectric chip arrays around the micro-crack, the acoustic nonlinearity parameter β related to the fundamental frequency and the sideband frequency for different micro-crack directions was calibrated. It was shown that β varied for different crack directions, which provides useful information about the scattering features of the nonlinear Lamb wave interacting with the micro-crack to characterize its directivity. Moreover, the scattering degree defined with the relative nonlinear parameter β′ of the micro-crack in different directions was investigated in detail by changing the size of the micro-crack. The outcomes showed that the forward scattering signal of the crack had a greater amplitude, whereas the backscattering signal had a smaller amplitude compared with the scattering signals in other directions from micro-cracks. In addition, the signal scattering degree in the forward direction from micro-cracks increased with the increasing micro-crack length, but decreased with increasing crack width. Furthermore, for the buried crack, the forward scattering degree of Lamb wave from micro-crack decreased as crack was buried deeper in plate. In summary, the findings of this study can help to further advance the use of nonlinear Lamb wave with the frequency-mixing technique for identifying the direction of micro-cracks.

Propagation of Non-Linear Lamb Waves in Adhesive Joint with Micro-Cracks Distributing Randomly

With the advantages of uniform stress transfer and weight reduction, adhesive joints are widely used in engineering. The propagation of non-linear Lamb waves in an adhesive joint with micro-cracks distributing in a random way is systematically investigated by using the numerical simulation method in this paper. A finite element model of the tri-layer adhesive structure with micro-cracks distributing randomly is established, and the Lamb wave mode pair with a matching condition of the phase velocity is chosen to examine the interaction of the micro-cracks with Lamb waves. The results show that the micro-cracks within the adhesive layer will lead to the generation of second harmonics. We also find that the Acoustic Non-linearity Parameters (ANP) increase with the propagation distance in the micro-crack damage zone and the density of the micro-cracks. However, ANPs are less concerned with the friction coefficients of the surface of micro-cracks. This numerical research reveals that non-linear Lamb waves can be employed to effectively characterize the micro-cracks related damages within an adhesive joint.

A Study on Fatigue State Evaluation of Rail by the Use of Ultrasonic Nonlinearity

Nonlinear ultrasonic testing has been accepted as a promising manner for evaluating material integrity in an early stage. Stress fatigue is the main threats to train safety, railways examinations for stress fatigue are more significant and necessary. A series of ultrasonic nonlinear wave experiments are conducted for rail specimens extracted from railhead with different degree of fatigue produced by three-point bent loading condition. The nonlinear parameter is the indicator of nonlinear waves for expressing the degree the fatigue. The experimental results show that the sensitivity of a third harmonic longitudinal wave is higher than second harmonic longitudinal wave testing. As the same time, collinear wave mixing shows strong relative with fatigue damages than a second longitudinal wave nondestructive testing (NDT) method and provides more reliable results than third harmonic longitudinal waves nonlinear testing method.

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.

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.