S0 Mode Waves Research Articles

Atypical second harmonic A0 mode Lamb waves in non-uniform plates for local incipient damage monitoring

Plates with non-uniform thickness, such as stiffened and notched plates, are commonly seen in engineering applications. Monitoring incipient damage in these structures is crucial to ensure their safety during service. Second harmonic Lamb waves hold great promise for structural health monitoring applications. However, the mechanisms underpinning the generation of the second harmonic Lamb waves in non-uniform plates are still not well understood due to the complex wave field. To tackle this issue, a theoretical analysis is first conducted to highlight the so-called atypical second harmonic A0 mode waves (2nd A0 waves) generated at the structural non-uniform section. Their existence, as well as their potential for local incipient damage monitoring applications, is then confirmed by finite element simulations. Experiments are carried out on a notched aluminum plate to monitor the incipient plastic damage induced by bending. Three mechanisms contributing to the generation of the atypical 2nd A0 waves in the non-uniform plate are identified: mode conversion from the second harmonic S0 mode waves, asymmetric nonlinear driving forces at the non-uniform section, and the mutual interaction between the mode-converted fundamental A0 and S0 waves. This study shows that the reported atypical 2nd A0 waves provide an effective means for monitoring local incipient damage in non-uniform structures.

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.

High-Precision Corrosion Detection via SH1 Guided Wave Based on Full Waveform Inversion.

Corrosion detection for industrial settings is crucial for safe and efficient operations. Due to its high imaging resolution, the guided-wave full-waveform inversion tomography technique has significant potential for corrosion detection of plate metals. Limited by the long wavelengths of A0 and S0 mode waves, this method exhibits inadequate detection resolution for the earlier shallow and small corrosion defects. Based on the relatively short wavelength characteristics of the SH1 mode wave, we propose a high-precision corrosion detection method via SH1 guided wave using the full waveform inversion algorithms. By conducting finite element simulations of ultrasonic-guided waves on aluminum plates with varying corrosion defects, a comparison was made to assess the detection precision across A0, S0, and SH1 modes. The comparison results showed that, whether for regular or irregular defects, the SH1 mode wave always exhibited higher imaging accuracy than the A0 and S0 mode waves for shallow and small-sized defects. The corresponding experiments were conducted on an aluminum plate with simple or complex defects. The results of the experiments reconfirmed that the full waveform inversion method using SH1 guided wave can effectively reconstruct the shape and size of small and shallow corrosion defects within aluminum plates.

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.

One-way Lamb mixing method in thin plates with randomly distributed micro-cracks

It is crucial to detect and evaluate early material degradation caused by micro-cracks in key engineering structures. This paper investigates the resonant behavior of one-way Lamb mixing waves in thin plates with randomly distributed micro-cracks by numerical simulations. It is found that when the resonance condition ωS0/ωA0=2κ/(κ+1) is satisfied, a resonant A0 mode wave can be generated by a pair of A0 and S0 mode waves mixed in the micro-crack damage region. Meanwhile, it is manifested that the acoustic nonlinearity parameter increases with the crack density and the length of the micro-crack region, which is also related to the resonant frequency. Furthermore, it is proven that the location of the micro-crack region can be determined by the time-domain signals of the resonant wave. This study numerically reveals that the one-way Lamb mixing method is feasible to quantitatively identify micro-crack damage in thin plates.

Characterizing excitability of Lamb waves generated by electromagnetic acoustic transducers with coupled frequency domain models

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.

A Boundary Element Model for Structural Health Monitoring Based on the S0 Lamb Wave Mode

The aim of this paper was to carry out numerical simulations of structural health monitoring applications for plate structures using the boundary element method (BEM). The fundamental symmetric Lamb mode (S0) is chosen for the SHM applications. The propagation, reflection and diffraction of the S0 mode Lamb wave are modelled using a boundary element formulation based on the plane stress theory. Piezoelectric (PZT) actuators are mounted on plate surfaces to excite the S0 mode wave. A semi-analytical method is adopted to couple the PZT actuators and the host plate. Numerical results show that BEM is a very efficient simulation method for the structural health monitoring of plates.

Interaction of Lamb Wave Modes with Weak Material Nonlinearity: Generation of Symmetric Zero-Frequency Mode

The symmetric zero-frequency mode induced by weak material nonlinearity during Lamb wave propagation is explored for the first time. We theoretically confirm that, unlike the second harmonic, phase-velocity matching is not required to generate the zero-frequency mode and its signal is stronger than those of the nonlinear harmonics conventionally used, for example, the second harmonic. Experimental and numerical verifications of this theoretical analysis are conducted for the primary S0 mode wave propagating in an aluminum plate. The existence of a symmetric zero-frequency mode is of great significance, probably triggering a revolutionary progress in the field of non-destructive evaluation and structural health monitoring of the early-stage material nonlinearity based on the ultrasonic Lamb waves.

A Fatigue Crack Size Evaluation Method Based on Lamb Wave Simulation and Limited Experimental Data.

This paper presents a systematic and general method for Lamb wave-based crack size quantification using finite element simulations and Bayesian updating. The method consists of construction of a baseline quantification model using finite element simulation data and Bayesian updating with limited Lamb wave data from target structure. The baseline model correlates two proposed damage sensitive features, namely the normalized amplitude and phase change, with the crack length through a response surface model. The two damage sensitive features are extracted from the first received S0 mode wave package. The model parameters of the baseline model are estimated using finite element simulation data. To account for uncertainties from numerical modeling, geometry, material and manufacturing between the baseline model and the target model, Bayesian method is employed to update the baseline model with a few measurements acquired from the actual target structure. A rigorous validation is made using in-situ fatigue testing and Lamb wave data from coupon specimens and realistic lap-joint components. The effectiveness and accuracy of the proposed method is demonstrated under different loading and damage conditions.

ラム波によるＣＦＲＰ板の非破壊検査

In order to improve the reliability and safety of composite materials, it is necessary to have non-destractive testing (NDT) available to detect defects in materials. Although conventional ultrasonic methods have, in principle, been used for NDT, they are inefficient and difficult to inspect large structures, such as ship hulls, because of the high attenuation of ultrasonic waves. In these cases, low frequency waves have an advantage over ultrasonic waves. Therefore, by using low frequency Lamb waves generated by tapping as a means of NDT in composite laminates, the following examinations were made; (1) predicting the thickness of plates, (2) detecting the delamination, (3) predicting the fiber contents in the composite laminates, and (4) measuring the wave velocities depending on propagating directions.(1) and (2) were carried out by using antisymmetric A0 mode waves. The results showed that it was possible to predict the thickness and to detect the delamination based on the relationship between the phase velocities of Lamb waves, which has dispersion characteristics, and the product of frequency and plate thickness. (3) was examined by the resonant method of symmetric S0 mode waves, and (4) was done by S0 waves. The results showed that the fiber content could be predicted from the stationary waves and the wave velocity propagating at an angle to the fiber direction could be calculated from the Young's modulus.