Multimodal Lamb Waves Research Articles

Characterization of viscoelastic moduli and thickness of isotropic, viscoelastic plates using multi-modal Lamb waves

This paper presents an approach exploiting the sensitivity of Lamb waves for characterizing the viscoelastic moduli and thickness of plates. The analytical sensitivity functions are first derived in the case of an isotropic plate and are integrated into an iterative inverse problem to optimize its viscoelastic moduli and thickness based on a zero-finding approach (Gauss–Newton algorithm for a multivariable problem). This method is validated numerically for a viscoelastic plate and shows high accuracy and low computational cost when compared to existing methods. Experimental validation demonstrates the ability of the algorithm to assess simultaneously the viscoelastic moduli and the thickness of isotropic plate-like structures.

Characterization of complex stiffness and thickness of isotropic, viscoelastic plates using multi-modal Lamb waves

This paper presents an approach exploiting the sensitivity of Lamb waves for characterizing the mechanical and geometrical properties of plates. The analytical sensitivity functions are first derived in the case of an isotropic plate and are integrated into an iterative inverse problem to optimize its mechanical and geometrical properties based on a zero-finding approach (Gauss-Newton algorithm for a multivariable problem). This method is validated numerically for a viscoelastic plate and shows high accuracy and low computational cost when compared to existing methods. The design af an experimental setup based on dedicated air-coupled transducers is proposed by optimizing the shape and size of the transducers in order to increase sensitivity of the measred signals with respect to the mechanical parameters of the structure of insterest. Experimental validation demonstrates the ability of the methodto assess simultaneously the viscoelastic properties and the thickness of isotropic plate-like structures.

Robust transport and topological valley refraction of fundamental symmetric lamb waves in perforated phononic crystal plates

Lamb waves can be divided into antisymmetric Lamb waves (type A) and symmetric Lamb waves (type S), which are widely used in health monitoring of engineering structures and nondestructive evaluation of materials. However, due to the fact that each mode of Lamb wave has the setting group velocity in a certain bandwidth range, it is easy to cause the aliasing of multi-mode Lamb waves, partly limiting the application scenarios of Lamb wave. In this paper, a hexagonal lattice meta-structure is designed and the zero-order symmetric (S0) Lamb wave in a finite thickness plate is successfully separated. By breaking the spatial C 3v symmetry, a valley topological phononic crystal (PnC) plate for the pure S0 mode is constructed, and its robust topological transports are demonstrated. Firstly, the valley topological phase transition of S0 mode is realized by changing the angle of scatterer in PnC plate and the valley edge state of S0 mode is obtained. Furthermore, by introducing structural mismatch, it is verified that the edge state of S0 mode is robust to various bends and defect. Finally, by changing the material property of the terminal, the valley refraction with different directionality is realized. The results offer a route to individually study the symmetric modes of Lamb waves, and have potential application prospects in rapid and accurate ultrasonic nondestructive testing based on Lamb waves.

Design and Analysis of Meander Coil Electromagnetic Acoustic Transducer (EMAT) for Multi-mode Lamb Waves in Thin Plate

Design and Analysis of Meander Coil Electromagnetic Acoustic Transducer (EMAT) for Multi-mode Lamb Waves in Thin Plate

Detection and localization of corrosion using identical-group- velocity Lamb wave modes

ABSTRACT Multimodal is the prominent characteristic of Lamb waves, which means a variety of Lamb wave modes propagate in the structure and each of them has unique propagation behaviour. For a wideband multimodal Lamb wave signal, it is possible that many different modes share the same group velocity at some frequency points, while their dispersion behaviours change differently to thickness variation. In this study, the diversity and difference of the interaction between the corrosion and Lamb wave modes are investigated. On this basis, a corrosion index (CI) is established to evaluate the time gap between two modes at their identical group velocity points. The simulation results show that the CI value of a corroded path is obviously larger than that of a healthy path, indicating the presence of the damage, which is independent of any base-line signal. Furthermore, the new reconstruction algorithm for the probabilistic inspection of damage (RAPID) was proposed, where the signal difference coefficient was replaced by the CI to visualise damage location. The experimental results demonstrate the effectiveness of the proposed multimodal Lamb wave baseline-free damage detection method.

A Two-Step Model-Based Reconstruction and Imaging Method for Baseline-Free Lamb Wave Inspection

Traditional Lamb wave inspection and imaging methods heavily rely on prior knowledge of dispersion curves and baseline recordings, which may not be feasible in the majority of real cases due to production uncertainties and environmental variations. In order to solve this problem, a two-step Lamb wave strategy utilizing adaptive multiple signal classification (MUSIC) and sparse reconstruction of dispersion reconstruction is proposed. The multimodal Lamb waves are initially reconstructed in the f-k domain using random measurements, allowing for the identification and characterization of multimodal Lamb waves. Then, using local polynomial expansion and derivation, the phase and group velocities for each Lamb wave mode could be computed. Thus, the steering vectors of all potential scattering Lamb waves for each grid in the scanning area can be established, thereby allowing for the formulation of the MUSIC algorithm. To increase the precision and adaptability of the MUSIC method, the local wave components resulting from potential scatters are extracted with an adaptive window, which is governed by the group velocities and distances of Lamb wave propagation. As a result, the reconstructed dispersion relations and windowed wave components can be used to highlight the scattering features. For the method investigation, both a simulation and experiment are carried out, and both the dispersion curves and damage locations can be detected. The results demonstrate that damage localization is possible without theoretical dispersion data and baseline recordings while exhibiting a considerable accuracy and resolution.

Dispersion compensation of Lamb waves based on a convolutional auto-encoder

Lamb wave-based detection has become a promising technique for structural health monitoring in plate-like structures. However, the dispersion effect of Lamb waves makes the wave packets elongated, which degrades the resolution for damage identification. Hence, it is necessary to develop effective methods for the dispersion removal of Lamb waves. Recently, deep learning has drawn much attention for Lamb wave detection due to its powerful feature extraction capability. Most current deep learning models are developed directly for damage classification or location estimation tasks on the Lamb wave signals, rather than signal processing for further manipulation. Therefore, in this paper, a novel approach based on a convolutional auto-encoder is proposed for the dispersion compensation of Lamb waves. The convolutional auto-encoder model is utilized to construct the mapping relationship between the dispersive signal and the time of flight of the wave packet. The dispersion compensated signal is reconstructed by combining the estimated time of flight from the network with the waveform of the excitation signal. Numerical and experimental validations on aluminum and composite plates are implemented to verify the effectiveness of the proposed method. Compared with conventional methods for dispersion compensation, the results demonstrate that our proposed method not only separates the overlapped wave packets but also enables dispersion compensation of multimodal and multi-packet Lamb wave signals. In addition, this method is still applicable in the case of inaccurate dispersion data due to the generalizability of the data-driven model.

Mode purification for multimode Lamb waves by shunted piezoelectric unimorph array

Guided wave-based nondestructive testing and structural health monitoring methods have been developed to exhibit attractive potentials and best prospects for rapid and sensitive detection of defects or damage in engineering structures. Different modes of guided waves can provide different sensitivities of damage detection. However, the multimode and mode conversion nature of guided waves poses significant challenges to mode purification of received signals. This study aims to design a metamaterial-based smart transducer for mode purification of Lamb waves in a plate, which can filter out an undesired mode of the Lamb wave to enhance sensing and actuating signals of a dominated mode. The smart transducer consists of a periodic array of shunted piezoelectric unimorphs with staggered polarization directions and is bonded on the surface of a host plate. Numerical and experimental results show that a local resonance bandgap for an anti-symmetric Lamb wave, rather than a symmetric Lamb wave, can be obtained and tuned through the shunting inductance circuit. Within such mode bandgap, the wave control for propagating a specific mode of the Lamb wave can be further realized, i.e., the mode of the Lamb wave is purified. The design presented herein offers enhanced capabilities in controlling guided wave propagation for engineering applications and nondestructive testing techniques.

Tunable asymmetric transmission of Lamb waves in piezoelectric bimorph plates by electric boundary design

The multi-mode and dispersion natures of elastic guided waves bring big challenges for wave manipulation, and also provide more possibilities for smart device design. In this study, a piezoelectric bimorph plate connected to a periodic arrangement of electric circuits is proposed, and both propagating and evanescent guided Lamb waves are investigated through the complex band structure resulting form using different shunting capacitor or inductor distributions. Results show that keeping and breaking the symmetry of the electric boundary condition can, respectively, lead to decoupling or hybridizing of multi-mode Lamb waves. Accordingly, the asymmetric transmission at a desired frequency can be realized by combining the symmetric and asymmetric electric boundary conditions. Harmonic analysis shows that numerical results are in good agreement with the prediction of complex band structure. Actively changing the electric boundary conditions can be used for guided wave propagation in piezoelectric bimorph plates to easily control the system without changing the structure’s geometry. The framework presented herein offers enhanced capabilities for controlling guided wave propagation for engineering applications and to develop nondestructive testing techniques.

Recurrence analysis of friction based dry-couplant ultrasonic Lamb waves in plate-like structures

In this study, the effect of friction on the generation of dry-coupled Lamb waves is experimentally investigated. Recurrence analysis is performed to analyze the complex behavior of friction based dry-coupled Lamb waves. In particular, the effect of the normal force, which is necessary for a stronger dry-coupled Lamb wave generation and the friction, on the transmission of mechanical energy and determinism characteristics of Lamb waves are investigated. The results verify that larger friction coefficient and friction force are crucial for generation and propagation of strong Lamb waves supporting the fact that the main mechanism to transfer mechanical energy using dry-couplant is friction. The sensitivity of Lamb waves to the friction coefficient, highlights the importance of designing specific pads with respect to condition of the surface. Besides, the results show that the normal force and friction coefficient can change the determinism characteristics behavior of multimode Lamb waves. Furthermore, it is shown that the determinism value is sensitive to the friction coefficient and normal force. A similar trend is observed in the determinism values and friction coefficient. In general, a smaller friction coefficient indicates smaller determinism value. Additionally, it is shown that a normal load can change the behavior of a system, as observed from recurrence plots, owing to changes in the Lamb waves trajectories in the phase-space domain. In addition, it is shown that recurrence plots enable the detection of mode transitions in multimode Lamb waves. Recurrence analysis is a complementary tool to frequency domain methods for accurate analysis of multimode Lamb waves behavior.

A Novel Single-Mode Lamb Wave Generation Method for Crack Localization of Beam Structures

Structure health monitoring of beam structures is important in civil and mechanical engineering. Lamb waves have the advantages of long propagation distance and low power loss, which are widely used in the field of nondestructive testing. However, Lamb waves generated via conventional methods usually contain multiple modes, and in many cases, the multi-mode Lamb waves cause difficulties in damage detection and localization. This research proposes a novel single-A<SUB>0</SUB> mode Lamb wave generation technique; the actuator is attached on the side surface of a beam structure, and the sensor is attached on the top or bottom surface, which is perpendicular to the side surface, such that the single-A<SUB>0</SUB> mode of the Lamb wave can be generated. Due to the mode conversion effect of the Lamb wave when it passes through a crack, the existence of the crack can be determined by evaluating the existence of the S<SUB>0</SUB> mode. In addition, the crack can be localized accurately using the proposed algorithm. Numerical and experimental investigations are performed to verify the performance of the proposed method. Comparisons with other single-mode Lamb wave generation methods are also performed to validate the advantages of the proposed method.

A novel time–frequency transform for broadband Lamb waves dispersion characteristics analysis

Owing to carrying rich information about structure flaws, broadband Lamb waves are considered as a promising tool for non-destructive testing. However, since every Lamb wave mode has its own dispersion characteristics, the feature extraction among broadband multimodal Lamb wave is challenging. Time–frequency representation is significantly effective to analyze dispersive signals. In this article, taking advantages of the idea of dispersion compensation, two kinds of time–frequency domain dispersion analysis methods for broadband Lamb wave were proposed. The first one is based on the concept of the general parameterized time–frequency transform. A kernel function related to group delay was designed and the time–frequency compensation transform was proposed. The other one combines the segment linear mapping technique and the short-frequency Fourier transform, called the time–frequency de-dispersion transform. Both these two methods work well in representing multimodal Lamb wave signals with high resolution. However, time–frequency de-dispersion transform outperforms in representing multipath Lamb waves than time–frequency compensation transform. Moreover, a mode purification strategy was also proposed for distinguishing the interested mode from interferences. According to verification in synthetic and experimental data, not only the multimodal components but also multipath echoes are represented in time–frequency plane with high resolution. Finally, the proposed method shows a great robustness to inaccuracies in the dispersion data.

A Damage Localization Method With Multimodal Lamb Wave Based on Adaptive Polynomial Chirplet Transform

Ultrasonic Lamb wave testing allows health monitoring for plate structures and has been extensively applied in the modern industry. To obtain the location and further form the damage imaging, the time of flight (TOF) is a pivotal parameter. However, the dispersive and multimodal nature of the Lamb wave obstructs the accurate measurement of TOF. The objective of this article is to develop efficient techniques to separate multimodal Lamb wave signals and accomplish accurate damage localization. The narrowband Lamb wave is generated by the excitation signal with a center frequency of 150 kHz. The fundamental symmetric and antisymmetric modes are exploited. The adaptive polynomial chirplet transform (CT) is proposed to decompose the Lamb wave signals and identify the modes. Then, the instantaneous frequency characteristics are utilized to extract time information. Thus, the TOF is obtained and damage location can be calculated. The reconstruction error is defined to quantitate the difference between the reconstructed signal and the received signal. The obtained reconstruction errors from the simulation and experiment are 0.1631 and 0.2875, respectively. The varied defect location is adopted to obtain the TOF estimation. The results show that the proposed method outperforms the CT and cross correlation, especially for the longer propagation distances where the dispersion effect is distinct. For experiments considering the defect and boundary reflection, the localization errors of the collinear defect are 2.51% and 3.04% for the two Lamb wave modes. In comparison with smoothed-pseudo-Wigner–Ville distribution and CT, the proposed method owns superior performance on mode identification and location accuracy.

A parameter estimation based sparse representation approach for mode separation and dispersion compensation of Lamb waves in isotropic plate

A response Lamb wave is usually a combination of dispersive wave packets corresponding to different modes, and the explicit dispersion curves are hard to acquire accurately sometimes. A parameter estimation based sparse representation approach is established to extract each pure single-mode component with dispersion removal from the dispersive multi-mode Lamb waves. The dispersion characteristic parameters of the Lamb modes are extracted from a response Lamb wave with a known propagation distance using a parameter estimation algorithm. A parametric dictionary is designed to sparsely decompose the dispersive multi-mode Lamb waves, and those parameters used for constructing the dictionary are extracted from a response signal based on a Lamb wave propagation model. In the process of reconstructing each mode component, the original dictionary is replaced with a multi-mode and non-dispersive dictionary so that the dispersion effect can be removed. Results from simulations and experiments both verify the effectiveness of the proposed approach.

A hidden corrosion detection method based on robust multimodal Lamb waves

A Lamb wave is a kind of elastic wave propagating in a plate-like structure with stress distributing through the whole thickness of the plate. A Lamb wave is multimodal, and each mode has unique through-plate-thickness stress profiles, called wave structure. The existence of a specific structure flaw at a certain position in the thickness direction will weaken the ability of the plate to support a specific component of stress, which means each Lamb wave mode would interact with structure flaws in a different way, or that each Lamb wave mode has a unique sensitivity to flaws. Conventionally, a sensitive single mode has been selected for defect detection. However, due to the inconsistency in actuators or sensors, the robustness of detection is limited. In this paper, the difference in the sensitivity of each mode to flaws, rather than a single mode, was used for defect detection. Based on this idea, numerical and experimental studies of the interaction between hidden corrosion and multiple modes were first conducted. Then, a new index, the relative amplitude coefficient, which evaluates the difference in sensitivity between lowest-order modes and higher-order modes, was proposed. Next, by using a double crosshole array and combining it with a probabilistic reconstruction algorithm, a multimodal Lamb wave corrosion detection method was developed. The results show greater robustness in corrosion location and better accuracy, compared with the location results of conventional single mode defect detection. Furthermore, by applying the double sensor strategy, the effective operating frequency range is extended and the location accuracy enhanced.

Interferences in the re-emission field of multimodal leaky lamb waves propagating in an immersed plate: Analytical modelling, simulation and experimentation

The transmission and re-emission of energy by leaky Lamb waves from an immersed plate is being studied in the case of multi-modal propagation. When more than two Lamb modes propagate together, interferences can be generated in the re-emitted field. The latter have to be well understood and mastered because they can distort the diagnosis of a Non-Destructive Testing of an immersed plate. They are experimentally observed with C-scan visualisation, but they are not consistent with the Bertoni and Tamir model which describes the theoretical re-emitted acoustic field by leaky Lamb modes excited by an incident ultrasonic beam. The same interferences are also observed by finite-element simulation. The Bertoni and Tamir model is then modified to take into account the incidence of side lobes generated by an immersed ultrasonic transducer. That way, the same interferences observed are theoretically predicted, confirming that side lobes are the cause of it. Side lobes can generate a second leaky Lamb mode which propagate and interfere with the mode generated by the main acoustic beam. This secondary Lamb mode is non-negligible if it has higher leaky attenuation than the targeted mode. Thus, to avoid multi-modal generation with an incident beam, the best method is to aim at the leaky Lamb mode with the highest leaky attenuation coefficient at the chosen frequency.

An enhanced Lamb wave virtual time reversal technique for damage detection with transducer transfer function compensation

The Lamb wave time reversal method has widely been investigated as a baseline-free damage detection technique for structural health monitoring. Due to the mode tuning effects from the transducer-wave interactions, even for a pristine wave path, the reconstructed signal waveform may differ much from the original excitation waveform. Consequently, it becomes difficult to distinguish the differences between undamaged and damaged wave paths. This article presents an enhanced Lamb wave virtual time reversal (VTR) algorithm with transducer transfer function compensation to eliminate the transducer influence for dispersive, multimodal Lamb waves. This VTR procedure builds upon a complete 2D analytical model for Lamb wave generation, propagation, and reception. The analytical solution shows that, with the transducer transfer function compensation, a perfect reconstruction of the original excitation waveform can be achieved for both symmetric and antisymmetric Lamb modes. In addition, finite element modeling and experimental validations are further performed to verify the enhanced time reversal procedure. Finally, a time reversal tomography experiment is conducted with a piezoelectric transducer array for structural damage imaging. The enhanced VTR method can achieve more accurate and robust damage imaging results. The paper finishes with discussion, concluding remarks, and suggestions for future work.

Lamb Waves Topological Imaging of Multiple Blind Defects in an Isotropic Plate

The study investigates the feasibility of the Lamb wave topological imaging method for detecting multiple blindholes in an isotropic plate. The topological imaging method is performed based on the computations of two wave fields, a forward and an adjoint, in the defect-free reference medium using different emitting sources. The image is computed by multiplying the forward and adjoint wave fields together and integrating them over time or frequency. The interferences of multimode aliasing and the scattering effect can thus be eliminated at the defectfree positions with an improved image resolution. To investigate the physical mechanism, the refocusing process of the multimode Lamb waves at the defect positions is presented by a face-to-face comparison between the snapshots of the forward and adjoint wave fields using the finite element simulation. The Lamb wave topological imaging method is numerically and experimentally verified to identify multiple blind-holes in an isotropic aluminium plate. The results demonstrate that the topological imaging method enables the suppression of the sartefacts resulting from the mode conversion and achieve high-resolution imaging of the blind defects

Higher-order structural theories for transient analysis of multi-mode Lamb waves with applications to damage detection

Addressing the need for more computationally efficient and accurate simulation tools for Lamb wave-based structural health monitoring (SHM) systems, this paper proposes the use of refined theories for the study of the wave propagation phenomena in thin-walled structures. When dealing with complex structures, classical plate models can be insufficiently accurate whereas 3D finite elements soon reach their limits due to the high computational requirements in ultrasonic wave analysis. As a solution to these issues, a finite element framework based on the Carrera's unified formulation (CUF) is presented for the simulation of Lamb waves in continua. Different structural theories are discussed and tested, showing that the Lamb modes can be well represented using beam elements with enriched kinematics. The validity and convergence rates of the proposed models are assessed through benchmark solutions. An example of damage detection in a typical reinforced panel is included to show the potential of the method.

Mode Separation for Multimodal Ultrasonic Lamb Waves Using Dispersion Compensation and Independent Component Analysis of Forth-Order Cumulant

Ultrasonic Lamb wave testing has been successfully applied in nondestructive testing. However, because of Lamb wave multimodal and dispersion characteristics, the received signals are often multimodal and overlapping, which makes them very complicated. This paper proposes a mode separation method by combining dispersion compensation with the independent component analysis of fourth-order cumulant. Taking two-mode overlapped signals as an example, the single-mode dispersion compensation is performed according to the measured distance difference between the two sets of signals. The two sets of signals are returned to the same distance. The fourth-order cumulant independent component analysis method is further used to process the Lamb wave signals of different superposition situations at the same distance. The corresponding mode signal contained in the two sets of signals is separated through the joint diagonalization of the whitened fourth-order cumulant matrix. The different modes are compensated and separated successively, achieving the multimodal signal separation. Experimental results in steel plates show that the presented method can accurately achieve mode separation for the multimodal overlapping Lamb waves. This is helpful for the signal processing of multimodal Lamb waves.