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Influence of attenuation on acoustic emission (AE) signals in Carbon Fiber Reinforced Polymer (CFRP) crossply and quasi-isotropic panels is examined in this paper. Attenuation coefficients of the fundamental antisymmetric (A 0 ) and symmetric (S 0 ) wave modes were determined experimentally along different directions for the two types of CFRP panels. In the frequency range from 100 kHz to 500 kHz, the A 0 mode undergoes significantly greater changes due to material related attenuation compared to the S 0 mode. Moderate to strong changes in the attenuation levels were noted with propagation directions. Such mode and frequency dependent attenuation introduces major changes in the characteristics of AE signals depending on the position of the AE sensor relative to the source. Results from finite element simulations of a microscopic damage event in the composite laminates are used to illustrate attenuation related changes in modal and frequency components of AE signals. [ABSTRACT FROM AUTHOR]

Defects that propagate from the inside of a structure can be difficult to detect by traditional non-destructive inspection methods. A non-contact inspection method is presented here that uses the near-field interactions of ultrasonic Lamb waves to detect defects propagating into a 1.5 mm thick aluminium sheet from the opposite side to that which is inspected. Near-field interactions of the S0 Lamb waves with the defects are shown to give rise to a characteristic increase in the wave magnitude, which is used to position and characterise these hidden defects. It is shown that such defects are difficult to detect from a study of their influence on ultrasonic transmission alone. Single defects of different depths, and systems of multiple defects with varying separations and relative depths, are successfully detected in both experimental trials and FEM simulations. Reliable single defect detection is achieved for defects with a minimum depth of 30 % of the plate thickness, and resolution of multiple defects is achieved for defect separations of 5 mm. [ABSTRACT FROM AUTHOR]

The present research focuses on detection and quantification of disbond present beneath the stiffener in a stiffened aluminium panel, using a Lamb wave based nonlinear technique. For this purpose, both experimental and finite element simulation studies are carried out. The contact nonlinearity at the disbond leads to the generation of higher harmonics in the Lamb wave response. This phenomenon is observed in both the experimental and the simulation studies. A Spectral Damage Index (SDI) defined by the authors is extracted from these higher harmonics. This SDI has a decreasing trend with the increase in the size of the breathing damage. The plots of the SDI against the disbond width observed in the cases of experimental and simulation studies are in the close agreement. Thus, the higher harmonics observed in the Lamb wave response and the SDI obtained from these higher harmonics together found to be effective in detection and quantification of the disbond in the stiffened aluminium panel. [ABSTRACT FROM AUTHOR]

• Sinusoidally-shaped phononic beam structures are proposed. • A multi-parameter designing technique is proposed for metasurfaces. • Mass of functional units does not varies with the change of design parameters. In this work, we propose a method to design subwavelength metasurfaces for flexural waves in thin plates based on sinusoidally-shaped phononic beam structures. In the proposed method, the effective bending stiffness of sinusoidally-shaped phononic beam structures is tuned, and the effective phase velocity of the flexural waves is modulated subsequently by adjusting two key geometry parameters, namely, the amplitude of the sinusoidal profiles and lattice constants of the phononic beam structures. Compared with the previous methods, which modulate a single design parameter, the proposed method is a two-parameter modulating method. Thus, it not only maintains the functionality of metasurfaces, but also is much more flexible when obtaining a high wave transmittance. In addition, the mass of functional units of metasurfaces designed by the proposed method is not relevant to the design parameters, which is particularly important in weight-critical applications. To validate the feasibility of the proposed design method, the transmission spectra of sinusoidally-shaped phononic beam structures are modeled using the finite element method, and results are compared with experiments of 3D-printed samples. In addition, two representative metasurfaces, refractive and focusing metasurfaces, are designed with an available minimum transmission coefficient of 0.93 for functional units. Numerical evaluation of these metasurfaces' performances confirms the effectiveness of the proposed method. This work paves a novel way to design elastic metasurfaces to manipulate flexural waves in thin plates and demonstrates a potential new direction to design metasurfaces for other wave types. [ABSTRACT FROM AUTHOR]

This work explores the generation of Lamb waves and their higher harmonics using a pattern source. An array of laser sources, when used with a short-pulsed laser, generate multiple Lamb modes in a plate-like component. The variation in duty ratio of the pattern source is found to influence the generation of fundamental modes and their harmonics. A two-dimensional finite element model is developed to simulate the narrowband Lamb wave generation process, and validated against targeted experiments. For a 'square-like' spatial profile of energy distribution, the second harmonic of the fundamental wave modes is fully suppressed at the duty ratio of 0.5, and the third harmonic of the fundamental wave modes is fully suppressed at duty ratios of 1/3 and 2/3. As the duty ratio increased from 0.2 to 0.8, the variation in amplitude of the fundamental modes is greater than that of the higher order modes. For duty ratio values less than 0.25 and greater than 0.75, the second harmonic component of the fundamental waves had approximately the same amplitude as the fundamental wave modes. Similarly, the third harmonic of the fundamental wave modes had the same amplitude or slightly higher amplitude than the higher order Lamb modes for duty ratio values less than 0.25 and greater than 0.75. [ABSTRACT FROM AUTHOR]

Highlights: [•] We developed a semi-analytical finite element method for calculating leaky Lamb waves. [•] The calculation results agreed well with the previous theoretical studies. [•] We discussed dispersion curves for total transmission mode and leaky plate modes. [•] Attenuation curves and displacement distributions were also analyzed. [Copyright &y& Elsevier]

Abstract: Piezoelectric wafer (PW) transducers used for Lamb wave actuation may get partially debonded from the host structure, because of their prolonged use, excessive voltage supply, or improper bonding onto the host structure. In this paper, higher harmonics induced in Lamb wave because of such debonding of the PW actuator are studied both experimentally and through finite element simulation. In experiments, an artificial partial debond is created while bonding the actuator patch onto a pristine aluminium plate. Lamb wave transduced by this actuator in the plate is picked up by a PW sensor which does not have any debonding. In FE simulation, Augmented Lagrangian algorithm is used to solve the contact problem at the breathing debond. Three higher harmonics are observed in the experiments and also in the FE simulation. To ensure that the generated higher harmonics correspond to Lamb wave, time–frequency analysis is carried out using Morlet wavelet transform, and the results are reported in the paper. Spectral damage index (SDI), obtained from spectral attributes of first four harmonics in experiments and simulation, is found to be decreasing with an increase in debonding area. This shows that actuator debonding introduces contact nonlinearity which induces higher harmonics in Lamb wave. Therefore, in damage detection using Lamb wave based nonlinear techniques, the higher harmonics produced may get influenced by the false higher harmonics produced by actuator debonding, leading to incorrect results, if bonding of the actuator is not taken care of properly. [Copyright &y& Elsevier]

Highlights: [•] Mode conversion of Lamb waves can be used to size notch-type defects in plates. [•] Spectral leakage can hide small amplitude modes in the frequency–wavenumber domain. [•] Baseline subtraction technique is applied to 2DFFT to detect low amplitude modes. [•] Lower limits of detection method are tested via the FEM. [Copyright &y& Elsevier]

Abstract: A finite element approach for modeling of acoustic emission sources and signal propagation in hybrid multi-layered plates is presented. Modeling results are validated by Laser vibrometer measurements and comparison to calculated dispersion curves. We investigate hybrid plates as typically found in composite pressure vessels, composed of fiber reinforced polymers with arbitrary stacking sequences and attached metal or polymer materials. Hybrid plate thickness, the ratio between anisotropic and isotropic materials and material properties are varied. Lamb-wave propagation in a geometry representative of a pressure vessel is modeled. It is demonstrated, that acoustic emission sources in multi-layered structures can cause Lamb-waves superimposed by guided waves within the individual layers. [Copyright &y& Elsevier]

• An anti-symmetric lamb wave is designed and achieved on a glass plate which enables a haptic effect. • The highly transparent haptic device is successfully fabricated. • An extremely low unipolar voltage of 10 V Peak-to-Peak achieved a commercial standard amplitude of 1 µm. [Display omitted] When a substrate is excited to exhibit more than 1 µm out-of-plane displacement at an ultrasonic frequency, a silent change of friction force could be clearly felt by human fingers when touch it. This is called the surface haptic feedback based on friction modulation. In this study, we designed and fabricated a highly transparent haptic device based on piezoelectric Pb(Zr,Ti)O 3 (PZT) films on glass. Standing lamb waves in the vibrating plate resulting in a haptic effect was generated under sinusoidal excitation at 22.5 kHz. An extremely low unipolar voltage of 10 V Peak-to-Peak achieved a displacement of 1 µm. The displacement reached as high as 4 µm when the voltage increased to 24 V Peak-to-Peak. The average transmittance of the whole films including the PZT and the electrodes on the glass reached about 75%. The key outcome of this technology is the design of vibration modes and the effective integration of 2-µm-thick PZT film with transparent indium tin oxide (ITO) electrodes on glass. [ABSTRACT FROM AUTHOR]

Two-dimensional model test of a vertical wall with overhanging horizontal cantilever slab has been carried out with the scale factor of 1:30. Different influences of wave condition and structural geometry on wave load are investigated. Wave pressure of cantilever slab highly depends on structural clearance and reaches the peak when clearance close to 0.2 times wave height. Larger wave steepness is responsible for larger wave pressure for vertical wall. With the increasing length of slab, wave forces are reduced on slab while enlarged on vertical wall. Besides, a negative correlation between rise frequency and rise time is observed and corresponding empirical formula has been proposed. Through finite element analysis, the structural response of a simple plate under wave load has been studied. In general, the cut-off frequency has a dramatic effect on the dynamic magnification factor, where the actual dynamic response keeps stable when cut-off frequency larger than 4 times structural natural frequency. Finally, it is adoptable to determine the adequacy of the structure under wave load by considering the quasi-static wave load and corresponding impact factor from 2.0 to 6.0. • Wave pressure of cantilever slab reaches the peak when relative clearance c / H s = 0.2. • The larger length of slab induces the smaller wave force on slab but larger on vertical wall. • Normalized negative correlation between rise frequency and rise time is presented. • Dynamic magnification factor is larger than 1.0 when relative cut-off frequency 0.5< f c / f nat <4.0. • Impact factor of a plate is located in the range from 2.0 to 6.0. [ABSTRACT FROM AUTHOR]

• A metamaterial ultrasound mode convertor is proposed and investigated to achieve complete mode conversion from Lamb waves into shear horizontal waves. • The mechanism behind the mode conversion phenomenon is revealed via finite element analyses. • The complete mode conversion behavior is demonstrated using both numerical simulations and experimental observations. • The mode convertor allows the switching of interrogative wave mode for SHM/NDE applications. This article reports a new mechanism involving a non-perforated resonant elastic metamaterial to achieve the complete conversion of Lamb waves (A 0 and S 0) into the fundamental shear horizontal (SH 0) wave. The proposed metamaterial ultrasound mode convertor is studied via the observation of the special resonant shear motion of its unit cells, initiating with a conventional additive stub design. Thereafter, such a stubbed structure is further modified to fully couple the Lamb modes with the shear horizontal stub motion. By investigating the band structure of the metamaterial unit cell through modal analysis and tuning the shear resonant motions, a complete SH 0 mode generation band within the simultaneous Lamb modes bandgap can be established in a wide frequency range. Such a special bandgap situation enables the complete mode conversion from Lamb waves into shear horizontal waves. The transformation capability of the proposed ultrasound mode convertor is further substantiated via the harmonic analysis of metamaterial chain model, showcasing the frequency spectrum of the transmitted wave modes. The optimal configuration is determined by conducting a parametric study to identify the most effective mode conversion performance. Finally, a coupled-field transient finite element simulation is carried out to acquire the dynamic response of the structure. The frequency-wavenumber analysis of the transmitted wave field illuminates the successful realization of the mode conversion behavior. Experimental demonstrations are presented to validate the numerical predictions. The proposed complete mode conversion capability may possess great potential for wave control and manipulation. [ABSTRACT FROM AUTHOR]

• Spectral FEM within the bi-potential framework is developed for modeling CAN. • A semi-explicit algorithm is proposed to facilitate high computational efficiency. • Contact force can be calculated by bi-potential method without defined parameters. • Computational efficiency of the proposed method is much higher than that of FEM. • The proposed method can capture classical contact acoustic nonlinearity features. Nonlinear ultrasonic guided waves are of great importance in structural health monitoring, since they have both the large-area inspection capability of guided waves and the desirable sensitivity to incipient defects from nonlinear ultrasonic features. Efficient numerical methods play a key role in investigating the nonlinear features of guided waves. In this work, a time domain spectral finite element method (TDSFEM) combined with the bi-potential contact theory is developed to capture the nonlinear interactions between guided waves and breathing cracks. The bi-potential approach has better accuracy than the conventional penalty method, since there is no any user-defined parameter for computation in the former method while the latter one requires a user-experience-based penalty factor. In addition, a semi-explicit algorithm is proposed to integrate the wave equation, which can take full advantage of the diagonal mass matrix of TDSFEM while not sacrificing numerical stability. Numerical verifications against ANSYS show that the computational efficiency of the bi-potential method-based TDSFEM is much higher than that of the FEM via the penalty method. Numerical case studies are then performed to investigate the nonlinear interactions between Lamb waves and breathing cracks. Results show that the proposed method can successfully capture the classical nonlinear features, such as higher harmonic generation and zero frequency (DC) response. Moreover, the influence of the length and gap of a breathing crack on the contact acoustic nonlinearity (CAN) is investigated. As an efficient numerical approach, the bi-potential method-based TDSFEM may be a good tool for investigating the CAN. [Display omitted] [ABSTRACT FROM AUTHOR]

Higher Order Modes Cluster (HOMC) guided waves are non-dispersive wave packets consisting of higher order Lamb wave modes. This paper investigates the effect of frequency and dominant mode(s) of an HOMC guided wave on its sensitivity to plate defects. The propagation of HOMC guided waves in a 10-mm thick mild steel plate is simulated by two-dimensional finite element model. The level of contribution of Lamb wave modes to the wave cluster is analyzed by using a two-dimensional Fast Fourier Transform (2D FFT) at various frequency-thickness products ranging from 15 to 35 MHz-mm. The normal stress profiles of the HOMC guided waves are plotted and used to show the changes in normal stress as a function of frequency-thickness product. The HOMC guided waves interactions with notches of 5%, 10%, 30% and 50% depths relative to the plate thickness are examined at various frequency-thickness products ranging from 15 to 35 MHz-mm. It is observed that the reflected energy from these notches decreases with increase in frequency-thickness product. Experimental measurements are also conducted on a similar plate. The experimental results are in line with simulations and confirm the changes observed in the reflection coefficient of notches at different frequency-thickness products. [ABSTRACT FROM AUTHOR]

• A new finite element method reproduced the impact damage in composite laminate. • The model describes the geometric properties of the actual impact damage. • Simulation of acousto-ultrasonic sensing was conducted to manifest the change of the Lamb wave. • Investigating the change of the Lamb wave which interacts with impact damage. • The simulation results ware compared with another finite element method and validated by the experiment. It is difficult to investigate the interaction between the Lamb wave and impact damage within a composite laminate if the interfaces caused by impact-induced delamination and cracks are not modeled precisely. In this study, a novel finite element modeling method was proposed to virtually reproduce multiple damage after observing the distribution and form of different impacts in a cross-ply carbon fiber reinforced plastic laminate. Further, a numerical simulation of acousto-ultrasonic sensing was performed to manifest the tone-burst Lamb wave that propagated in the laminate. The calculated stress and displacement contours distinguished the dispersed modes and exhibited the wave attenuation after it interacted with multiple interfaces. The change in amplitude provided a reference for impact damage evaluation. The proposed method was compared with another existing modeling method and validated by the acousto-ultrasonic sensing experiment, which demonstrated its accuracy and capability to study the phenomena in acousto-ultrasonic sensing for low-velocity impact damage. [ABSTRACT FROM AUTHOR]

Abstract: The propagation of guided Lamb waves in metallic foam sandwich panels is described in this paper and analyzed numerically with a three-dimensional finite element simulation. The influence of geometrical properties of the foam sandwich plates (such as the irregularity of the foam structure, the relative density or the cover plate thickness) on the wave propagation is investigated in a parametric study. Open-cell and closed-cell structures are found to exhibit similar wave propagation behavior. In addition to the finite element model with fully resolved microstructure, a simplified, computationally cheaper model is also considered – there the porous core of the sandwich panel is approximated by a homogenized effective medium. The limitations of this homogenization approach are briefly pointed out. [Copyright &y& Elsevier]

Abstract: The paper aims to describe the guided Lamb wave propagation in honeycomb sandwich panels. The application of Lamb waves is a well-known method in modern online structural health monitoring techniques. To analyze the wave propagation in such a complicated geometry with an analytical solution is hardly possible; therefore a dimensional finite element simulation is used. A piezoelectric actuator is used to excite the waves on the sandwich panel surface. The extended model of the honeycomb sandwich panel is consisting of two plate layers and a mid-core layer. In addition, a simplified model is used to reduce the computing costs, where the mid-core of the sandwich panel is replaced by a homogeneous layer. The results from the extended model and the simplified model are in most cases in a good agreement; however the limitations of using the simplified model are discussed. A parametric study is used to show the influence of the geometrical properties of honeycomb plates, the material properties of the skin plates and the loading frequency on the group velocity, the wave length and the energy transmission. Each of these properties provides valuable information to design an efficient health monitoring system. Finally, an experimental test is presented. [Copyright &y& Elsevier]

Abstract: This paper deals with the investigation of the Lamb wave propagation in particle reinforced composites excited by piezoelectric patch actuators. A three-dimensional finite element method (FEM) modeling approach is set up to perform parameter studies in order to better understand how the Lamb wave propagation in particle reinforced composite plates is affected by change of central frequency of excitation signal, volume fraction of particles, size of particles and stiffness to density ratio of particles. Furthermore, the influence of different arrangements is investigated. Finally, the results of simplified models using material data obtained from numerical homogenization are compared to the results of models with heterogeneous build-up. The results show that the Lamb wave propagation properties are mainly affected by the volume fraction and ratio of stiffness to density of particles, whereas the particle size does not affect the Lamb wave propagation in the considered range. As the contribution of the stiffer material increases, the group velocity and the wave length also increase while the energy transmission reduces. Simplified models based on homogenization technique enabled a tremendous drop in computational costs and show reasonable agreement in terms of group velocity and wave length. [Copyright &y& Elsevier]

Abstract: Structural Health Monitoring (SHM) applications call for both efficient and powerful numerical tools to predict the behavior of ultrasonic guided waves. When considering waves in thin-walled structures, so called Lamb waves, conventional linear or quadratic pure displacement finite elements soon reach their limits. The spatial as well as temporal discretisation, required to obtain good quality results has to be very fine. This results in enormous computational costs (computational time and memory storage requirements) when ultrasonic wave propagation problems are solved in the time domain. To resolve this issue several higher order finite element methods with polynomial degrees are proposed. The objective of the current article is to develop such higher order schemes and to verify their capabilities with respect to accuracy and numerical performance. To the best of the authors’ knowledge such comparison has not been reported in literature, yet. Specifically, spectral elements based on Lagarange polynomials (SEM), p-elements using the normalized integrals of the Legendre polynomials (p-FEM) and isogeometric elements utilizing non-uniform rational B-splines (NURBS, N-FEM) are discussed in this paper. By solving a two-dimensional benchmark problem, their advantages and drawbacks with respect to Lamb wave propagation are highlighted. The results of the convergence studies are then used to derive guidelines for estimating the optimal element size for a given finite element type and polynomial degree template. These findings serve the purpose to determine the optimal mesh configuration a priori and thus, save a considerable amount of computational effort. The proposed guideline is then tested on a three-dimensional structure with a conical hole showing an excellent agreement with the predicted behaviour. [Copyright &y& Elsevier]

Abstract: A parametric 2D finite-element inversion scheme is used for sizing cracked zone type strip defect caused by a linear and uniform impact on a composite material plate. The reflection and transmission coefficients produced by mode conversion phenomenon when a pure incident S 0 Lamb wave mode is sent towards the defect are used as input data for the inversion process. The inversion process consists in quantifying two unknown parameters, i.e., width and depth representing the assumed triangular geometry of cracked zone like defect. The inversion scheme consists of a finite element based model, which is used to simulate the Lamb wave scattering for various values of the aimed parameters, and specific post-processing based on Shkerdin''s orthogonality relation is applied to predict the needed reflection and transmission coefficients. A laboratory experiment is performed for creating a linear and uniform impact on a carbon epoxy composite plate sample. Then another ultrasonic experiment is performed in laboratory for measuring reflection and transmission coefficients by sending a pure S 0 mode towards the defect. The measured coefficients are then used for the inversion purpose. The two principles used in inversion process give almost similar optimised values for these parameters, showing the usefulness of this technique. [Copyright &y& Elsevier]

Abstract: In this paper, a computationally efficient scheme to simulate Lamb wave propagation in symmetric laminated composite is presented and used to study time reversibility of Lamb wave. The technique proposed is a modified version of the wavelet spectral finite element (WSFE) which has been earlier developed for one- and two-dimensional wave propagation. The method follows a finite element procedure in the transformed frequency-wavenumber domain. The transformations are done using Daubechies scaling function approximation in time and one spatial dimension. Here, the modified WSFE method is used to simulate time domain Lamb wave response in doubly bounded, symmetric composite laminates. The results have been validated by comparing the wave velocities derived from these simulations with those obtained from experiments. The technique has also been used to emphasize and analyze the time reversibility phenomenon of Lamb wave. Finally, the constraint of the simulation in terms of wrap-around problem is explained with numerical examples. [Copyright &y& Elsevier]

Abstract: In this article, the complete characterization of the interface delamination in a composite T-joint using ultrasonic guided Lamb waves is discussed. Correlation between the numerically simulated and experimentally obtained B-scans was established. In the B-scan images, different Zones were identified and could be utilized for differentiating the healthy and delaminated T-joints. The length and the width of delamination were computed from traversing the transducers in two orthogonal directions (i.e. called the B-scans, and the D-scans). For the first time, backward propagating mode (called “Turning Lamb Modes”) that are generated at corner of the T-joint was observed and verfied. Using a single linear line scan of the “Turning Lamb Modes”, both the width and length of interface delamination could be computed. In the present study, the experiments were carried out employing air-coupled ultrasonic transducers. [Copyright &y& Elsevier]

Abstract: This paper deals with developing a parametric 2D finite-element technique, which can size strip-like defects in elastic or viscoelastic, isotropic or anisotropic material plates. A pure incident Lamb wave mode is sent towards the defect and reflection and transmission coefficients produced by mode conversion phenomenon are used as input data for the inversion process, which consists in quantifying two unknown parameters representing the geometry of the defect. A finite-element-based model is used to simulate the Lamb wave scattering for various values of the aimed parameters, and specific post-processing based on Shkerdin’s orthogonality relation is applied to predict the needed reflection and transmission coefficients. The target is known reflection and transmission coefficients initially obtained from an experiment, which can be either a numerical experiment for validation purposes, or proper measurements on a sample for NDE application purposes. The inversion process is stopped when the predicted reflection and transmission coefficients fit at best those obtained from initial experiment. In this paper, we have quantified two geometrical parameters for three types of defects in different waveguides: the through-thickness depth (or position) and width (or radius) of (1) a circular hole inside an aluminium plate, (2) a rectangular notch at the surface of a Perspex plate, (3) a cracked zone inside a composite plate, representing an impact damage. [Copyright &y& Elsevier]

Abstract: The scattering of Lamb waves by a two-dimensional rectangular notch is investigated for rapid inspection of defects in a structure. To derive the reflection and transmission coefficients of the scattered waves in a simple way, the scattering caused by the notch is analyzed through the composition of individual scattering processes. Linear equations corresponding to the reflection and transmission coefficients are constructed along with scattering graphs. For an illustration of the efficacy of the presented method, the scattering of fundamental symmetric and anti-symmetric modes are inspected according to the depth and width of a notch in a plate. Validity of these expressions is demonstrated by the comparison of the theoretical analysis results with those from the finite element analysis. [Copyright &y& Elsevier]

Abstract: In the present work, the interaction of the fundamental anti-symmetric guided Lamb mode (A o) with a structural discontinuity in a composite structure was studied through Finite Element numerical simulations and experiments. The structural component selected for this study was a T-joint section made from glass/epoxy material. This co-cured composite structure is made-up of an upper shell (skin) and a spar as the sub-components. It was observed that when A o mode interacts with the junction (structural discontinuity) of these sub-components, a mode-converted S o mode is generated. Experiments were conducted using air-coupled ultrasound to validate the numerical simulations. The back-propagating “Turning modes”, which propagate from the thin region to the spar web and vice versa, were also numerically simulated and experimentally verified. [Copyright &y& Elsevier]

Abstract: In this study, the Lamb mode attenuation constants were derived in terms of the attenuation coefficient, group velocity and central frequency of excitation of the Lamb mode, using the Rayleigh damping model. Attenuation of Lamb waves, both fundamental symmetric and anti-symmetric modes, propagating through viscoelastic media (cross-ply glass/epoxy laminate) was modelled using the Finite Element Method. Numerically simulated attenuation of Lamb waves using Lamb mode attenuation constants was found to be in good agreement with the assumed attenuation. Experiments were performed on a quasi-isotropic laminate, employing air-coupled ultrasonic transducers, to measure the attenuation coefficient. Lamb mode attenuation constants, computed using the attenuation coefficient, were used to model the attenuation of the Lamb mode in quasi-isotropic laminates. Numerically simulated amplitude variation was found to be in good agreement with that computed from experiments. [Copyright &y& Elsevier]

Abstract: A computer simulator, to facilitate the design and assessment of a reconfigurable, air-coupled ultrasonic scanner is described and evaluated. The specific scanning system comprises a team of remote sensing agents, in the form of miniature robotic platforms that can reposition non-contact Lamb wave transducers over a plate type of structure, for the purpose of non-destructive evaluation (NDE). The overall objective is to implement reconfigurable array scanning, where transmission and reception are facilitated by different sensing agents which can be organised in a variety of pulse-echo and pitch-catch configurations, with guided waves used to generate data in the form of 2-D and 3-D images. The ability to reconfigure the scanner adaptively requires an understanding of the ultrasonic wave generation, its propagation and interaction with potential defects and boundaries. Transducer behaviour has been simulated using a linear systems approximation, with wave propagation in the structure modelled using the local interaction simulation approach (LISA). Integration of the linear systems and LISA approaches are validated for use in Lamb wave scanning by comparison with both analytic techniques and more computationally intensive commercial finite element/difference codes. Starting with fundamental dispersion data, the paper goes on to describe the simulation of wave propagation and the subsequent interaction with artificial defects and plate boundaries, before presenting a theoretical image obtained from a team of sensing agents based on the current generation of sensors and instrumentation. [ABSTRACT FROM AUTHOR]

Abstract: The aim of this study is to quantitatively assess debonding in sandwich CF/EP composite structures with a honeycomb core using acoustic waves activated and captured by surface-mounted PZT elements. For experimental investigation, debonding was introduced at different locations in sandwich CF/EP composite beams. The fundamental anti-symmetric A 0 Lamb mode was excited at a low frequency. The transmitted and reflected wave signals in both surface panels were captured by PZT elements after interacting with the debonding damage and specimen boundaries. Aided by finite element analysis (FEA), the differences in wave propagation characteristics in sandwich composite beams and composite laminate (e.g. skin panel only) were investigated. The debonding location was assessed using the time-of-flight (ToF) of damage-reflected waves, and the severity of debonding was evaluated using both the magnitude of the reflected wave signal and the delay in the ToF of Lamb wave signals. Good correlation between the experimental and FEA simulation results was observed. The results demonstrate the effectiveness of Lamb waves activated and captured by surface-mounted PZT elements on either surface of sandwich composite structures in assessing debonding. [Copyright &y& Elsevier]

Abstract: In recent years, much attention has been paid to the use of Lamb waves for structural health monitoring. This choice is prompted by the high speed of Lamb wave inspection, although their dispersive nature can complicate the interpretation of results, especially when dealing with closely-spaced reflectors. In this paper, the objective is to improve the time resolution and signal-to-noise ratio of signals obtained from inspection of plates by the S 0 Lamb mode. The signal processing scheme used is based on deconvolution of the measured signal by Wiener filtering, followed by autoregressive spectral extrapolation. The deconvolution technique is applied to signals obtained from finite element models and also to experimentally measured signals; both sets of data are based on plates with various types of notch discontinuities. Using this technique, the separation distance between adjacent notches was estimated with high accuracy in both simulated and experimental ultrasonic signals. [ABSTRACT FROM AUTHOR]

Abstract: This paper reports simulations of the generation of Lamb wave modes in thin plates using a meander coil (meander line) EMAT, which works under the principle of Lorentz force mechanism in non-magnetic materials. The numerical simulations have been compared with measurements. The numerical work presented in this paper is divided into two parts. First, a 2D electromagnetic model is developed for calculating the Lorentz force density, which is the driving force for elastic wave generation within the plate. Second, the calculated force at each point in the metal is used as the driving force for generating elastic wave modes in the plate. These calculated Lamb wave modes are compared with those generated experimentally in a thin plate. Additionally, the measured wave modes are analyzed with the help of dispersion curves and a time–frequency analysis. Our numerical work is also extended to analyze the interaction of Lamb wave modes with defects. The simulations compare favorably with the measurements presented here. [Copyright &y& Elsevier]

Abstract: In this paper, wave propagation in straight and curved mechanical waveguide is investigated. The main objective of the study is to develop a numerical model that can determine the response of the intact or damaged waveguide structure which is subjected to the incident waves. The wave finite element method, which is based on the simple development of standard finite element procedures, is used for the extraction of eigenmodes and analysis of the wave propagation properties. To make an effective use of those eigenmodes, a criterion that is based on the properties of eigensolutions is proposed to condense the mode bases. By using the reduced eigenmode bases, the high frequency wave motion due to the presence of curved part in the waveguide is examined through the wave propagation approach. Numerical analysis indicates that, in order to choose the appropriate wave modes for inspection, it is necessary to obtain both the eigenmode and wave propagation properties, thus the incident wave could be optimised for better monitoring of the structural features and detection of the local damages. [Copyright &y& Elsevier]

Abstract: A spectral element model is developed to represent the dynamic response of a coupled piezoelectric wafer and beam system (CPBS) in which either a single or collocated piezoelectric wafers are bonded to a base beam. The Mindlin–Herrmann rod theory and the Timoshenko beam theory are employed to represent the displacement field of the base beam. The Euler–Bernoulli beam theory and linear piezoelectricity are used to model the electro-mechanical behavior of the piezoelectric wafer. Detailed spectral element formulation for the CPBS is presented. The validity of the proposed spectral element is demonstrated through numerical examples in time and frequency domains, respectively. [Copyright &y& Elsevier]

Abstract: The aim of this work is to study the fundamental Lamb modes interaction with defects in isotropic plates. For these experimental investigations, symmetrical notches with various depths milled in aluminum plates are considered. Moreover, the incident Lamb wave of a specific mode is generated by means of two identical thin piezoceramic transducers placed at the opposite sides of the plate. The waves scattered by the notch are recorded with conventional transducers located on the plate surface in front and behind the defect. The selection of the A 0 or the S 0 modes is obtained by exciting the transducers with anti-phased or in-phased signals, respectively. Furthermore, a calibration process is investigated to correct errors caused by the presence of the receiver between the emitters and the defects. The power reflection and transmission coefficients are then obtained and the power balance is verified. Finally, these measurements are compared successfully with those obtained by a numerical method using the finite-element modeling described in a previous work. [Copyright &y& Elsevier]

[Display omitted] • Piezoelectric diaphragms are formally evaluated for Lamb wave inspections. • These devices are mass-produced in standard sizes and are readily available. • Diaphragms are numerically and experimentally compared with conventional ceramics. • Results indicate that piezoelectric diaphragms are feasible for Lamb wave inspections. • This can expand research on Lamb wave inspections and reduce installation costs. Lamb wave-based inspection has been extensively investigated and reported in the literature as a non-destructive technique in structural health monitoring and other applications. The generation and reception of Lamb waves are typically performed with piezoelectric ceramics operating as actuators and sensors, respectively. This article presents a study of the feasibility of piezoelectric diaphragms as an alternative transducer, allowing to expand the research as well as to accelerate the implementation of Lamb wave-based SHM systems with lower installation costs. Piezoelectric diaphragms are sound components widely used in everyday electronic devices and, in addition to the low cost, they have the advantage of being mass-produced by different manufacturers in standard sizes and are readily available. To assess the feasibility of these components, basic analysis by finite element method (FEM) and experimental tests were carried out on aluminum plates and the results obtained with the diaphragms were compared with those obtained using conventional piezoelectric ceramics. Structural damage was simulated by making cracks and drilling holes in the structure and an imaging algorithm together with damage index based on the wavelet transform was used to detect and locate damage. In addition, tests were carried out to evaluate and compare the reproducibility of the results and the effects of temperature variation on the two types of transducers. FEM and experimental results show that piezoelectric diaphragms are feasible for generating and receiving Lamb waves, as well as detecting structural damage. Therefore, these commercial sound components can also be alternative transducers for applications involving Lamb waves. [ABSTRACT FROM AUTHOR]

The limitations of the dynamic theories for the thin layered elastic structures, which very often have different physical and geometrical contrast properties of the layers in today's high-tech applications, bring a number of challenges in the numerical computation of the dynamic response. This is a strong motivation to develop a suitable computational methodology for accurate evaluation and implementation of the numerical results, aiming at accurate interpretation of the vibration spectra and the associated displacement and stress fields. In this paper, a newly developed numerical engineering approach is presented for the study of elastic wave dispersion in composite plates (sandwich plates) with high-contrast properties of the layers using modal finite element method (FEM) analysis implemented in commercial software. The obtained results are compared with the iterative numerical solution of the Rayleigh-Lamb dispersion equation for the fundamental flexural wave and the first shear harmonic. It is shown that the complexity of the dispersion phenomena, including the cut-off frequencies of higher order vibrational modes, has been captured very accurately and that the developed computational methodology provides a valuable insight into the frequency range in which the respective mode can be activated. This perspective shows a great potential of the approach to be employed in many engineering applications involving multi-layered structures with arbitrary number of layers. • Lamb wave dispersion in high-contrast three-layered composite plates is studied. • Numerical engineering approach to analyze wave dispersion phenomena is developed. • Frequency ranges in which the respective mode can be activated are determined. • The dispersion curves and the cut-off frequencies are captured very accurately. • The approach enables to separate fundamental flexural mode and first shear mode. [ABSTRACT FROM AUTHOR]

Abstract: We suggest that Lamb wave band gap in one-dimensional phononic crystals can be substantially enlarged by using the combination of periodic and Fibonacci quasiperiodic composite thin plates. A narrow band also can be obtained by using Fibonacci quasiperiodic or the combined composite thin plates. This is possible because each substructure shows a different band gap which is different from those in the phononic crystals and photonic crystals of the bulk waves. This effect has been demonstrated by using the finite element method. [Copyright &y& Elsevier]

Abstract: In this work, a Lamb wave based technique has been developed for delamination detection in cross-ply laminated beams. By measuring the propagation speed of S 0 Lamb mode and the traveling time of a signal reflected from a delamination site, the location of the delamination can be identified. It has been also confirmed by the experiment that the location of a delamination can be accurately determined by only using the data collected from the sensors in a defect-containing beam, without referring to the baseline signals. Finally, to gain a better understanding of the complex interaction between a Lamb wave and a long delamination, numerical simulations have been carried out using finite element method (FEM). The signal modes generated at the boundaries of the delamination have been analyzed. [Copyright &y& Elsevier]

Abstract: The interaction of Lamb wave modes at varying frequencies with a through-thickness crack of different lengths in aluminium plates was analysed in terms of finite element method and experimental study. For oblique-wave incidence, both numerical and experimental results showed that the wave scattering from a crack leads to complicated transmission, reflection and diffraction accompanied by possible wave-mode conversion. A dual-PZT actuation scheme was therefore applied to generate the fundamental symmetrical mode (S 0) with enhanced energy to facilitate the identification of crack-scattered wave components. The relationship between crack length and the reflection/transmission coefficient obtained with the aid of the Hilbert transform was established, through which the crack length was quantitatively evaluated. The effects of wavelength of Lamb waves and wave diffraction on the properties of the reflection and transmission coefficients were analysed. [Copyright &y& Elsevier]

Abstract: Experimental and numerical results are presented on the behavior of guided waves in elastic plates in plane strain that include a Gaussian variation of their section, located between two areas of constant thickness. The area of varying section is wide compared to the used wavelengths, which allows wave propagation inside this area. The experimental results show that an incident Lamb wave is indeed converted into an adiabatic wave inside the varying section domain. A trapped wave in the Gaussian domain is also observed, depending on the incident mode and on the Gaussian maximum height. Outside the varying section domain, conversion into different Lamb waves is observed. This conversion phenomenon is experimentally quantified by the measurement of the Lamb wave normal displacement and of its carried energy. A numerical study, based on the Finite Elements Method is performed, and successfully compared to the experimental results. [Copyright &y& Elsevier]

Abstract: The mode selection of Lamb waves generated in thin aluminium plates by using 2-2 piezocomposites has been studied. In this paper, 2-2 piezocomposite square plates have been designed, made, and compared with standard piezoceramic plates to test the improvement on the generation and propagation of symmetric and antisymmetric Lamb modes. An optical interferometer was used to measure the out-of-plane displacement of the propagating Lamb wave modes generated with the piezoceramic plates. Different Finite Element Models, using a commercial simulation program (PZFlex) were also developed to calculate the displacement signals and to compare them with the experimental ones. Next, the same measurements were done with two different 2-2 piezocomposites to see the mode selection of the Lamb waves generated. Different excitation frequencies were used experimentally and implemented in PZFlex to calculate the displacement signals, verifying the mode cancellations. The experimental measurements show good agreement with the models. [Copyright &y& Elsevier]

Abstract: This paper presents a combined finite element and modal decomposition method to study the interaction of Lamb waves with damaged area. The finite element mesh is used to describe the region around the defects. On the contrary to other hybrid models already developed, the interaction between Lamb waves and defects is computed in the temporal domain. Then, the modal decomposition method permits to determine the wave reflected and transmitted by the damaged area. Modal analysis allows also identifying the mode conversions induced by the defects. These numerical results agree with previous finite element results concerning the interaction of Lamb modes with a notch. Experiments, carried out with gauged defects on an aluminum plate, are also compared to numerical predictions to validate the simulation. Compared to classical techniques of simulation, this new method allows us to investigate the interaction of Lamb modes generated at high frequency-thickness product with micro-defects as corrosion pitting. [Copyright &y& Elsevier]

In this paper, the edge mode vibration is studied with three different methods: the reciprocal work method, already used by Torvik [J. Acoust. Soc. Am. 41 (1967) 346] to model this phenomenon, the S-parameter method and a finite element model that are applied for the first time to the study of the edge resonance. Moreover, laser probe measurements of the edge mode have also been performed and compared to the numerical predictions. The good agreement between the numerical predictions and the experimental data allows full understanding of the resonant phenomenon. The edge resonance is linked to the strong increase in amplitude of two complex Lamb waves, and the edge mode is proved to radiate into the plate as the first symmetrical Lamb mode S0. Displacements at the edge and away from the edge have been computed and measured to evaluate the spatial and temporal behaviour of the edge mode. The dependence of the edge resonance frequency and amplitude on the Poisson coefficient has also been studied. [Copyright &y& Elsevier]

A new extension of the shear deformation theory to fifth order in order to calculate the spectrum of Lamb waves in orthotropic media over a wide frequency range is developed and analyzed. The aspiration of the proposed method is to create an alternative framework to exhaustive 3D elasticity based solutions by increasing computational efficiency without losing accuracy, nor robustness. A new computational framework is introduced which allows to estimate the dispersion curves for the first nine symmetric and nine anti-symmetric Lamb modes. Analytically calculated dispersion curves using 5-SDT for different propagation directions and polar plots for selected frequency of different materials are compared with the results from both the semi analytical finite element method, and lower order shear deformation theories. Careful analysis for individual laminae and for symmetric composite laminates exhibits a good agreement between the new higher order plate theory and the semi analytical finite element method over an extensive frequency range. In addition, attenuation plots show that the proposed method can also be used for visco-elastic materials (or highly damped materials). The advantage of the new higher order plate theory and its numerical implementation is that it is much more computationally efficient compared to comprehensive methods as Lamb wave polar plots of composite plates as function of incidence angle, polar angle and frequency can be calculated in less than a second on a standard laptop. Consequently, the use of this framework in inversion routines opens up the possibility of quasi real-time Structural Health Monitoring for visco-elastic composites covering a sufficiently wide frequency range. • Novel 5th order shear deformation theory (5-SDT) to model multilayered plate waves • New computational framework based on the standard reduction method • Estimate of dispersion curves for first nine S and A modes in less than a second • Simultaneous estimate of attenuation and loss factor for viscoelastic materials • 5-SDT results in good agreement with the semi analytical finite element method [ABSTRACT FROM AUTHOR]

• A model was proposed for analyzing the static component (SC) generation of primary Lamb wave tone burst. • Influence of the interfacial property on the generated SC was quantitatively analyzed. • The SC of primary Lamb wave shows a potential to assess a minor change in the interfacial property. Modeling of the acoustic-radiation-induced static component (SC) generation of primary Lamb wave tone burst propagating in a layered plate is conducted. Accompanying the propagation of primary Lamb wave tone burst, there are the finite-duration SC bulk driving force in the interior of the layered plate, and the finite-duration SC traction stress on each surface/interface. According to the modal analysis approach for waveguide excitation, the function of the finite-duration SC bulk driving force and traction stress is to generate the finite-duration SC of primary Lamb wave tone burst. Compared with the second harmonic (SH) generation of Lamb wave propagation in a layered plate, the phase velocity matching is no longer required for the generation of the SC with a cumulative growth effect. Based on modeling of the finite-duration SC generation, it is found that the integrated amplitude of the finite-duration SC generated by propagation of the primary Lamb wave tone burst does grow with propagation distance. Meanwhile, the numerical analyses and the finite element (FE) simulations are conducted to investigate the effect of the said SC generation. It is found that, although the interfacial layer of the layered plate considered is quite thin compared with the upper and lower layers, the numerical analyses indicate that the influence of the interfacial property on the cumulative growth effect of the SC of primary Lamb wave is significant. Furthermore, the FE simulations demonstrate that the cumulative SC of primary Lamb wave tone burst will exhibit a monotonic and sensitive response to the degree of interfacial degradation. This investigation provides an physical insight not previously available into the process of the SC generation of Lamb wave propagation in a layered plate. [ABSTRACT FROM AUTHOR]

This paper presents a benchmark for three-dimensional explicit asynchronous absorbing layers for modeling unbounded domains through a standard displacement-based finite element method: Three-dimensional Perfectly Matched Layers (PML) is compared to recently proposed Absorbing Layers with Increasing Damping (ALID) based on Rayleigh and Kosloff damping formulations. The coupled problem, including the interior subdomain and the absorbing layers, is implemented in the framework of Heterogeneous Asynchronous Time Integrator (HATI), enabling the absorbing layers to be handed with an explicit Central Difference scheme, with fine time steps, independently from the time stepping procedure adopted in the interior subdomain. Simple 3D Lamb's tests are considered by using different kinds of absorbing layers. The superiority of the PML in terms of the accuracy and computation time is highlighted. Finally, realistic 3D applications are investigated, such as the Lamb's test and the study of the screening effect provided by a horizontal wave barrier in mitigating the ground surface vibration generated by an excited plate. [ABSTRACT FROM AUTHOR]