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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: Fiber reinforced composite materials risk to suffer from subsurface, barely visible, damage induced by transverse relatively low energy impacts. This two-paper series presents a method for the localization of an impact and identification of an eventual damage using dynamic strain signals from fiber Bragg grating (FBG) sensors. In this paper, the localization method allowing to predict the impact position based on interpolation of a reference data set is developed and validated. The data utilized in the method are the arrival times of the asymmetric zero order Lamb waves at the different sensors. A high rate interrogation method based on intensity modulation of the Bragg wavelength shift is used to acquire the FBG signals. The localization method allows to predict the impact position with a good accuracy and therefore the inspection of the laminate can be limited to this region. [Copyright &y& Elsevier]

Abstract: In this work, the influence of viscoelastic material properties, as featured by fibre reinforced plastics, on the measurement of Lamb waves with the aid of surface-applied piezoelectric sensors is examined. The focus points are frequency dependent material dampening and dispersion on the one hand and the impact of sensor size, wave excitation and measurement method on the other hand. The dependence of the measured wave propagation characteristics and the deviation from the actual characteristics is investigated to assess the relevance for Lamb wave based nondestructive testing and structural health monitoring methods. The sensor responses of piezoelectric sensors bonded to the surface of a viscoelastic composite are predicted by a comprehensive model including these influencing factors. The modelling approach is compared with experimentally measured values to evaluate both the methods and the relevance of the influencing factors. [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: Propagation of the anti-symmetric fundamental Lamb mode (A 0) in a composite laminate containing a semi-infinite delamination was studied through numerical simulations and experimental studies. Here, the wave was generated on a sub-laminate above the delaminated region, and the reflection and transmission of the Lamb modes at the edge of the discontinuity were quantitatively studied. The wave group (named as ‘turning mode’), which was made to propagate from one side of the delamination to the other side (through delaminations) was captured and its transmission factor was estimated. Reflection and transmission factors of wave groups were estimated for three different laminates – quasi-isotropic, unidirectional and cross-ply, containing delamination at various interfaces across thickness. Propagation of ‘turning modes’ were also captured experimentally, employing air-coupled transducers, in quasi-isotropic laminates containing delaminations at different interfaces. Attenuation compensation was incorporated in the experimental signals to improve the comparison of transmission and reflection factors between numerical simulations and experiments. [Copyright &y& Elsevier]

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]

Ultrasonic guided waves-based Structural Health Monitoring (SHM) is a promising solution to perform damage diagnosis in plate-like structures. In this field, the Reconstruction Algorithm for Probabilistic Inspection (RAPID) is one of the most widely used tomographic algorithms to perform active damage detection and localisation. Even though this algorithm is easily implementable, very versatile and satisfactorily accurate, it presents some disadvantages, such as the production of artefacts determined by non-uniform distributions of the sensing network density. In the present article, a processing and spatial filtering technique is proposed, which strongly mitigates the aforementioned problem. The proposed methodology is validated using a numerical database created for a large carbon fibre reinforced polymer (CFRP) with a through-the-thickness hole. [ABSTRACT FROM AUTHOR]

Many structural health monitoring systems are being developed to detect the impact damages in carbon fiber reinforced plastic (CFRP) structures, which are widely adopted in the aviation industry. In this study, a refined finite element model is established to simulate a Lamb wave propagating through impact damage in a CFRP skin-stringer structure. The accurate stiffness constants are determined for toughened CFRP laminates, which include the resin layers. The impact damage of toughened CFRP laminates is modeled as a truncated-cone-shaped region in which the rigidity is homogeneously reduced. Furthermore, the directive generation of the Lamb wave through a macro fiber composite (MFC) actuator is incorporated in the model. Simulations are performed for several configurations of the MFC and impact damage. The observed tendency of the delay in the arrival time of the lowest antisymmetric Lamb wave mode is noted to be consistent with the experimental results. The proposed model can facilitate the determination of the optimized configuration of MFCs in CFRP structures. [ABSTRACT FROM AUTHOR]

• Acoustic emission wave is studied in honeycomb sandwich panel on different scales. • Honeycomb cells were found to act as conduit of AE wave energy. • Honeycomb cells is allowing AE wave to transmit from one skin to the other. • Lamb waves are bound in top and bottom skins of the honeycomb sandwich panel. • The honeycomb ribbon direction affects the S o mode velocities. • Concept of insertion loss is introduced as a measure of effect of cell on AE waves. This paper studies acoustic emission (AE) wave propagation in a glass fibre aluminium honeycomb sandwich panel (HSP). Of particular novelty is the quantification of the through-thickness propagation of AE from one surface of the HSP to the other, which is a real-world monitoring consideration for applications where AE instrumentation is only be permissible on one surface, i.e. aerofoils. Complexity was introduced to the specimens in stages to enable a thorough understanding; first investigating propagation in a large glass fibre laminated plate (GFLP) alone; then in bespoke sandwich specimens with a limited number of honeycomb cells; and, finally, in a large HSP. The results of this paper demonstrate that, whilst some energy is transmitted through the honeycomb core, AE propagating in an HSP becomes bound in the outer plates. Despite this, propagation in these outer plates differs to that in an equivalent plate of the same material in isolation due to the complex interactions with the structural elements of the HSP. Further, propagation of AE transmitted from one surface to the other was quantified for the first time, giving insight into expected attenuation rates and characteristics for practical applications. [ABSTRACT FROM AUTHOR]

The problem of dispersion of guided waves propagating in stratified composite plates containing layers with alternating physical properties is analyzed by using combination of sextic formalism Cauchy, exponential fundamental matrices and Thomson – Haskell method for constructing transfer matrices. The developed method is applicable to analyzing stratified media containing homogeneous anisotropic periodic layers with arbitrary elastic anisotropy. It is revealed that the dispersion portraits of guided waves in plates containing even (asymmetric layout) or odd (symmetric layout) number of alternating layers are significantly different, remaining different even at large number of alternating layers. It is also found that the observed discrepancy between even and odd sets should in principle, be persistent for any composite plates with odd and even numbers of alternating layers. The latter circumstance prevents application of the existing methods of homogenization for obtaining dispersion portraits of guided waves in the stratified media with alternating layers. [ABSTRACT FROM AUTHOR]

Lamb wave is a promising means for active structural health monitoring and nondestructive evaluation of laminated composite plates. The inevitable reflections from structural geometric boundaries and other interferences limits the imaging performance of many existing imaging methods. The image generated through the well-known delay-and-sum method holds a wide mainlobe width and high level of sidelobes. Although the sparse reconstruction method is free from those deficiencies, it is sensitive to the regularization parameter. To overcome those limitations, a Lamb wave imaging method to locate anomalies or damage in laminated composite plates is proposed. The scattering signals are sparsely decomposed one by one with a prior weights penalized on the undetermined sparse coefficients, and the minimum variance distortionless response algorithm is adopted to process those sparse coefficients so as to generate the image. Experimental results on a quasi-isotropic laminated composite plate demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

• Guided ultrasonic wavefield measurements performed on quasi-isotropic CFRP laminate. • Scattering at artificial, ellipse delamination, located at an asymmetric depth. • Wave trapping on top of delamination and forward scattered wave verified. • Numerical, Finite Element simulations validated from experiments. • Parameter study of guided wave scattering at different delamination shape and depth. Carbon fibre composite laminates are increasingly being used for aerospace structures due to their low weight and improved mechanical performance. Impact damage can cause delaminations below the visible surface of the structure due to limited interlaminar strength. Guided ultrasonic waves can detect and characterize delaminations in composite laminates. The scattering of the A 0 Lamb wave mode at an artificial delamination, located at an asymmetric depth in a quasi-isotropic laminate, was investigated. Full field non-contact laser measurements were used to visualise wave trapping and scattered waves. A three-dimensional finite element model was developed and validated against the experiments. The influence of delamination shape and depth on guided wave scattering were studied. Small variations in delamination shape significantly affected the interference pattern on top of the delamination, but had limited effect on the scattered wave outside the delamination. Delamination depth was found to strongly influence the angular direction and amplitude of scattered waves. Implications for structural health monitoring were discussed. [ABSTRACT FROM AUTHOR]

Abstract: This work is devoted to the characterization of defects in the bonding of two carbon epoxy composite plates using Lamb waves. First, artificial defects are located by a C-scan performed by two air-coupling transducers. Next, Lamb wave propagation is studied with a laser interferometer. The behavior of the incident wave is interpreted and related to the nature of the defect. The size of the flaw area is estimated. [Copyright &y& Elsevier]

Abstract: A program to implement cross-borehole tomography using a simultaneous iterative reconstruction technique (SIRT) has been written. The effectiveness of the program in detecting damages in flat plates has been tested through utilising a combination of computer simulations and experimental tests. Images of sample areas were reconstructed from the generation of simulated data for sample areas containing damage zones of different shapes and sizes located at various positions within the region. Conclusive findings were made from the analysis of the resulting reconstructed images. Cross-borehole tomography is one of several stress wave tomographic techniques that has been used successfully in other industries, but have not fully matured in its use in the health monitoring of metallic and composite structures. [Copyright &y& Elsevier]

This paper investigates how Lamb waves respond to the presence of material degradation in a plate-like structure using a series of finite element analyses. To facilitate this study, the propagation of these guided waves was interpreted with the dispersion characteristics and displacement profiles were analysed in the frequency and wave number domain. The results show that the material degradation simulated by a local stiffness reduction which leads to changes in the dispersive characteristic of the propagating waves has made the Lamb waves technique become an effective tool to assess the material degradation. [Copyright &y& Elsevier]

With the development of new technology and use of lightweight material such as composite laminates, new methods must be developed for in situ structural health monitoring of these materials. This paper introduces an approach for the detection of delamination present in GLARE aluminium specimens. The approach is based on the change in group velocity of Lamb waves with frequency–thickness product as the determinant parameter for the detection of delamination. Two methods are applied: a surface contact method, which utilises a wedge probe tuned to excite a single Lamb mode, and the embedded PZT method, which involves incorporating lead zirconate titanate (PZT) elements in the glass fibre reinforced resin matrix during the manufacture of the GLARE aluminium specimens. It was found that both methods enabled the detection of delaminations in the GLARE aluminium specimens, within certain limits, which are stated. [Copyright &y& Elsevier]

The technique of permanently attaching piezoelectric transducers to structural surfaces has demonstrated great potential for quantitative non-destructive evaluation and smart materials design. For thin structural members such as composite laminated plates, it has been well recognized that guided Lamb wave techniques can provide a very sensitive and effective means for large area interrogation. However, since in these applications multiple wave modes are generally generated and the individual modes are usually dispersive, the received signals are very complex and difficult to interpret. An attractive way to deal with this problem has recently been introduced by applying piezoceramic transducer arrays or interdigital transducer (IDT) technologies. In this paper, the acoustic wave field in composite laminated plates excited by piezoceramic transducer arrays or IDT is investigated. Based on dynamic piezoelectricity theory, a discrete layer theory and a multiple integral transform method, an analytical–numerical approach is developed to evaluate the input impedance characteristics of the transducer and the surface velocity response of the plate. The method enables the quantitative evaluation of the influence of the electrical characteristics of the excitation circuit, the geometric and piezoelectric properties of the transducer array, and the mechanical and geometrical features of the laminate. Numerical results are presented to validate the developed method and show the ability of single wave mode selection and isolation. The results show that the interaction between individual elements of the piezoelectric array has a significant influence on the performance of the IDT, and these effects can not be neglected even in the case of low frequency excitation. It is also demonstrated that adding backing materials to the transducer elements can be used to improve the excitability of specific wave modes. [Copyright &y& Elsevier]

In this paper, results from a numerical study on the use of Lamb wave propagation for the detection of disbond growth beneath a composite repair patch are presented. Comparison carried out against experimental results that were done previously shows good agreement. The Lamb wave simulated in the numerical study was generated by surface bonded ceramic piezoelectric transducer. The power transmission of Lamb wave can be used to quantify the relative growth of the disbond. [Copyright &y& Elsevier]

The paper presents a set of numerical results on the use of surface mounted piezoelectric transducers to analyse the effects of impact damage and delamination of plate-like structures on the Lamb wave mode. The effects of the size, properties and orientation of the damage upon a propagating Lamb wave is qualitatively determined. In this paper, impact damage was simulated by a local change in the stiffness of the material in the structure and a delamination. The effects on the transmission of the incident Lamb wave when it propagates through a region of change in density are analysed. This paper will also demonstrate how the properties of a propagating Lamb wave can be affected by the existence of a delamination in a plate. [Copyright &y& Elsevier]

In this study, a damage identification approach was developed for carbon fibre/epoxy composite laminates with localized internal delamination. Propagation of the Lamb wave in laminates and its interaction with the delamination were examined. The fundamental symmetric Lamb wave mode, S0, and the lowest order shear wave mode, S0′, were chosen to predict damage location. A real-time active diagnosis system was therefore established. This technique uses distributed piezoelectric transducers to generate and monitor the ultrasonic Lamb wave with narrowband frequency. The two-way switches were employed to minimize the number of transducers. A signal-processing scheme based on the time–frequency spectrographic analysis was utilised to extract useful diagnostic information. Also, an optimal identification method was applied on damage searching procedure to reduce errors and obtain the diagnostic results promptly. Experiments were conducted on [0/−45/45/90]s CF/EP laminates to verify this diagnosis system. The results obtained show that satisfactory detection accuracy could be achieved. [Copyright &y& Elsevier]

• Two strategies for determination of elastic constants of carbon fibre-reinforced composites. • SEM models by using determined elastic constants and homogenised elastic constants investigated. • Guided wave modelling improvement underlined. • Validation on quasi-isotropic CFRP plate. • The analysis shows good agreement between optimised wavenumber profiles and the experimental one. There is a great potential for model-based approaches in which guided waves are utilised for damage detection, localisation and size estimation. However, to be effective, the model must accurately represent guided wave propagation behaviour, especially wave velocity dependence on the angle of propagation. Unfortunately, improperly assumed or derived through homogenisation elastic material properties can lead to larger wave velocity changes than caused by damage. In order to account for this problem, the elastic constants are estimated based on experimental measurements of Lamb waves and optimisation techniques. In the proposed approach, experimental measurements of full wavefield data of propagating Lamb waves are conducted by scanning laser Doppler vibrometer. The obtained wavefield data is processed by using the 3D Fourier transform. Slicing the data at selected frequencies yields wavenumber profiles. These profiles can be directly translated to wave propagation velocity dependence on the angle of propagation. Data can also be sliced at selected angles giving dispersion curve images. At the same time, wavenumber profiles or dispersion curves can be calculated by using a semi-analytical model for the range of material properties. A genetic algorithm is used in which the best fit between experimental data and the semi-analytical model is optimised. Experiments were conducted on a unidirectional CFRP panel and the above-mentioned procedure was applied. Identified material properties were used in the in–house code of the time domain spectral element method for simulations of the propagating waves. Finally, numerical results were compared to the experimental full wavefield data showing much better accuracy than in case of application of homogenisation techniques. Furthermore, the correctness of elastic constants determined by the proposed method was validated against the elastic constants obtained through static test standards. [ABSTRACT FROM AUTHOR]

An extension of the Legendre polynomial method is proposed, which allows to model coupled Lamb wave propagation in anisotropic multilayers with Kelvin-Voigt viscoelastic properties in a carbon-epoxy-layer sequence [0/ϕ/0]. In spite of complicated nonlinear dependences of the constituent equations on the viscoelastic properties, a linear relationship is found between the attenuation curves calculated by Hysteretic model, and the attenuation curves calculated by the Kelvin-Voigt model. In view of verifying the feasibility of using wave propagation analysis for non-destructive testing of composite materials, predictions are made concerning the dependence of the experimentally accessible phase velocities and attenuation coefficients of the modes on (virtual, defect induced, changes of) the viscoelastic constants in general and the fiber orientation in particular. In order to get a deeper insight in the material property sensitivity of the waves and in how to excite and detect them efficiently, also the through-thickness of displacements and energies profiles of different wave modes and frequencies are investigated, and how these depend on the viscoelastic moduli C ij. [ABSTRACT FROM AUTHOR]

This work focuses on the propagation characteristics of Lamb-type waves in a functionally graded piezoelectric (FGP) small-scale plate. Based on the modified couple stress theory, Legendre orthogonal polynomial method (LOPM) is extended to perform the solving process. By introducing the rectangular window function and expanding the electric potential and displacement vectors to Legendre orthogonal polynomial series, the governing equations satisfying the electric-open and electric-short circuit boundary conditions are presented respectively. The solutions based on the global matrix method (GMM) are deduced to verify the correctness of this extended LOPM. Since there is no layered processing, the extended LOPM provides a more realistic analysis model for the FGP small-scale plate and has a high computational efficiency. Furthermore, the dispersion characteristics, stress and electromechanical coupling factor are investigated in details. Results show that the size and piezoelectric effect increase the phase velocity, and the piezoelectricity suppresses the influence of couple stress on the dispersion characteristics. The Lamb wave phase velocities of the first and second modes with different L y always converge to two fixed values at different convergence speeds. The conclusions obtained can be applied to the design and dynamic response evaluation of composite small-scale structures. [ABSTRACT FROM AUTHOR]

Lamb waves can be used in carbon fiber reinforced plastics (CFRP) for establishing both structural health monitoring systems and nondestructive inspection techniques. In this study, we investigated the dispersion relation of Lamb waves propagating in a cross-ply CFRP laminate. Using a formalism of the multi-layer Lamb wave model, we compared a homogeneous single-layer model and multi-layer models. The results suggest that the velocity of the S 0 mode was the same for all the models in the low-frequency region. Thus, the use of homogeneous parameters is valid for the S 0 mode. However, it was found that in high-frequency regions, there was a discrepancy between the velocities of Lamb wave modes for the homogeneous model and multi-layer models. This is because Lamb waves can be localized in a particular layer, and the velocity can be affected by the stiffness constants of the layer. This work elucidates the characteristics of Lamb wave propagation by showing that the stacking sequence of the laminate can have an effect on the wave velocities and wave structures, enabling researchers to improve Lamb wave-based defect detection. [ABSTRACT FROM AUTHOR]

Lamb waves are used in various non-destructive testing (NDT) and structural health monitoring (SHM) applications due to their velocity sensitivity to the properties of the material and their propagation over the entire thickness of the object over a long distance with low attenuation. However, the interpretation of the received signals is complex due to the Lamb waves dispersion nature, multiple mode generation, reflections and other. This work presents a novel method for the Lamb waves fundamental modes phase velocity dispersion evaluation and reconstruction of these curves segments using only two signals measured at two close points. The carried out investigation using simulated signals has shown that the proposed method works with an extremely high accuracy - the mean relative error from the true values is less than 0.01%. The proposed method has been experimentally verified in two different mediums: isotropic – aluminium plate and anisotropic GFRP plate. The obtained results have indicated have that the mean relative error from the true values is less than 1% in the aluminium case. The comparison of the results obtained in the GFRP plate case has indicated that the proposed method allows to reconstruct the phase velocity dispersion curves segments in the object of complex structure. [ABSTRACT FROM AUTHOR]

The current work is devoted to the problem of the validation of dispersion curves and numerical simulations of fundamental Lamb wave and shear horizontal elastic wave modes for fiber metal laminates (FML). In the present study, two types of FM laminates are considered. In the first case, the studied composite material consists of 7 layers: one layer is made of aluminum alloy AW-6060 while the rest of the layers are made of carbon/epoxy resin. In the second case, the FML is constructed of one layer of aluminum alloy and the rest six layers are made of glass/epoxy. In order to extract the dispersion curves for the fundamental S0, SH0, and A0 modes, as well as higher modes from the range 5 up to 1000 [kHz], the stiffness matrix method, is employed. In the first case the computations are performed for the following cross-ply stacking sequences: [Al, ±5° 6 ], [Al, ±15° 6 ], [Al, ±25° 6 ], ... , [Al, ±85° 6 ]. Next, the FEM simulations of elastic wave propagation are performed in the case of plates, which are made of analyzed FML composites. In the first studied FML material, the fundamental symmetric mode S0 is generated while in the second case the fundamental antisymmetric mode A0 is excited. It occurred that in the case of aluminum alloy/carbon fibers the generation of the pure fundamental symmetric mode S0 is very difficult. In addition, the fundamental symmetric mode S0, the shear horizontal SH0, and the antisymmetric A0 wave modes are also present. In the case of aluminum alloy and carbon/epoxy, the pure antisymmetric mode A0 can be relatively easily generated. However, a significant dispersion phenomenon is visible. For the aluminum alloy and glass/epoxy, the obtained results are experimentally verified. [ABSTRACT FROM AUTHOR]

Carbon fibre reinforced polymer (CFRP) has proved to be effective in strengthening ageing steel structures, due to its outstanding properties. However, debonding problems which can occur at the interface severely impair the performance of retrofitted structures. In this paper, a guided wave based structural health monitoring (SHM) method is employed to detect debonding in CFRP-reinforced steel structures. The proposed samples are CFRP-reinforced steel plates with different sizes of debonding. Due to its sensitivity to interfacial damage, the anti-symmetrical Lamb wave mode is chosen as the incident wave and surface-mounted piezoelectric (PZT) wafers are employed to excite and collect the signals. Theoretical derivation is introduced to find the relationship between the time-of-flight (ToF) of the first arrival wave package in the received signals and the extent of debonding damage. A linear relationship is obtained, in that the ToF decreases linearly with the increase in the size of debonding. When corresponding numerical simulation and experimental study are performed to verify the relationship, similar trends are observed. [ABSTRACT FROM AUTHOR]

• The effect of delamination on reflection coefficient of Stoneley wave is discussed. • The variation of reflection coefficient is half-sine. • The variation of reflection coefficient can be interpreted by interference principle. • The variation of reflection coefficient is verified by experimental validation. Stoneley wave is a kind of ultrasonic guided wave propagating along a solid-solid bonded interface with two different materials. In this paper, the influence of interfacial delamination size on the reflection coefficient of Stoneley waves in a double-layered medium is investigated. According to the energy distribution of Stoneley waves, an appropriate integral region is selected, and the reflection coefficient of Stoneley waves encountering delamination is derived via reciprocity theorem. An example of delamination composed of two arcs is introduced. The effects of delamination radius, delamination width and Stoneley wave wavelength on the reflection coefficient are discussed. It is observed that the reflection coefficient decreases and gradually stabilizes as the delamination radius increases. Meanwhile, the variation of reflection coefficient with the ratio of the delamination width to the Stoneley wave wavelength is half-sine and this can be interpreted by the interference principle. Finally, some experimental validations are carried out on an aluminum-steel plate. The delamination location is tested by pulse-echo approach and the half-sine variation of the reflection coefficient with the ratio of the delamination width to the Stoneley wave wavelength is measured. The variation of reflection coefficient provides a reference for the measurement of the interfacial delamination size in nondestructive testing. [ABSTRACT FROM AUTHOR]

• One-sided approach for determination of elastic constants of woven fabric reinforced composite. • Semi-analytical spectral element method for dispersion curves calculation. • Parametric studies of material properties of composite constituents on dispersion curves of guided waves. • Original objective function proposed for optimisation of elastic constants. • The analysis shows good agreement between optimised dispersion curves and the experimental one. Typically, material properties are estimated by destructive tests and used in computational models in the design and analysis of structures. This approach is well-established in relation to isotropic homogenous materials. However, if this approach is used for composite laminates, inaccuracies can arise that lead to vastly different stress distributions, strain rates, natural frequencies, and velocities of propagating elastic waves. In order to account for this problem, the alternative method is proposed, which utilise Lamb wave propagation phenomenon and optimisation technique. Propagating Lamb waves are highly sensitive to changes in material parameters and are often used for structural health monitoring of structures. In the proposed approach, the elastic constants, which are utilised to determine dispersion curves of Lamb waves, are optimised to achieve a good correlation between model predictions and experimental observations. The dispersion curves of Lamb waves were calculated by using the semi-analytical spectral element method. The resulting dispersion curves were compared with experimental measurements of full wavefield data conducted by scanning laser Doppler vibrometer and processed by 3D Fourier transform. Next, elastic constants were determined by using a genetic algorithm which resulted in a good correlation between numerical and experimental dispersion curves. [ABSTRACT FROM AUTHOR]

This paper presents a baseline-free damage detection method which leverages the multipath reflected Lamb waves for structural prognosis. From the viewpoint of ray tracing, the reflection of a propagating wave at a free edge is considered as a virtual transducer sitting at the mirrored location of the actual one, injecting excitation into the structure, or recording Lamb waves traveling from the source. These extra echoes arise waves that inspect the structure from different directions, which is equivalent to adding sensing paths into the sensor network. On this basis, the reciprocity breaking effects of each sensing path is quantitatively evaluated by measuring the waveform differences of the associated wave packets in the two response signals that recorded before and after the transmitter and receiver exchange their roles. Note that the indirect sensing paths related to edge reflections consist of several segments. The probabilistic imaging method is modified to accommodate both direct and indirect paths. The proposed multipath Lamb wave imaging algorithm is validated using an experiment conducted on a composite plate with simulated damages. The results demonstrate its availability and effectiveness, i.e., damage detection and localization is achieved using a single transmitter–receiver pair. [ABSTRACT FROM AUTHOR]

In this paper, the hybrid Delay-And-Sum (DAS) with Sparse Reconstruction (SR) method was further developed for damage location in composite plates. In composite materials, anisotropy leads to some challenges in using conventional damage location methods, which are developed for isotropic materials. In the hybrid DAS-SR method, the DAS and SR methods were combined as a complement of each other. To investigate the DAS-SR method for composite structures, the group velocity of the travelling wave for different directions was first measured experimentally via PZTs. The DAS and SR formulations were then modified to be compatible with the direction-dependent group velocities. The results show that this modification increases the accuracy of the DAS and SR methods for damage location in a composite plate. However, using group-velocity instead of phase-velocity in the standard SR method, causes some model mismatch and errors in the damage localization and this problem was solved by using the modified hybrid DAS-SR method. The experimental results demonstrated that the performance of the modified hybrid method for detection and location of barely visible impact damages as well as for multi-location artificial damages is better than that of the DAS and SR methods when separately used. [ABSTRACT FROM AUTHOR]

• Lamb wave propagation method can be used for the detection of matrix cracking. • The Lamb wave velocity and amplitude decreased with matrix crack density. • Artificial intelligence methods helped the classification of matrix cracking. • Employing the linear discriminant analysis enhanced the classification accuracy. The guided wave propagation and artificial intelligence (AI) approaches were used to propose an intelligent model for automatic detection and classification of the matrix cracking in composites. Glass/epoxy cross-ply laminated composites were fabricated and the matrix cracking with several densities was induced in 90° layers. A non-destructive testing procedure using the fundamental antisymmetric Lamb wave propagation was performed on the intact specimens and those with 0.05, 0.15, and 0.25 matrix cracking density. The velocity of propagated Lamb wave, wave amplitudes in four different distances from the actuator, and the ratio of these amplitudes to the first received wave amplitude, in three frequencies of 100, 200, and 330 kHz were extracted from the acquired signals. The extracted sensory features were used to train three types of supervised machine learning models for the crack density classification. The linear discriminant analysis (LDA) was performed for dimensional reduction to find a linear combination of features that can better discriminate the classes. Support vector machines (SVM), linear vector quantization (LVQ) neural network (NN), and multilayer perceptron (MLP) NN were used for the classification. It was shown that SVM accounted for the highest classification accuracy (91.7%) followed by LVQ NN (88.9%) and MLP NN (77.8%), respectively. [ABSTRACT FROM AUTHOR]

In this paper, we present our investigation of impact damage modeling in a quasi-isotropic CFRP plate in which guided Lamb waves propagate. Because impact damages in CFRP structures consist of multiple microscopic damages, such as delamination, shear cracks, and transverse cracks, it is difficult to precisely model the impact damages for FEM analysis. However, in order to investigate the SHM systems to detect impact damages, we need to model various kinds of impact damages easily. Therefore, we attempt to establish a simple modeling method of impact damages. When the wavelength of a Lamb wave is much longer than the microscopic damages, we can assume the impact-damaged area as a homogeneous region with the stiffness degradation. The benefit of this model is to reduce the time to construct FEM models. In particular, we can easily set several damages in various positions of the structure. [ABSTRACT FROM AUTHOR]

• Polynomial method for Lamb wave in anisotropic multilayered piezoelectric laminates. • The proposed method is validated by comparing it with MRRM. • Illustrates the effect of initial stress on the phase and group velocities of Lamb waves. • Tensile initial stress makes phase and group velocities increasing. In this paper, the influence of an initial stresses on the Lamb waves propagation in an anisotropic multilayered piezoelectric laminates is investigated. Formulations are given for only open circuit surface; while the Legendre polynomial method is employed for calculate the wave propagating characteristics. To validate our numerical strategy, this polynomial approach was applied to simulate lamina composite structures. Relatively good results were obtained compared to reliable data available from the literature ones, with relatively significant computation effort. Convergence of the present method is discussed. Influence of initial stresses and fiber orientation angle on the behaviors of Lamb waves is analyzed. Results confirm that the behavior of Lamb modes depends not only on the initial stress but also on fiber orientation. Next, the dispersion curves of fundamental Lamb modes in sandwich plates with 0°/θ°/0 configuration are calculated. Finally, the optimal angles in PVDF-θ° with initial stresses for which the Lamb modes exist are also analyzed. These results for the composite structures may render as a useful reference for the design of ultrasonic transducers in industry for non-destructive testing especially that encounters initial stresses. [ABSTRACT FROM AUTHOR]

This study presents a combined experimental and numerical study on the determination of the stiffness matrix of transversely isotropic thin laminated composite structures non-destructively with the use of group velocity measurements. The approach relies on the usage of A0 and S0 modes of Lamb waves, triggered the by pencil-lead break, which propagate in the composite material, and enables the evaluation of various elements of the stiffness matrix. It is proven that the experimental Lamb wave method can be reliably utilized for determining the components of the stiffness matrix, C ij . The results are validated with respect to those of mechanical characterization and finite element analysis. [ABSTRACT FROM AUTHOR]

In this study, experimental and numerical approaches based on the nonlinear ultrasonic Lamb wave are used to detect the barely visible impact damages (BVID) in orthotropic CFRP laminates due to low velocity impact (LVI). A drop-weight impact test system and a RITEC nonlinear ultrasonic system are adopted for experimentally measuring the higher harmonics of lamb wave in the damaged CFRP laminates. An integrated finite element (FE) model is proposed to further identify the interaction between Lamb wave and impact damages, in which Hashin criterion and triangular cohesive zone model (TCZM) are used to predict the initiation and evolution of delamination and other damages under LVI. Then, the displacement–time signal and the relative acoustic nonlinear parameters (RANP) of the Lamb wave excited by sinusoidal displacement load are extracted to evaluate the damage in the same FE model. Finally, the relevance between LVI damage and RANP is investigated by numerical and experimental analyses under LVI with different energies, and shows that the amplitudes of harmonics and RANP increase with the raise of the impact energy, as well as the delamination areas. Therefore, the amplitude of harmonics and RANP can be used as indicators to detect BVID. [ABSTRACT FROM AUTHOR]

The purpose of the present study is to develop a nondestructive evaluation method and propose a model-independent viscoelastic characterization approach for the identification and classification of the matrix cracking in polymeric composites using the Lamb wave propagation method. To this end, cross-ply laminated composite specimens were fabricated and matrix cracking with different crack densities was induced in specimens using a tensile testing machine. The crack density was first measured by an optical microscope and compared with that of predicted by the Hashin model. Then, the fundamental anti-symmetric Lamb wave (A 0) at a frequency of 206 kHz was propagated in specimens using an ultrasound actuator and an ultrasound probe to obtain the characteristics of the induced waves including the displacement phase and the amplitude at different locations of the specimens along the propagation direction. Then, the corresponding inverse Lamb wave propagation problem was solved and the elastic and viscoelastic properties of specimens were estimated. The elastic modulus measured by the present method was in good agreement with the results obtained by an optical microscope and predicted by the Hashin model. The viscoelastic properties of specimens also showed good sensitivity to the severity of the induced matrix cracking. [ABSTRACT FROM AUTHOR]

Developing the approach outlined in Part I, the wavenumber spectrum is evaluated. Firstly, for the n th complex dispersion curve the asymptotics of the wavenumber's static value is considered as n → + ∞. Two approaches to obtain this asymptotics are compared. Then, for any n the exact value in statics is calculated using iterations, starting with the asymptotic value as the initial approximation. The parametric analysis revealed a specific (critical) value of the geometrical parameter at which the wavenumbers are redistributed. Secondly, the low frequency asymptotics of the dispersion curves are obtained. They exibit the flat initial segment of each complex dispersion curve which is the longer, the larger is the index n of the curve. Thus, this part of spectrum can be described by simple analytical formulas. The exact dispersion curves are evaluated using another iterative algorithm for improving the approximations. For both steps the numerical results are in a good agreement with the asymptotics. Finally, the perspectives of the method for other composite structural members are discussed. [ABSTRACT FROM AUTHOR]

A new method combining the asymptotic and iteration approaches to study the total wavenumber spectrum for a plate made of isotropic layers is suggested. In this part we use the propagator matrices to deduce the dispersion equation and its static limit in a closed form with the use of symbolic calculations. The roots in statics which are analyzed at the first step play the key role. Then, the low frequency approximations for the dispersion curves are derived. The method is aimed to evaluate a dispersion curve of any order n and to describe it in a closed form by an asymptotic formula. Especially it concerns the case n → + ∞ which causes difficulty for the pure numerical approaches. [ABSTRACT FROM AUTHOR]

This study aims to use the passive and active acoustic-based health monitoring methods for impact damage assessment of composite structures. To this aim, a Carbon Fiber Reinforced Polymer (CFRP) composite plate was fabricated and subjected to a simulated low-velocity impact by performing repeated quasi-static indentation tests where a loading-unloading-reloading test profile with 5 repetitions was adopted. Two Acoustic Emission (AE) broadband sensors and a network of eight piezoelectric (PZT) sensors were attached on the composite plate surface. AE (passive method) was employed during the loading and reloading phases of the indentation tests to online monitor the critical damage occurrence and also specify the damage type while scanning of the plate with Lamb waves (active method) was done to localize the damage when the structure was unloaded. Felicity Ratio (FR) index which was calculated based on the AE data could accurately detect that critical damage occurred during the 5th loading-unloading-reloading stage when the structural integrity dropped to 60% of its initial stage. Furthermore, Lamb wave signals of central frequency 150 kHz localized the impact damage with error of 0.89 cm (3.6% error respect to the shortest dimension of the scanned area). [ABSTRACT FROM AUTHOR]

Stiffened composite panels are widely used in industry, and their safety requirements have drawn great attention. However, non-destructive testing and evaluation (NDT&E) methods for these panels are still limited. This is due to the fact that the stiffeners induce complex signals during damage detection. This paper presents a new damage detection method for stiffened composite panels based on Lamb waves. The method combines a quantitative wavefront expression for an anisotropic composite and the conventional time-of-flight (ToF) method to detect debonding damage between stiffeners and the composite skin as well as low-velocity impact damage in the skin sheet. Initially, Lamb wave propagation characteristics are evaluated by numerical simulations to obtain mode conversion at the stiffener and delay after transmission through the stiffener. Then the numerical simulations and experiments are implemented in stiffened cross-ply composite laminates to verify the effectiveness and accuracy of the proposed method. Results indicate that the proposed method can accurately locate damage and has potential for industrial application. [ABSTRACT FROM AUTHOR]

A narrowband tone burst excitation is usually required in most Lamb wave inspection techniques in order to reduce the dispersion effect and maintain mode purity, especially in the case that dispersion compensation is hard to implement, such as the scenarios prior knowledge of accurate dispersion curves is not available. The duration of the excitation is relatively large because of its narrow bandwidth, which degrades the resolution for inspection. Following the emerging sparse representation theory, a combined method of sparse reconstruction and delay-and-sum (DAS) for high resolution Lamb wave inspection is proposed in this paper. The scattering signals are compressed in time domain without losing the information of the arrival time of each echo. Unlike most methods that signal decomposition and reconstruction use the same dictionary, the proposed approach utilizes two different dictionaries: one for signal decomposition and another for feature extraction. The DAS imaging method combined with the feature signals is applied to damage imaging for carbon fiber reinforced plastic (CFRP) laminates. The effectiveness of the proposed approach is validated on a quasi-isotropic laminated CFRP plate. The imaging results show that the proposed approach can achieve a higher localization resolution and lower noise floor without degrading the localization accuracy. [ABSTRACT FROM AUTHOR]