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Purpose: Most Lamb wave-based damage detection techniques use scattering signals obtained from the subtraction of baseline and current signals. This article presents a baseline-free damage detection method based on the signals scattered by the damage in plate-like structures containing a circular hole with edge cracks using guided ultrasonic waves (GUWs) and signal processing. Methods: First, the GUWs were generated by simulating 16 transducers, using finite element analysis and ABAQUS. The location of transducers on the plate were set in a way that similar paths were made for waves traveling from actuators to sensors. Then, the differences between the similar path signals (residual signals) were obtained. The damaged path and arrival time of the scattered wave from the defect to the sensor location were determined using the wavelet coefficients obtained from continuous wavelet transform of the residual signals. Finally, to identify damage locations, arrival time data is applied in a probabilistic approach. Results and Conclusion: The numerical simulation results reveal that the baseline-free approach is able to accurately detect the location of the multiple damages occurred at the hole edge. Further, in order to investigate the effect of the edges of the plate on the results of damage detection, the transducers were considered at different distances from the edge of the hole. By ignoring the damage index values obtained at the edges of the plate, it can be stated that even when the transducers are located near the edges of the plate, the proposed method can detect the crack location at the edge of the hole. [ABSTRACT FROM AUTHOR]

The scattering phenomena of the fundamental antisymmetric Lamb wave mode with a horizontal notch enabling the partial energy transfer (PET) option is addressed in this paper. The PET functionality for a given waveguide is realized using the material interface. The energy scattering coefficients are identified using two methods, namely, a hybrid approach, which utilizes the finite element method (FEM) and the general orthogonality relation, and the semi-analytical approach, which combines the modal expansion technique with the orthogonal property of Lamb waves. Using the stress and displacement continuity conditions on the present (sub)waveguide interfaces, one can explicitly derive the global scattering matrix, which allows detailed analysis of the scattering process across the considered interfaces. Both methods are then adopted on a simple representation of a surface breaking crack in the form of a vertical notch, of which a certain section enables not only the reflection of the incident energy, but also its nonzero transfer. The presented results show very good conformity between both utilized approaches, thus leading to further development of an alternative technique. [ABSTRACT FROM AUTHOR]

• Construction of transparent boundary conditions (TBCs) for exural wave cavity scattering in two dimensions, ensuring the satisfaction of the sommerfeld radiation conditions. • Deduction of a decomposed problem for the biharmonic plate wave equation using two auxiliary functions and establishment of the unique-ness of the solution for the decomposed problem. • Proposal of the linear _nite element method with interior penalty term (IP-FEM) and boundary penalty term (BP-FEM) to solve the coupled boundary helmholtz and modi_ed helmholtz equations, leading to stable numerical solutions. • Introduction of an analytical solution for exural wave scattering by a circular cavity with a clamped boundary, facilitating comparative analysis. Flexural wave scattering plays a crucial role in optimizing and designing structures for various engineering applications. Mathematically, the flexural wave scattering problem on an infinite thin plate is described by a fourth-order plate wave equation on an unbounded domain, making it challenging to solve directly using the regular linear finite element method (FEM). In this paper, we propose two numerical methods, the interior penalty FEM (IP-FEM) and the boundary penalty FEM (BP-FEM) with a transparent boundary condition (TBC), to study flexural wave scattering by an arbitrary-shaped cavity on an infinite thin plate. Both methods decompose the fourth-order plate wave equation into the Helmholtz and modified Helmholtz equations with coupled conditions on the cavity boundary. A TBC is then constructed based on the analytical solutions of the Helmholtz and modified Helmholtz equations in the exterior domain, effectively truncating the unbounded domain into a bounded one. Using linear triangular elements, the IP-FEM and BP-FEM successfully suppress the oscillation of the bending moment of the solution on the cavity boundary, demonstrating superior stability and accuracy compared to the regular linear FEM when applied to this problem. [ABSTRACT FROM AUTHOR]

• Semi-analytical approach presenting derivation of the scattering matrix related to the region with adhesively bonded joint. • Effect of the energy balance convergence of local sub-waveguide sections on the global scattering matrix. • Effect of the number of considered complex wavenumbers entering the computational process on the predicted results accuracy. Problems related to scattering phenomena of the antisymmetric fundamental Lamb wave mode with an adhesively bonded lap joint containing a disbond in the adhesive layer is being solved within the framework of this paper. Overall, two methods are used in order to identify energy scattering coefficients of reflected as well as transmitted Lamb waves. These methods include a hybrid approach, which incorporates the finite element method (FEM) with general orthogonality relation, and semi-analytical approach, combining the modal expansion technique and orthogonal property of Lamb waves. With the use of the stress and displacement continuity condition on selected interfaces, it is possible to explicitly derive the global scattering matrix, containing the information related to the scattering process of present Lamb wave modes in a given geometry. Both approaches are then adopted on three configurations of the adhesively bonded lap joint in terms of the length of the disbond, which is then positioned within the overlapped region. The obtained results, among others, clarify the relationship between geometric parameters of the region containing the overlapping with the horizontal disbond and the role of non-propagating modes in the computational process of energy scattering coefficients of propagating modes. [ABSTRACT FROM AUTHOR]

The second-harmonic generation of the fundamental antisymmetric Lamb wave at a closed parallel crack in an elastic plate is studied by numerical analysis. The closed crack is modeled as a spring-type interface with quadratic nonlinearity. Based on a perturbation method, the problem of nonlinear Lamb wave scattering is decomposed into two linearized problems, i.e., for the linear reflection/transmission of the incident Lamb wave at the crack and for the generation/radiation of the second-harmonic Lamb waves due to the contact nonlinearity. The reduced problems are solved by the finite element method in the frequency domain. Numerical results demonstrate significant effects of the crack resonance on the linear and nonlinear Lamb wave scattering responses, which appear as sharp peaks/dips in the reflection/transmission spectra and enhanced second-harmonic amplitudes at some frequencies. Two simple frequency selection rules are established which explain the enhanced generation of the second-harmonic Lamb waves. The time-domain analysis is also carried out to supplement the frequency-domain analysis, which confirms that the incident Lamb wave interacts with the crack at some specific frequencies in its bandwidth in a selective manner and enhances the generation of the second-harmonic components. [ABSTRACT FROM AUTHOR]

This paper presents an inexpensive but accurate analytical method to calculate the scattering of straight-crested Lamb waves from cracks parallel to the plate surface. The same method is applicable for the disbond problem. In this method, the scatter field is expanded in terms of complex Lamb wave modes with unknown amplitudes. These unknown amplitudes are obtained from the boundary conditions using vector projection utilizing the power expression. The process works by projecting the stress conditions onto the displacement eigen-spaces of complex Lamb wave modes and vice versa. The authors call this technique “complex modes expansion with vector projection” (CMEP). The CMEP approach is versatile and can be readily applied to corrosion, cracks, or disbonds. In this paper, the CMEP method is applied to a horizontal crack in a plate. For verification of the results the authors compared them with the results obtained by using the finite element method (FEM) and literature. The FEM analysis was conducted in the frequency domain with non-reflecting boundaries. It was found that CMEP results correspond very well with FEM results over a wide frequency-thickness range up to 1.5MHz mm with CMEP being orders of magnitude faster than FEM. [ABSTRACT FROM AUTHOR]

The study investigates the accuracy of analytical solutions to the fundamental anti-symmetric Lamb wave scattering at delamination in multilayered isotropic plates. The analytical models are based on the wave function expansion method and Born approximation within the framework of Mindlin plate theory. The study validates the accuracy of modeling the delamination as an inhomogeneity with reduced bending rigidity in predicting Lamb wave scattering induced by geometry change at the delaminated region. A good agreement is observed between the analytical solutions and results of experimentally verified 3D explicit finite element (FE) simulations. The findings support the inhomogeneity assumption in Lamb wave scattering problems and show the feasibility of employing it in delamination characterization. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a theoretical and finite element (FE) investigation of the scattering characteristics of the fundamental anti-symmetric (A 0) Lamb wave at delaminations in a quasi-isotropic (QI) composite laminate. Analytical models based on the Mindlin plate theory and Born approximation are presented to predict the A 0 Lamb wave scattering at a delamination, which is modelled as an inhomogeneity, in an equivalent isotropic model of the QI composite laminate. The results are compared with FE predictions, in which the delamination is modelled as a volume split. The equivalent isotropic model and QI composite laminate are used to investigate the feasibility of the common theoretical approach of modelling the delamination as the inhomogeneity. A good correlation is observed between the theoretical solutions and FE results in the forward scattering amplitudes, but there exists a larger discrepancy in the backward scattering amplitudes. The FE results also show that the fibre direction of the outer laminae has a pronounced influence on the forward and backward scattering amplitudes, which is not predicted by the analytical models. [Copyright &y& Elsevier]

This article investigates the scattering characteristics of Lamb waves from a debonding at a structural feature in a composite laminate. This study specifically focuses on the use of the low frequency fundamental antisymmetric (A0) Lamb wave as the incident wave for debonding detection. Three-dimensional finite element (FE) simulations and experimental measurements are used to investigate the scattering phenomena. Good agreement is obtained between the FE simulations and experimental results. Detailed parameter studies are carried out to further investigate the relationship between the scattering amplitudes and debonding sizes. The results show that the amplitude of the scattered A0 Lamb wave is sensitive to the debonding size, which indicates the potential of using the low frequency A0 Lamb wave as the interrogating wave for debonding detection and monitoring. The findings of the study provide improved physical insights into the scattering phenomena, which are important to further advance damage detection techniques and optimize transducer networks. [ABSTRACT FROM AUTHOR]

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]

This study focuses on the three-dimensional (3D) scattering characteristics of the fundamental anti-symmetric (A0) Lamb wave at a delamination in composite laminates. The understanding of the scattering characteristics plays an important role in the application of Lamb wave based damage detection techniques. One critical factor affecting the performance of Lamb wave based damage detection techniques is the angular distribution of the scattered wave amplitudes at the delamination. Analytical solutions for this problem do not exist due to the anisotropic nature and multilayer characteristics of composite laminates. This paper employs a 3D fi nite element method to analyse the A0 mode Lamb wave scattering characteristics at delaminations. Good agreement is found between the simulations and experimental measurements. Extended parameter studies show that the angular distribution of the scattered wave amplitudes depends on the stacking sequence of the laminates, the damage size to wavelength ratio and the through-thickness location of delamination. The results of these studies provide improved physical insight into the scattering phenomena at a delamination, which can be used to validate and improve the performance of Lamb wave based damage detection methods by selecting transducer locations and excitation frequency. The study also investigates the feasibility of simulating delamination damage by bonding masses to the surface of composite laminates for Lamb wave based damage detection and characterisation methodologies verifi cation. The results suggest that simulating delamination damage by bonded masses requires careful design and is not as straight forward as suggested in the literature. [ABSTRACT FROM AUTHOR]

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]

This study uses a spectral method to study wave scattering by the local defect in the structural waveguide. The force response is decomposed into some subproblems by combining with standard finite element method with lower computational cost. Dynamic reduction method is used for both the narrowband and wideband analyses of wave scattering by defects or some standard structural features. Numerical study of plate mode scattering by defects indicates that the mode conversions complicate the resultant signal, and a set of modes with different frequencies is necessary to properly estimate the defect type and severity. If the wideband wave modes are generated, some signal processing, such as time-frequency analysis, should be used for mode identification or defect localization. Numerical study can also be extended to more complex structures, and some conclusions from the presented investigations are also suitable to those cases. [ABSTRACT FROM AUTHOR]

This paper considers the scattering of Lamb waves due to the discontinuity of elastic plate waveguide. A method of analysis is presented which is a combination of the finite-element method and analytical solution. The analytical solution is derived taking the cut-off mode into consideration. Consequently, the region of application of the finite-element method is reduced drastically compared with the traditional method of analysis by finite-element method ignoring the cut-off mode. In the past, the formulation has been made by restricting the discontinuities to symmetrical distribution in regard to the central plane of the plate. In this paper, this restriction is removed and discontinuities of any distribution in regard to the elastic plate can be handled. The effectiveness of taking the cut-off mode into consideration is verified by applying the proposed method to the scattering of Lamb waves by a free-edge of the elastic plate and by a slit which is symmetrical in regard to the central plane of the plate. As examples of discontinuities with asymmetrical distribution in regard to the central plane of elastic plate, a slit on one of the surfaces and wedge-shaped crack are considered. The result of analysis is presented for the scattering characteristics when a fundamental symmetric Lamb wave or fundamental antisymmetric Lamb wave is incident. [ABSTRACT FROM AUTHOR]

The scattering phenomena of the zero-order antisymmetric Lamb wave mode with a horizontal crack of finite length, symmetrically positioned with respect to the median plane of the plate is being solved within the framework of this paper. The identification of the scattering coefficients is carried out with the use of a semi-analytical model incorporating the mode-matching technique. Thanks to explicit expression of the transmission and reflection scattering matrices at the local as well as, global scale, it is possible to analyze the scattering process more comprehensively. Moreover, the results affiliating to the scattered modes with real wavenumbers are confronted with ones obtained using the hybrid model based on the finite element method utilization and the general orthogonality relation. The scattering process is being investigated on three regions characterized by specific crack length intervals for which the study related to the role of non-propagating modes in the energy balance process on present interfaces formed by adjacent waveguide sections is performed. [ABSTRACT FROM AUTHOR]