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Composite structures are widely used for aerospace applications but are prone to barely visible impact damage from low velocity impacts. Guided wave measurements using sparse arrays of distributed sensors provide an important structural health monitoring (SHM) tool for detecting and localizing impact damage in composites. However, the anisotropy of composites needs to be considered as it can affect guided wave propagation and scattering, impacting imaging performance. Improved defect characterization can be achieved by considering the scattering characteristics for the signal processing. Scattering around two different damage types for multiple incident wave directions in a quasi-isotropic carbon fiber reinforced polymer (CFRP) panel were investigated. Full 3D Finite Element (FE) simulations were compared to the measured scattered guided wave field at an artificial insert delamination. Permanent magnets mounted on an undamaged region of the plate were used as scattering targets and both numerical and experimental scattering patterns were compared to the delamination results. Strong directional dependency was observed for both damage types, with energy focusing along the fiber directions of the outer ply layers. For the delamination, mostly forward scattering is observed for all incident wave directions, whereas the magnet blocked forward wave transmission and scattered wave energy in all directions. 2D scattering matrices were calculated, demonstrating distinct scattering behavior for each damage type. Implications of anisotropy and angular scattering on SHM guided wave sparse array imaging are discussed. [ABSTRACT FROM AUTHOR]

The aim of this work is to present theoretical tools to study wave propagation in elastic waveguides and perform multi-frequency scattering inversion to reconstruct small shape defects in elastic waveguides and plates. Given surface multi-frequency wavefield measurements, we use a Born approximation to reconstruct localized defect in the geometry of the plate. To justify this approximation, we introduce a rigorous framework to study the propagation of elastic wavefield generated by arbitrary sources. By studying the decreasing rate of the series of inhomogeneous Lamb mode, we prove the well-posedness of the PDE that model elastic wave propagation in two- and three-dimensional planar waveguides. We also characterize the critical frequencies for which the Lamb decomposition is not valid. By using these results, we generalize the shape reconstruction method already developed for acoustic waveguide to two-dimensional elastic waveguides and provide a stable reconstruction method based on a mode-by-mode spacial Fourier inversion given by the scattered field. [ABSTRACT FROM AUTHOR]

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]

Structural health monitoring of riveted aircraft panels is a real challenge for maintenance engineers. Here, a diffused Lamb wave field is used for fatigue-crack detection in a multi-riveted strap-joint aircraft panel. The panel is instrumented with a network of low-profile surface-bonded piezoceramic transducers. Various amplitude characteristics of Lamb waves are used to extract information on fatigue damage. A statistical outlier analysis based on these characteristics is also performed to detect damage. The experimental work is supported by simplified modelling of wave scattering from crack tips to explain complex response features. The Local Interaction Simulation Approach (LISA) is used for this modelling task. The results demonstrate the potential and limitations of the method for reliable fatigue-crack detection in complex aircraft components. [ABSTRACT FROM AUTHOR]

A thorough understanding of the scattering mechanism of Lamb waves at discontinuities is of interest for quantitative evaluation of structural properties and mode control. This study extends the generalized scattering matrix method to investigate the interaction of straight crested Lamb waves with multiple cascaded rectangular notches. Based on the orthogonality and completeness of Lamb modes, the mode matching method is utilized to determine the scattering matrices of downward and upward step discontinuities. After that, the generalized scattering matrix method is employed to determine the scattering matrices of a single rectangular notch and the recurrence relations between the scattering matrices of n + 1 cascaded notches and those of n cascaded notches. Finally, the scattering matrices of multiple cascaded notches can be easily obtained taking advantage of the recurrence relations. As the number of cascaded notches increases, more and sharper peaks appear in the scattering coefficient curves. The finite element simulations conducted in the time domain validate the theoretical results for cascaded notches with identical or different depths, which demonstrate that this method can be applied to find the scattering coefficients at piece-wise periodic or nonperiodic waveguides. The generalized scattering matrix method may have potential applications in quantitative nondestructive evaluation and mode control. [ABSTRACT FROM AUTHOR]

The interaction between an oblique gravity wave and a partial porous flexible plate barrier in a two-layer fluid with an undulating bottom has been studied using small amplitude and structural response theory. Separate cases for (a) scattering of wave and (b) trapping of wave by porous flexible plate in the presence of an impermeable sea wall are discussed. The submerged plate of two typical configurations, bottom standing and surface piercing, is considered. The effects of surface waves, interfacial waves, and the induced energy among the layers due to undulated bottom have been taken into consideration. An approximation technique, i.e. modified mild-slope equation and the Fourier method together with the method of least-square, is adopted as a solution procedure. By applying the continuity condition and mass flux at the interface along with the plate boundary conditions, the problem is converted into a system of equations. Different physical characteristics are investigated, including reflection and transmission coefficients, wave load on the plate and impermeable sea wall, and bottom effect against parameters like incident wave angle and bottom slope length. This study finds that bottom-standing plate dissipated much surface wave energy, whereas the surface-piercing plate dissipates much interfacial wave energy. An opposite effect of surface and interfacial waves on membrane deformation for any given bottom, with maximum deformation due to propagating wave along surface and interface for plane and sinusoidal bottoms, respectively, is observed. The influence of undulated sea bottom on surface wave generated force upon sea wall is almost insensitive, whereas interfacial wave-induced force on sea wall varies significantly with changing bottom profiles. The study carried out in this article holds good potential in deepening our understanding of wave scattering and trapping by a partial porous flexible barrier. [ABSTRACT FROM AUTHOR]

This paper presents a detailed study on detecting defects in isotropic plates by studying scattering analysis of first and second harmonics of symmetric Lamb wave (S0) at cracks in aluminium plates induced by Contact Acoustic Nonlinearity (CAN) using experimental and 3D Finite Element (FE) simulation approaches. In this study, a set of models with different crack sizes and orientations are studied. The effects of crack size and crack orientation on scattering behaviour of first and second harmonics of Lamb waves are investigated. The results show that the Scattering Directivity Pattern (SDP) of Lamb wave around the cracks is significantly influenced by crack size and crack orientation. It is also shown that the largest amplitude of scattered S0 wave is acquired from forward scattering waves for linear waves while the largest amplitude of scattered S0 Lamb wave is obtained from backward scattering waves for nonlinear waves. Therefore, it is expected that pulse-echo sensor configuration enhances nonlinear wave damage detection while pitch-catch configuration may suit better when linear wave is used. It is shown that selecting proper propagation direction for incident wave and proper geometry and angle for monitoring points are the key factors to achieve successful damage detection in isotropic plates. [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]

The interactions between ultrasonic waves and damage provide crucial information for developing effective damage detection techniques in various fields, including non-destructive testing and structural health monitoring, and they can be investigated through wave propagation. Then, this article presents an approach to investigate the longitudinal wave in thin plates with symmetric damage considering oblique incidence. The approach includes a strategy to determine the plate thickness reduction due to the damage presence by considering an oblique incidence of waves generated by the actuator. Modeling is developed to compute each wave packet of reflected and transmitted waves separately, which allows one to describe the wave scattering. Numerical simulations are carried out and the results show that the sensor size can be adjusted to improve the existence of damage detection and the determination of the damage depth. Results from experimental tests are presented to demonstrate the approach considering a circular actuator. The findings contribute to improving the comprehension of the interaction between guided waves and discontinuities, potentially encouraging the use of waves for damage sizing purposes rather than only for detection and improve the current state of the art in wave propagation by investigating the effects of different excitation frequencies and the influence of the damage parameters and sensor sizing on the resulting waves. • Analysis of the scattering of longitudinal waves in plates with symmetric damage. • A model that describes each wave packet is presented. • Optimal frequencies to detect symmetric damage are presented. • The optimal frequencies depend on the incidence angle. • The sensor size can be adjusted to improve the damage detection process. [ABSTRACT FROM AUTHOR]

• Method for multiple scattering by scatterers with unmatched midplanes is proposed. • The method can analyze coupled flexural and in-plane extensional motions. • Mode conversions between different elastic waves are observed. • Stop bands of shear and flexural waves are captured simultaneously. • Broadband scattering polarization of flexural waves is achieved by multiple scattering. Out-of-plane flexural and in-plane extensional motions are independently analyzed in available studies of multiple scattering due to the assumption of the consistent mid-plane between the scatterer and host medium. When mid-planes of the scatterer and the host medium are inconsistent, such as flat-bottomed indentations, the coupled out-of-plane flexural and in-plane extensional motions should be considered. This paper aims to investigate a general numerical procedure to solve the three-dimensional multiple scattering problem of elastic waves on a plate with cylindrically flat-bottomed indentations. Wave expansion functions derived from the Poisson and Mindlin plate theories are used to express three-dimensional displacements of the host plate and flat-bottomed indentations. A linear matrix representing analytical relationships between wave expansion coefficients of exciting and scattered fields is deduced by the continuity conditions of flat-bottomed indentations. A set of linear algebraic equations is then developed by the fact that the exciting fields around a scatterer are the sum of scattered fields coming from all other scatterers. The numerical collocation method is used to solve the preceding algebraic equations. Simulation results verify mode conversions between compressional, shear, and flexural waves. Details of stop-band formations of shear and flexural waves are captured simultaneously. Furthermore, far-field scattering polarizations of shear and flexural waves are found in the case of multiple scattering. [Display omitted] [ABSTRACT FROM AUTHOR]

For layered half spaces in which the shear wave (S-wave) velocity of layer increases with the layer depth, the subsurface seismic wave field generated by surface sources is dominated by the fundamental mode Rayleigh waves (R-waves). When a cavity full of air is present in the underlying half space, the forward (or incident) R-waves are scattered. The scattered wave field in front of the cavity is dominated by the back-scattered R-waves and the interference fringes are formed. Under the conditions that the length (i.e. horizontal extent) of cavity is enough large relative to the wavelength and the burial depth, the majority of the diffracted waves over the cavity approach the fundamental mode plate waves. The displacement structures (variations of displacement with depth) of the diffracted waves are different from those of R-waves within the burial depth. The differences could result in the decrease of the spectral amplitude over the cavity relative to that in front of the cavity. In the surface wave-field behind the cavity, the diffracted waves under the cavity could cause the increase of the spectral amplitude relative to that over the cavity at some low frequencies. By transforming the spectrum into the wavelength domain, a method is proposed to estimate the horizontal extent and burial depth of a cavity from the spectral changes in the offset-wavelength domain. The feasibility is verified by a preliminary experiment. ∙ The normalized depth of energy distribution in a layered half space is smaller than that in a half space with the Poisson's ratio equal to that of the first layer. ∙The majority of the diffracted waves over a cavity behave as the fundamental mode plate waves under conditions that the length of cavity is large compared to the wavelength and the burial depth. ∙The spectral changes over a cavity are explained using displacement structure differences between R-waves and the diffracted waves. ∙The spectral density over a cavity is weaker than that in front of the cavity. ∙In the wave field behind a cavity, the frequency content relatively increases for the waves with the wavelengths larger than the burial depth. ∙The location and burial depth of cavity can be estimated from the spectral changes in front of and behind a cavity in the offset-wavelength domain. [ABSTRACT FROM AUTHOR]

• The 2D scattering feature of the second harmonic A0 waves due to incipient damage is investigated. • The damage scattering nonlinear wave fields are visualized. • A dedicated incipient damage localization algorithm is proposed. • The feasibility and flexibility of the proposed method are validated and evaluated. Inspection of incipient structural damage is of great significance. Existing techniques based on nonlinear guided waves have shown great promise for the detection of incipient damage due to material microstructure changes, but with only limited success for damage localization, which is technically more challenging. Our previous work uncovered the existence of the second harmonic A0 mode Lamb waves in a PZT-driven system, as a result of the mixing of the primary A0 and S0 mode Lamb waves, thus pointing at the possibility of performing damage localization through tuning the size of the wave mixing zone. In the present study, a two-dimensional incipient damage localization method is proposed based on this newly discovered wave phenomenon. By visualizing the nonlinear wave field, damage-induced nonlinear wave scattering features are first investigated. A dedicated localization algorithm is then proposed and evaluated. Numerical results show that the energy of the scattered nonlinear wave is mainly confined to a narrow region along the actuator-damage path, the spatial variation of which can be approximated by a simple Gaussian function. Embedding this information into the proposed localization strategy, damage localization can be achieved using a simple physical system. Experiments are finally carried out to validate the 2nd A0 wave scattering features and the proposed damage localization method. [ABSTRACT FROM AUTHOR]

The aim of this work is to propose a numerical methodology based on the finite element (FE) method to investigate the dispersive behavior of guided waves transmitted, converted, and reflected by reinforced aluminum and composite structures, highlighting their differences. The dispersion curves of such modes can help designers in improving the damage detection sensitivity of Lamb wave based structural health monitoring (SHM) systems. A preliminary phase has been carried out to assess the reliability of the modelling technique. The accuracy of the results has been demonstrated for aluminum and composite flat panels by comparing them against experimental tests and semi-analytical data, respectively. Since the good agreement, the FE method has been used to analyze the phenomena of dispersion, scattering, and mode conversion in aluminum and composite panels characterized by a structural discontinuity, as a stiffener. The research activity allowed emphasizing modes conversion at the stiffener, offering new observations with respect to state of the art. Converted modes propagate with a slightly slower speed than the incident ones. Reflected waves, instead, have been found to travel with the same velocity of the incident ones. Moreover, waves reflected in the composite stiffened plate appeared different from those that occurred in the aluminum one for the aspects herein discussed. [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]