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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]

The multiple scattering of flexural waves on an elastic plate with circular scatterers is analyzed in the frequency domain based on the Mindlin plate theory accounting for the rotary inertia and shear deformation of the plate. To this purpose, a semi‐analytical numerical method is formulated as an extension of the previous study based on the Kirchhoff plate theory. It consists of expressing the flexural wave field in terms of the superposition of the wave function expansion, and determining the expansion coefficients by a collocation technique. As demonstrative examples, the transmission of a plane flexural wave across a square array of circular through‐thickness holes or thin‐plate inclusions is analyzed using the proposed method. The comparison between the results based on the Mindlin and Kirchhoff theories is shown for the case of multiple holes. The analysis shows that the transmission amplitude of the flexural wave is reduced at certain frequencies due to the Bragg reflection by the inclusions. In the case of thin‐plate inclusions, the resonance of the inclusions also brings about a sharp decrease of the transmission amplitude. [ABSTRACT FROM AUTHOR]

In the field of offshore renewable energy, impermeable plates are used as underwater lenses to amplify the wave amplitude, and perforated plates can harness wave energy as a power takeoff device. Within the framework of the linear potential-flow theory, the water wave scattering by impermeable and perforated horizontal plates is investigated in the present study, and both circular and elliptical plates are considered. The hypersingular integral equation is constructed to model the interaction between water waves and plates of small thickness. For wave scattering by impermeable plates with the focus on wave amplification, wave interference effects due to multiple plates can be utilized to achieve large wave amplification. For perforated plates used for harnessing wave energy, deploying an array of elliptical plates is promising if the deployment line coincides with the major axis and the incident wave propagates along the minor axis. The study gives insight into harnessing energy from water waves by horizontal plates. [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]

In this paper, we discuss two problems concerning scattering and localisation of flexural waves in structured elastic plates. Firstly, we compare the scattering amplitudes of waves in a thin plate, generated by a point source, due to a single mass and to a large number of smaller masses, having the same equivalent mass and located around a circle. We show that in the second case, the scattering can be reduced, in particular in the medium- and high-frequency regimes. Secondly, we develop a homogenised model for a double-ring cluster of spring-mass resonators, connected to an elastic thin plate. We determine the conditions for which the plate exhibits vibration modes trapped between the two rings. Further, we show that the frequencies of the localised modes can be tuned by varying the geometry of the two rings and the characteristics of the resonators. The analytical results are corroborated by numerical simulations performed with independent finite element models. [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]

Detection of mechanical damage using Lamb or Rayleigh waves is limited to relatively simple geometries, yet real structures often incorporate features such as free or clamped edges, welds, rivets, ribs and holes. All these features are potential sources of wave reflections and scattering, which make the application of these types of guided waves for damage detection difficult. However, these features can themselves generate so-called 'feature-guided' waves. This article details the first application of the fundamental mode of transient edge waves for detection of mechanical damage. The fundamental edge wave mode (ES0) – a natural analogue to Rayleigh waves – is weakly dispersive and may decay with propagation distance. The phase and group velocities of the ES0 wave mode are close to the fundamental shear horizontal (SH0) and symmetric Lamb (S0) wave modes, at low and high frequencies, respectively. It is therefore quite challenging to excite a single ES0 mode and avoid wave coupling. However, it was found experimentally that at medium range frequencies the ES0 mode can be decoupled from SH0 and S0 modes, and its decay is small, allowing for distant detection of defects and damage along free edges of slender structural components. This article provides a brief theory of edge waves, excitation methodology and successful examples of distant detection of crack-like and corrosion damage in I-beam sections, which are widely applied in engineering and construction. [ABSTRACT FROM AUTHOR]

A hydrodynamic model, with incorporation of porosity, is considered to investigate oblique water wave scattering by two fully submerged parallel porous plates with the wave propagating over a porous bed in a homogeneous fluid flow with the upper surface exposed to atmosphere. The porous plates are assumed to follow the theory of thin plates and the wave propagation through the porous structure follows porous wave-maker theory. The behavior and properties of the roots of the dispersion relation are analyzed by adopting counting argument and contour plot. Time-harmonic propagating waves propagate with exactly one wavenumber along the free surface for any given frequency. Methods of eigenfunction expansion and least square are employed to acquire the complete analytical solution for interaction of water waves with submerged porous plates. Subsequently the reflection and transmission coefficients as well as the energy loss are computed. Then those are examined corresponding to various values of parameters such as porous-effect parameter, the submergence depth of plates from free surface, angle of incidence, porosity of the sea-bed. Present investigation clearly demonstrates that the wave reflection is of oscillatory nature. It further shows that the occurrence of minima in wave reflection is due to an increase in the inertial effect of the porous plates which dissipate a significant portion of the wave energy. The effect of the porous bed under consideration on surface gravity waves is carried out by introducing various numerical values to the hydrodynamic wave characteristics and it is noticed that a reasonable change in porosity of the sea-bed has a significant impact when the propagating wave encounters the submerged structure. The present approach is expected to be of great significance in designing and construction of different types of effective wave absorbers utilized in sea for studying reflection as well as dissipation of wave energy in coastal regions and hence for the purpose of coastal as well as offshore engineering. The present model is validated by comparing it with some established result. [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]

In the active Lamb wave based monitoring of plate structural health, it is difficult to extract damage information from active Lamb waves based on single sensor collection. Based on the Hilbert–Huang transform (HHT) instantaneous processing method, this paper proposes to study the damage information carried by a single sensor monitoring signal from the instantaneous parameter characteristics of the signal. The instantaneous phase change caused by the phase difference between the damage scattering wave and the direct wave is studied. The change of the marginal spectrum amplitude in the effective range caused by the damage scattering wave is studied in continuous multiple frequency bands. Finally, the damage information extraction based on a single sensor monitoring signal is realized. From the model analysis and experimental results, it is reliable and feasible to realize the active Lamb wave based monitoring of plate structural health according to the instantaneous parameter change characteristics from a single sensor signal. [ABSTRACT FROM AUTHOR]

This paper addresses a forward problem using an analytical global–local (AGL) method based on the physics of the Lamb wave propagation in the presence of a crack in the complex structure which would be beneficial for the inverse problem of damage detection. Discontinuity in a structure acts as a damage source and interacts with a Lamb wave. The global analytical solution determines the wave generation by a transmitter, wave propagation through the structure, and detection by a receiver. The local analytical solution determines the scattering coefficients for the Lamb waves at the discontinuity location. These frequency-dependent scatter coefficients are calculated considering transmission, reflection, and mode conversion. An analytical method called "complex mode expansion with vector projection (CMEP)" is used to calculate the scattering coefficients of Lamb wave modes from geometric discontinuities. The scattered wave field from a discontinuity is expanded in terms of complex Lamb wave modes with unknown scatter coefficients. These unknown coefficients are obtained from the boundary conditions using a vector projection utilizing the power expression. Two test cases are considered in this paper: (a) a plate with a pristine stiffener and (b) a plate with a cracked stiffener. Complex-valued scattering coefficients are calculated from 50 to 350 kHz for S0 incident waves. Scatter coefficients are compared for both cases to identify the suitable frequency range to excite a Lamb wave to detect the crack. The frequency-dependent complex-valued scattering coefficients are then inserted into the global analytical model. Therefore, in combination AGL method provides the exact analytical Lamb wave solution for the simulation of Lamb wave propagation and interaction with a discontinuity. By comparing the waveforms for both pristine stiffener and cracked stiffener, the crack can be detected. An FEM transient analysis was also performed to calculate the scattered wave signals. FEM results agree well with the AGL predicted results. An experiment was also performed to validate the AGL result. The obtained experimental results match well with the CMEP analytical predictions. The present AGL method is a highly computationally efficient simulation approach which allows performing virtual experiments for structural health monitoring applications. [ABSTRACT FROM AUTHOR]

Numerical and experimental studies of guided waves diffraction by surface-bonded obstacles of rectangular shape serving as a preliminary model for realistic stiffeners are presented. The simulations are performed within the semi-analytical hybrid approach based on the frequency-domain spectral element method and the boundary integral equation method employing integral transforms of Green's matrices. The mathematical model is verified by comparison with the results calculated by the finite element method and with experimental data. The developed hybrid method allows investigating the scattering of each of the excited guided elastic waves separately, so along with the evaluation of diffraction eigenfrequencies, the conversion of Lamb waves at the obstacle is carefully analyzed. Analysis of complex resonance frequencies demonstrates that eigenfrequencies have large absolute values of the imaginary parts, that explains the absence of strong resonances. Nevertheless, eigenfrequencies with smallest absolute values of imaginary part pronounce themselves in resonance scattering of Lamb waves. [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]

This paper presents a theoretical and finite element (FE) investigation of the generation and propagation characteristics of the fundamental Lamb waves symmetrical mode S0 and anti-symmetrical mode A0 after testing with different types of defects in the plates. The reflection and transmission of Lamb waves at a micro symmetry defect and asymmetry defect are analyzed numerically in the two-dimension (2D) model. Mode conversion of Lamb waves can occur upon encountering the asymmetry discontinuities leading to newly-converted modes apart from wave reflection and transmission. When testing the symmetry defects, the reflection and transmission waves have no modal separation phenomenon. To describe the mode conversion and reflection and transmission degree, and evaluate the micro defect severity, a series of defects are simulated to explore the relationships of defect reflection and transmission with the length and depth of a defect in the 2D FE model. In the three-dimension (3D) FE model, the straight-crest Lamb waves and circular-crest Lamb waves are simulated and researched by contrast analysis. Then the straight-crest Lamb waves are motivated to study the scattering laws of Lamb waves interacting with the circle hole defects and rectangular hole defects. S0 mode and SH0 mode are contained in the scattering waves after S0 mode testing the through holes defects. Corresponding mode energy percentages were analyzed at different micro defect severities changed in different ways. Simulation results illustrated that the modal energy percentages varied in a different character and provided support for the analytically determined results of Lamb waves in the non-destructive testing and evaluation. [ABSTRACT FROM AUTHOR]

• An efficient approach to the investigation of nonlinear scattering of guided waves. • The GPU implementation and the small-size model profile make the model highly efficient. • The wave damage interaction coefficients concept is extended for nonlinear scattering problems. • Super harmonic generation and selective mode conversion phenomena are observed. • The rough crack surfaces are considered. This article presents an efficient numerical approach to the investigation of nonlinear scattering and mode conversion phenomena of Lamb waves as they interact with breathing cracks. A Local Interaction Simulation Approach (LISA) is adopted, which possesses the versatility to capture arbitrary damage profiles. The stick-slip contact dynamics is implemented in the LISA model via the penalty method, which captures the nonlinear interactions between Lamb waves and breathing cracks. The LISA framework achieves remarkable computational efficiency with its parallel implementation using Compute Unified Device Architecture (CUDA) executed on powerful GPUs. A small-size LISA model with absorbing boundaries is tailored for the purpose of extracting the Lamb wave scattering and mode conversion features. Due to the explicit parallel CUDA implementation and the small-size model setup, the computation is highly efficient. Numerical case studies on nonlinear scattering of Lamb waves from breathing cracks are given. Distinctive higher harmonic generation and selective mode conversion phenomena are presented using the complex-valued Wave Damage Interaction Coefficients (WDICs) containing both amplitude and phase information of the scattered wave field. The effect of oblique incident angle on nonlinear scattering phenomenon is investigated. The rough crack surface feature with initial openings and closures is also considered to better approximate fatigue cracks in practical engineering scenarios. In addition, the wave amplitude effect on the nonlinear scattering and mode conversion is studied. This research may provide guidelines for the effective design of sensor arrays utilizing nonlinear Lamb waves for fatigue crack detection. [ABSTRACT FROM AUTHOR]

Abstract The present paper is aimed to test the idea of using scattering resonance frequencies, which are sensitive to the crack's size and depth variation, for the express non-destructive estimation of its severity. The width and depth of artificial strip-like delaminations are estimated by matching theoretical eigenfrequencies, calculated in the framework of a corresponding 2D elastodynamic boundary value problem, with the experimentally obtained resonance frequencies. The high accuracy of the delamination characteristics obtained by this way indicates its potential utility for practice. Graphical abstract Image 1 Highlights • Delamination eigenfrequencies depend strongly on its width and depth. • Experimental scattering resonance frequencies are evaluated from LDV B-scans. • Matching theoretical and experimental resonances reliably estimates damage severity. [ABSTRACT FROM AUTHOR]

We propose a complete Mueller matrix polarimeter using dual photoelastic modulators and rotating half wave plates. The complete Mueller matrix of a sample is obtained by combining four partial Mueller matrices (nine elements each), by rotating the half wave plates in four different orientations. By considering the effect of retardance errors of the wave plates, a more general calibration method is developed. We demonstrate the accuracy of the system by measuring a Babinet-Soleil compensator and the scattering coefficient of an intralipid sample, whereas the depolarization characteristics is shown for different column density of intralipid. Simultaneous determination of optical rotation and depolarization is verified by conducting studies on glucose concentrations ranging from 0 to 400 mg/dl mixed with 2% v/V intralipid. [ABSTRACT FROM AUTHOR]

Highlights • Incremental Lamb wave scattering from a notch emanating from a through-hole is analyzed. • Multiple frequencies and hole diameters are considered as well as a notch with no hole. • Numerical results are validated with experimentally measured scattering patterns. • The presence of even a small hole significantly affects notch incremental scattering. • Incremental scattering from off-angle incident waves is a strong function of frequency. Abstract Lamb wave scattering from a crack originating at a through-hole is of practical importance because of the abundance of fastener holes used in engineering structures. Notches are often used to simulate cracks so that Lamb wave methods can be more conveniently investigated in the laboratory. A linear, three-dimensional finite element model is employed in this paper to study incremental scattering of the fundamental anti-symmetric (A 0 ) Lamb wave mode from notches emanating from through-holes. The term “incremental scattering” refers to the change in scattering caused by introduction of the notch and is motivated by structural health monitoring for which transducers are fixed and signal changes are interpreted to detect damage. Far-field angular scattering patterns are generated for multiple incident angles and frequencies, and such patterns are experimentally validated at one frequency by laser vibrometry measurements. Comparisons are made between a vertical notch alone (no hole) and notches located above and below the through-hole. Additionally, holes of different sizes are considered to investigate the effect of hole diameter on incremental scattering patterns. Results show that the presence, location and size of the through-hole affect both the shape and strength of notch incremental scattering patterns. [ABSTRACT FROM AUTHOR]

Damage detection in uniform structures has been studied in numerous previous researches. However, damage detection in non-uniform structures is less studied. In this paper, a damage detection algorithm for identifying rectangular notch parameters in a stepped waveguide using Lamb waves is presented. The proposed algorithm is based on mode conversion and scattering phenomena because of interaction of Lamb wave modes with defects. The analysis is divided into two steps: notch localization and notch geometry detection. The main advantage of this method is its ability to detect all of the notch parameters in a waveguide with arbitrary number of step discontinuities. The method is applied to a numerical example and the results show that it can successfully identify the notch location, depth, and width in a multi-step plate. [ABSTRACT FROM AUTHOR]

Three-dimensional scattering and dynamic stress concentration of Lamb-like waves around a spherical inclusion (inhomogeneity and a cavity) in a thick spherical shell are investigated theoretically and numerically. Two spherical coordinates, located at the spherical shell center and the inclusion center, are established to express the incident and scattered wave potential functions. By a kind of addition formulas, all the potential functions can be transformed into the same coordinate, then the analytical solution of the displacements and stresses are derived, and all the undetermined coefficients are solved by satisfying the boundary condition and the interface condition. In order to describe the 3-D stresses concentration, multiple DSCFs are employed and the 3-D distributions are depicted. The results reveal the influences of inclusion material and the cavity on the distributions of DSCFs, and the influence of incident wave frequency and inclusion position are also calculated. This research is expected to provide theoretical understanding on dynamic analysis and mechanical properties evaluation of the spherical shells. [ABSTRACT FROM AUTHOR]

The scattering of high frequency guided ultrasonic waves by a fatigue crack at the side of a fastener hole has been studied. The guided wave pulse consists of the superposition of the two fundamental Lamb modes A 0 and S 0 above the cut-off frequencies of the higher modes. The scattered field was simulated using a three-dimensional finite difference algorithm with a staggered, Cartesian grid for the limited area of interest around the hole and an analytical phase angle correction for the additional, variable propagation distance. Experimentally, the modes were selectively excited using a standard ultrasonic wedge transducer and measured using a laser interferometer, resulting in good spatial resolution. The scattered field was measured and simulated for an undamaged hole, a small, part-thickness quarter-elliptical fatigue crack, and a through-thickness fatigue crack. Good agreement was found and a significant influence of the fatigue cracks on the scattered field was observed. The complex difference of the scattered field due to additional scattered waves at the fatigue cracks of variable depth and length was evaluated. This allows for the prediction of high frequency guided wave sensitivity for fatigue crack detection at fastener holes, a significant maintenance problem for ageing aircraft. [ABSTRACT FROM AUTHOR]

A table of contents for the 2016 issue of the journal "Annalen der Physik" is presented.

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]

• 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]

Multiple-damage-inflicted scattering signals usually overlap with each other due to Lamb wave dispersion and multi-mode characteristics. As a result, it is difficult to accurately distinguish damages that occur relatively close to each other using the conventional ultrasonic phased array method. In order to solve this problem, an improved linear mapping (ILM) dispersion compensation method is proposed and is applied to enhance the ultrasonic phased array monitoring resolution. Through a uniform linear array arrangement, the damage scattering signals are collected in a round-robin pattern of ultrasonic phased array, and then compensated based on the linear relation wavenumber curve from actual measurement. At last, the scan can be obtained by monitoring the energy scattered by the damages using delay-and-sum method. To verify the proposed method, experiments are performed on an aluminum (LY-12) plate. Two results of multiple artificial damages show that the proposed method can effectively compensate the dispersion characteristics of Lamb waves. The direction estimation error and distance estimation error are less than 4° and 2 cm, respectively. [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]

We investigate a new approach for characterizing class separability based on topological measures for use with identifying flaw severity in plates. Multi-mode Lamb waves are propagated across a flat-bottom hole of varying depth. Lamb wave tomography reconstructions are first generated to locate and size the flaw at each depth. As the flaw depth increases, scattering and mode conversion effects dominate the raw time-domain signals, obscuring information about flaw severity. Pattern classification provides an alternate means for processing the ultrasonic waveforms to identify flaw severity. High-dimensional feature spaces are generated from the Lamb wave signals using the dynamic wavelet fingerprinting technique. In order to achieve high classification accuracy, an optimal feature space is required. An intelligent feature selection routine is explored here that identifies favorable class distributions in multidimensional feature spaces using computational homology theory. Betti numbers and formal classification accuracies are calculated for each feature space subset to establish a correlation between the topology of the class distribution and the corresponding classification accuracy. [ABSTRACT FROM AUTHOR]

An analytical model of Lamb wave scattering from a circular blind hole in isotropic plates is presented using the Mindlin plate theory for describing in-plane and flexural wave modes simultaneously. The model makes use of the wave function expansion technique and the boundary conditions at the hole edge to evaluate the scattered far fields of three fundamental guided wave modes. Comparisons are made to existing approximate models using Poisson/Kirchhoff theory and Poisson/Mindlin theory and a 3D model using the exact 3D equations. The results reveal that the present model is more consistent with the exact 3D model at higher frequencies than existing approximate models. [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]