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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]

• 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]

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]

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]

• 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]

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]

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]

• 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]

• 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]

The study deals with the scattering of obliquely incident gravity waves by a horizontal floating flexible porous plate in the water of finite depth having a variable bottom bed. The problem when a vertical rigid wall is placed in the downstream of the plate is also considered. The problem is analyzed under the assumptions of small amplitude water wave theory and structural responses. The undulated bottom bed is finitely extended and lies beneath the floating plate regions. A coupled eigenfunction expansion - boundary element method is used for the solution purpose. Energy balance relations for wave scattering in the presence of the flexible plate and when the vertical rigid wall is placed in the downstream are derived and used to check the accuracy of the numerical results. The effect of sinusoidally varying bottom topography, plate porosity and heading angle of the incident wave on the Bragg resonance is analyzed. Moreover, various results are computed and analyzed to study the role of the wave parameters, bottom undulation and floating porous flexible plate on wave scattering. The proposed solution methodology can be easily extended to deal with wave-structure interaction problems of varied structural configurations and bottom bed. • The study deals with the scattering of obliquely incident gravity waves by a horizontal floating flexible porous plate. • The resonance bands around the primary Bragg value shifted towards the right with an increase in the depth ratio. • Plate porosity can reduce the Bragg resonance drastically. • The resonance bandwidth around the primary Bragg value is wider for a plate having fixed edges than the free edges. • For ℎ 2 /ℎ 1 = 0.5 there is a drift in the resonance bands away from the primary Bragg value in the leftward direction. [ABSTRACT FROM AUTHOR]