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This study investigates the higher harmonic generation of the Lamb wave at a delamination due to contact acoustic nonlinearity, which is a clapping phenomenon between sublaminate surfaces due to the Lamb wave interaction with the delamination. In this study, higher harmonics of the Lamb wave induced at the delamination in composite laminates are studied in detail. This study performs both numerical and experimental studies. A three-dimensional finite element model is proposed for predicting the propagation of nonlinear Lamb waves in composite laminates and is verified using experimentally measured data. The results show the proposed numerical model can reasonably predict higher harmonic generated by contact acoustic nonlinearity. It is found that the delamination is the major source of contact acoustic nonlinearity in the composite laminates. A mode conversion study is also carried out to gain further physical insight into the higher harmonic generation of the Lamb wave at the delamination.

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.

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.

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.

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. Web of Science 11 10 art. no. 4508

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.

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 (A0) 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.

Since stringers are often applied in engineering constructions to improve thin-walled structures&rsquo, strength, methods for damage detection at the joints between the stringer and the thin-walled structure are necessary. A 2D mathematical model was employed to simulate Lamb wave excitation and sensing via rectangular piezoelectric-wafer active transducers mounted on the surface of an elastic plate with rectangular surface-bonded obstacles (stiffeners) with interface defects. The results of a 2D simulation using the finite element method and the semi-analytical hybrid approach were validated experimentally using laser Doppler vibrometry for fully bonded and semi-debonded rectangular obstacles. A numerical analysis of fundamental Lamb wave scattering via rectangular stiffeners in different bonding states is presented. Two kinds of interfacial defects between the stiffener and the plate are considered: the partial degradation of the adhesive at the interface and an open crack. Damage indices calculated using the data obtained from a sensor are analyzed numerically. The choice of an input impulse function applied at the piezoelectric actuator is discussed from the perspective of the development of guided-wave-based structural health monitoring techniques for damage detection.

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 A0 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.

This paper presents the interaction of Lamb waves with rivet hole cracks from multiple directions of incident using the finite element approach. Lamb waves undergo scattering and mode conversion after interacting with the damage. Shear horizontal waves appear in the scattered waves because of the mode conversion. Instead of analyzing the whole large structure, the local damage area is analyzed using finite element analyses and analytical formulation is used to analyze the whole structure. The scatter fields are described in terms of wave damage interaction coefficients that involve scattering and mode conversion of Lamb waves. Lamb wave mode (S0 and A0) hit the damage from multiple directions and corresponding wave damage interaction coefficients are obtained around the damage. Harmonic analysis has been performed over the fundamental frequency domain and “scatter cubes” of complex-valued wave damage interaction coefficients are formed. The scatter cube provides the information of relative amplitude and phase of scattered waves around the damage that can be used for designing the sensor installation. An application based on real time domain signal has been illustrated for the problem of multiple-rivet-hole cracks using the scatter cubes with the analytical framework.

This paper presents a study of Lamb wave scattering and mode conversion at a delamination in quasi-isotropic (QI) composite laminates. The study employs the fundamental antisymmetric mode (...

Numerical simulations such as Finite Element (FE) modelling allow the simulation and prediction of guided wave propagation and scattering. Specific considerations concerning the choice of mesh, element type, time step, and analysis method are required to ensure stable and accurate simulations. Modeling considerations and validation against experimental results are shown for two examples of increasing complexity. The approximation of complex geometries and the effects on guided wave propagation are discussed. Examples concerning guided wave scattering at defects in single and multiple metallic layers of plate structures were compared against experimental results.

In this paper, a modified boundary element method (BEM) is proposed to solve the two-dimensional scattering fields of lamb waves in plates with a defect. For an infinite long plate, the infinite boundary integral in the traditional BEM is directly replaced by finite integral. Therefore, Spurious reflected waves are generated due to the truncated boundaries, which will cause calculation errors. In order to avoid these errors, the omitted integral terms in the traditional BEM are calculated by the reciprocity theorem in elastodynamics and the results are substituted into the traditional BEM. Meanwhile, this modified method is applicable to solving scattered fields for both single-layer and multi-layer models. At the end of this paper, the calculated results for single-layer and multi-layer plates with typical defects are shown, and the convergence of scattering coefficients is verified. Furthermore, the modified BEM, as an efficient numerical calculation method, can be used to study the forward problems of defect detection.

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

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 1.5 MHz mm with CMEP being orders of magnitude faster than FEM.

Lamb wave based structural health monitoring technique is one of the promising techniques for detecting damage in structures. Among different types of guided waves, the fundamental anti-symmetric mode of Lamb wave (A0) has attracted considerable attention for damage detection in plates due to its outstanding properties, such as sensitivity to small and different types of defects, which make it a powerful tool for damage detection. Cracks are one of the major culprits in metallic structures which affect their durability and serviceability. Once the crack appears on the structures, it can affect its serviceability. It is important to detect cracks at early stage to avoid any catastrophic failure of the structures. This paper presents a study on the capability of using the A0 Lamb wave in detecting crack-like defects in aluminium plates, in which the scattering behaviour of the A0 Lamb wave at through-thickness notches in aluminium plates is studied in detail. 3D explicit finite element simulations are used to provide a comprehensive study on the scattering characteristics of the A0 Lamb wave at notches with different sizes and orientations. This study also considers different incident and scattered wave directions on the scattering characteristics. The results show that scattering characteristics of the A0 Lamb wave are sensitive to the size and orientation of notches. The findings of this study can improve the understanding of the capability of the A0 Lamb wave in detecting the crack-like defects and further advance damage detection techniques.

The instantaneous out-of-plane displacement two-dimensional (2-D) maps associated to the scattering generated by the interaction of Rayleigh-Lamb waves with defects in plate structures can be measured using pulsed TV-holography (PTVH) and employed to characterize damage in non-destructive inspection applications. On the basis of visual comparisons we have shown previously that, except for the amplitude in the backscattering zone, a reasonable description of the measured experimental scattering patterns produced by holes both in harmonic and transient regimes can be obtained using the finite element method (FEM) combined with a 2-D model based on the scalar wave equation. In this work a systematic quantitative analysis of the agreement between FEM simulated maps and filtered experimental PTVH maps is developed considering both the spatial distribution of the local (pixel-wise) error in amplitude and phase and the corresponding global (averaged) errors over different areas in the 2-D image of the acoustic field. Changes produced in the experimental values by the speckle noise and variations introduced in the numerical values by the uncertainty in the characterization of the incident acoustic wave and the shape and position of the hole are characterized in order to obtain the net value of the error between theory and experiment.

Acoustic backscattering from a rubber spherical shell in water is observed to contain a delayed enhancement, demonstrated to be associated with a waveguide path along the shell. This path is somewhat analogous to that of the Lamb wave observed on metallic shells. Rubber is a unique material because of its subsonic sound speed relative to water, and because shear coupling is often small enough to be neglected in typical models, making it fluid-like. This makes rubber a material of interest for coating and cloaking underwater devices and vehicles. Both fluid and elastic rubber partial wave series models are tested, using experimentally measured longitudinal and shear speeds, attenuation, and rubber density. A finite element model for the shell is also developed. Comparison of the models and experiments highlights the importance of the waveguide path to the overall scattering. Estimates for the group and phase velocities of the lowest order propagating mode in the shell are determined through waveguide normal mode analysis and Sommerfeld-Watson theory, and are shown to give good agreement with experiments in predicting the time of arrival of the waveguide path.

In this chapter, fundumental study is performed on topology optimisation of 1D bi-material PhP unit-cell for highest specific bandgap width of Lamb waves at prescribed filling fraction of stiff scattering inclusion. Moreover the bandgap efficiency and multiscale functionality of gradient PhP structures comprising of unit-cells with various filling fractions and optimised topologies are investigated. Specialised FEM model is developed for this purpose calculating the dispersion curves and modal band structure of guided waves in a layered medium.

Guided waves can effectively be used for inspection of large scale structures. Surface corrosion is often found as major defect type in large scale structures such as pipelines. Guided wave interaction with surface corrosion can provide useful information for sizing and classification. In this paper, the elastodynamic reciprocity theorem is used to formulate and solve complicated scattering problems in a simple manner. The approach has already been applied to scattering of Rayleigh and Lamb waves by defects to produce closed form solutions of amplitude of scattered waves. In this paper, the scattering of the lowest axially symmetric torsional mode, which is widely used in commercial applications, is analyzed by the reciprocity theorem. In the present paper, the theorem is used to determine the scattering of the lowest torsional mode by a tapered defect that was earlier considered experimentally and numerically by the finite element method. It is shown that by the presented method it is simple to obtain the ratio of amplitudes of scattered torsional modes for a tapered notch. The results show a good agreement with earlier numerical results. The wave field superposition technique in conjunction with the reciprocity theorem simplifies the solution of the scattering problem to yield a closed form solution which can play a significant role in quantitative signal interpretation.

Localized and distributed guided ultrasonic waves array systems offer an efficient way for the structural health monitoring of large structures. The detection sensitivity for fatigue cracks depends on the orientation of the crack relative to the location of the sensor elements. Crack-like defects have a directionality pattern of the scattered field depending on the angle of the incident wave relative to the defect orientation and on the ratio of the defect depth and length to the wavelength. From FE simulations it has been shown that for cracks and notches almost no energy is scattered in certain directions from the defect, i.e., the data processing algorithm must take into account that for some transducer combinations no change in the signal even for a significant defect will be detected. The scattered wave field directionality pattern for an incident low frequency A0 Lamb wave mode was predicted from 3D Finite Element simulations and verified from experimental measurements at machined part-through and t...

This paper presents the numerical modeling and simulations of PZT-induced Lamb wave propagation in plate-like structures by using the spectral finite element method. A novel spectral plate finite element, which can efficiently model the three-dimensional (3D) behavior of Lamb waves, is proposed. In the formulation, linear displacement distributions in the thickness direction are assumed for both the PZT layer and the base plate. A way to avoid the thickness locking is proposed and used in the formulations. Two examples, one for the validation of the proposed two-dimensional (2D) spectral finite element and the other for the demonstration of crack detection in plates, are presented and discussed. The contact between the two faces of crack is considered. Numerical results show that (1) only the anti-symmetric mode is prone to thickness locking thus remedy should be made only on this part, (2) the proposed 2D spectral finite element can adequately model the Lamb wave propagation in plate-like structures and the complex scattering for the crack, and (3) crack location can be well determined by a PZT-induced Lamb wave-based diagnosis algorithm.

In this paper wave scattering from an asymmetrical change of cross-sectional area in a beam is numerically studied. Incident symmetric and antisymmetric Lamb waves are considered and multiple wave mode conversion due to interaction with the discontinuity are investigated up to high frequency (above the cut-off of the second symmetric Lamb wave mode, S 2). Results are presented in terms of transmission power coefficients, kinetic energy, and energy velocity. These are evaluated using the Wave Finite Element method to predict the wave modes from FE cross-sectional nodal displacements and nodal forces. It is shown that the methodology proposed can give an insight into wave scattering and multiple converted Lamb wave modes, which can be useful in Structural Health Monitoring.

This paper reports on findings that extend previous work for the purpose of in-situ structural health monitoring of defects on the blind side of open holes using plate waves. A series of computational studies is presented to understand how and why the ultrasonic scattered wave field can be detected on the accessible surface. The uniqueness of these findings is that the length-scale of the defect and the incident waves are comparable. The combination of the experimental-computational-analytical approach gives rise to new insights and guidance for the quantification of defects located in hard-to-inspect regions of future unitised metallic and composite structures. The outcomes advance the knowledge base of inspection of hard-to-access regions with actuators and sensors placed in easily accessible locations.

The interaction of the fundamental anti-symmetric Lamb wave (A0) with debondings at structural features is investigated using experimental data and finite element (FE) simulations. In this study explicit three-dimensional (3D) FE simulations are employed, which allows the study of the scattered wave along different propagation directions. Good agreement between the FE predictions and the measurements are obtained that demonstrates that the 3D FE scattering model is able to accurately predict the Lamb wave scattering characteristics at debondings. The study show that the characteristics of Lamb wave reflected from the debondings at the structure feature is much more complicated than that from defects in flat composite laminates. Parameter studies show that the backward and forward scattering coefficient of Lamb wave is a function of debonding size to wavelength ratio and debonding location. This shows the potential of employing Lamb wave to identify the size and monitor the growth of the debondings. The findings of the study provide improved physical insights into the scattering phenomena, which are important to further advance damage detection techniques for complex structures made by composite laminates.

In this article, ultrasonic guided wave propagation and interaction with the rivet hole cracks has been formulated using closed-form analytical solution while the local damage interaction, scattering, and mode conversion have been obtained from finite element analysis. The rivet hole cracks (damage) in the plate structure gives rise to the non-axisymmetric scattering of Lamb wave, as well as shear horizontal (SH) wave, although the incident Lamb wave source (primary source) is axisymmetric. The damage in the plate acts as a non-axisymmetric secondary source of Lamb wave and SH wave. The scattering of Lamb and SH waves are captured using wave damage interaction coefficient (WDIC). The scatter cubes of complex-valued WDIC are formed that can describe the 3D interaction (frequency, incident direction, and azimuth direction) of Lamb waves with the damage. The scatter cubes are fed into the exact analytical framework to produce the time domain signal. This analysis enables us to obtain the optimum design parameters for better detection of the cracks in a multiple-rivet-hole problem. The optimum parameters provide the guideline of the design of the sensor installation to obtain the most noticeable signals that represent the presence of cracks in the rivet hole.

Carbon fiber laminate composites, consisting of layers of polymer matrix reinforced with high strength carbon fibers, are increasingly employed for aerospace structures. They offer advantages for aerospace applications, e.g., good strength to weight ratio. However, impact during the operation and servicing of the aircraft can lead to barely visible and difficult to detect damage. Depending on the severity of the impact, delaminations can occur, reducing the load carrying capacity of the structure. Efficient structural health monitoring of composite panels can be achieved using guided ultrasonic waves propagating along the structure. The guided ultrasonic wave (A0 Lamb wave mode) scattering at delaminations was modelled using full three-dimensional Finite Element (FE) simulations. The influence of the delamination size was systematically investigated from a parameter study. The angular dependency of the scattered guided wave amplitude was calculated using a baseline subtraction method. A significant influence of the delamination width on the guided wave scattering was found. The sensitivity of guided waves for the detection of barely visible impact damage in composite panels has been predicted.

Carbon fiber laminate composites are increasingly used for aerospace structures as they offer a number of advantages including a good strength to weight ratio. However, impact during the operation and servicing of the aircraft can lead to barely visible and difficult to detect damage. Depending on the severity of the impact, delaminations can occur, reducing the load carrying capacity of the structure. Efficient nondestructive testing of composite panels can be achieved using guided ultrasonic waves propagating along the structure. The guided wave (A0 Lamb wave mode) scattering at delaminations was modeled using full three-dimensional Finite Element (FE) simulations. The influence of the delamination size was systematically investigated from a parameter study. A significant influence of the delamination width on the guided wave scattering was found, especially on the angular dependency of the scattered guided wave amplitude. The sensitivity of guided ultrasonic waves for the detection of delamination dama...

A parametric 2D finite-element inversion scheme is used for sizing cracked zone type strip defect caused by a linear and uniform impact on a composite material plate. The reflection and transmission coefficients produced by mode conversion phenomenon when a pure incident S 0 Lamb wave mode is sent towards the defect are used as input data for the inversion process. The inversion process consists in quantifying two unknown parameters, i.e., width and depth representing the assumed triangular geometry of cracked zone like defect. The inversion scheme consists of a finite element based model, which is used to simulate the Lamb wave scattering for various values of the aimed parameters, and specific post-processing based on Shkerdin's orthogonality relation is applied to predict the needed reflection and transmission coefficients. A laboratory experiment is performed for creating a linear and uniform impact on a carbon epoxy composite plate sample. Then another ultrasonic experiment is performed in laboratory for measuring reflection and transmission coefficients by sending a pure S 0 mode towards the defect. The measured coefficients are then used for the inversion purpose. The two principles used in inversion process give almost similar optimised values for these parameters, showing the usefulness of this technique.

A three-dimensional finite element model for analysis of ultrasonic-guided wave scattering from a hidden notch on a through-thickness circular hole is presented in this article. The structure is representative of an aircraft wing spar with a fuel weep hole. In contrast to the high-frequency bulk-wave wedge transducer methodology traditionally used for weep hole inspection, the length scales of the in situ technique are such that the wavelength of the incident guided waves are comparable with the hole diameter and larger than the defect length. The ability to accurately model acousto-ultrasonic elastic wave dynamics is crucial for future developments in this research field. Three-dimensional laser vibrometry is used to measure the deformation of a low-profile surface-bonded piezoelectric disc. The measurements provide the input conditions for a force-actuated computational model. The computational scattered wave field from a notch on the blind side of the hole is compared with experimental data for model validation. It is concluded that the boundary conditions for wave scattering from the hidden notch are a complex combination of the incident wave field and the dispersive edge-guided Rayleigh-type flexural wave that is formed on the free surface of the hole.

This paper demonstrates a novel frequency domain analysis (FDA) to evaluate the scattering behavior of a waveguide mode at arbitrary scattering geometries by a time harmonic simulation based on the finite element method (FEM). To this end, we add an injection-damping mechanism (IDM) to avoid interference at the acoustic input port. The IDM can be easily constructed by a numerical operation. Our approach offers improved time consumption and calculation power necessary over the established method in the time domain. After checking the validity of the proposed method, we discuss the importance of considering wave scattering phenomena in film bulk acoustic wave resonator (FBAR) devices by applying the proposed method to two simplified models of an FBAR device.

Ultrasonic guided waves (GWs) are being extensively investigated and applied to nondestructive evaluation and structural health monitoring. Guided waves are, under most circumstances, excited in a frequency range up to several hundred kilohertz or megahertz for detecting defect/damage effectively. In this regard, numerical simulation using finite element analysis (FEA) offers a powerful tool to study the interaction between wave and defect/damage. Nevertheless, the simulation, based on linear/quadratic interpolation, may be inaccurate to depict the complex wave mode shape. Moreover, the mass lumping technique used in FEA for diagonalizing mass matrix in the explicit time integration may also undermine the calculation accuracy. In recognition of this, a time domain spectral element method (SEM)—a high-order FEA with Gauss–Lobatto–Legendre (GLL) node distribution and Lobatto quadrature algorithm—is studied to accurately model wave propagation. To start with, a simplified two-dimensional (2D) plane strain model of Lamb wave propagation is developed using SEM. The group velocity of the fundamental antisymmetric mode (A0) is extracted as indicator of accuracy, where SEM exhibits a trend of quick convergence rate and high calculation accuracy (0.03% error). A benchmark study of calculation accuracy and efficiency using SEM is accomplished. To further extend SEM-based simulation to interpret wave propagation in structures of complex geometry, a three-dimensional (3D) SEM model with arbitrary in-plane geometry is developed. Three-dimensional numerical simulation is conducted in which the scattering of A0 mode by a through hole is interrogated, showing a good match with experimental and analytical results.

The scattering of guided waves by complex shaped defects in three-dimensional (3D) waveguides is considered. For such problems, analytical solutions do not exist, and modal decomposition techniques based on the establishment of the displacement and stress fields in the vicinity of the scatterer are quite heavy and complicated to perform. On the other hand, finite elements (FE)-based methods constitute a powerful way to obtain solutions, but they are known to be very memory consuming. This paper proposes a post-processing technique, based on a 3D orthogonality relation, to decompose a complex acoustic field produced by a scatterer and predicted by a 3D FE model, into plane waves, the amplitudes of which are quantified in the far field. This technique allows important reductions in the size of the FE models to be made. Two applications are presented to demonstrate the potential of this method. The first one concerns the scattering of the S(0) Lamb wave incident on a flat bottom circular hole. In this example, the amplitude of each mode is calculated via the orthogonality relation-based method, and compared to that obtained by simply monitoring the displacements at appropriate through-thickness positions. In the second application, the incident S(0) Lamb mode is converted into five modes scattered by a defect of complex geometry.

The generation of axisymmetric Lamb waves and interaction with wall thinning (corrosion) defects in hollow cylinders are simulated using the finite element method. Guided wave interaction with defects in cylinders is challenged by the multi-mode dispersion and the mode conversion. In this paper, two longitudinal, axisymmetric modes are generated using the concept of a time-delay periodic ring arrays (TDPRA), which makes use of the constructive/destructive interference concept to achieve the unidirectional emission and reception of guided waves. The axisymmetric scattering by the wall thinning extending in full circumference of a cylinder is studied with a two-dimensional FE simulation. The effect of wall thinning depth, axial extension, and the edge shape on the reflections of guided waves is discussed.

Non-destructive testing methods based on ultrasonic waves are one of the most popular methods for damage detection in structures. Of these ultrasonic waves Lamb waves are of particular interest for the inspection of large structures for various reasons. Therefore scattering of Lamb waves from flaws has generated a considerable amount of research over last couple of decades. Most of the work has been done using computational tools like Finite Element Methods and experimental technique. In this paper an analytical approach is presented to develop a fundamental understanding of the scattering of Lamb waves from geometric discontinuities in 2 dimensions. We have considered simplest of all geometric discontinuity – a step, as this fundamental understanding can easily be extended to corrosion or crack.

The non-destructive testing of materials can be conducted by various techniques. Amongst these, method based on ultrasonic waves is one of the most common one. Of these ultrasonic waves Lamb waves are of particular interest for the inspection of large structures for various reasons. Scattering of Lamb waves from flaws has generated a considerable amount of research over last couple of decades. Most of the work has been done using computational tools like Finite Element Methods and experimental technique. In this paper an analytical approach is presented to develop a fundamental understanding of the scattering of Lamb waves from geometric discontinuities in 2 dimensions. We have considered simplest of all geometric discontinuity – a step, as this fundamental understanding can easily be extended to corrosion or crack.

Carbon fiber laminate composites, consisting of layers of polymer matrix reinforced with high strength carbon fibers, are widely employed for aircraft structures. For aerospace applications they offer a number of advantages including a good strength to weight ratio. However, impact during the operation and servicing of the aircraft can lead to barely visible and difficult to detect damage. Depending on the severity of the impact, fiber and matrix breakage or delaminations can occur, reducing the load carrying capacity of the structure. Efficient nondestructive testing of composite panels can be achieved using guided ultrasonic waves propagating along the structure. The guided wave propagation in intact composite plates was measured using a noncontact laser interferometer, quantified, and compared to numerical predictions using full three-dimensional (3D) Finite Element (FE) simulations. Good agreement between experiments and predictions for the wave propagation was found. The guided wave scattering at delaminations was simulated using 3D FE models and the influence of the delamination modelling investigated. Limited influence of the material damping and the delamination shape on the scattering patterns was found, but the modelling of the specimen anisotropy was observed to have a significant influence. The effects of the delamination size and depth on the guided wave scattering were investigated in a systematic parametric study, in order to help building up information for an accurate interpretation of guided wave experiments.

In this paper we propose an efficient way to post-process output data predicted by Finite Element (FE) or Boundary Element (BE) codes, when the scattering of Lamb modes by defects in plate-like structures is considered. The use of a general orthogonality relation is compared to classical post-processing made with spatial FFT. To get the amplitudes of incident or scattered modes, this orthogonality relation requires the numerical prediction of the through-thickness displacements, and stress-fields distributions, on each side of the scatterer. The distance between the location where these fields are predicted and the scatterer can be very small, thus allowing huge reductions in the size of the mesh. Through two examples, this orthogonality relation is used to calculate the reflection and transmission coefficients of a pure Lamb mode incident on a notch-like defect, in either an elastic or a viscoelastic plate. Thanks to efficient absorbing regions, the FE meshed domains are reduced to the vicinity of the de...

This paper presents an innovative method, called the mode-exciting method, to solve Lamb wave-scattering problems in an infinite plate. In this method, a set of Lamb wave modes is excited by appropriate boundary conditions given on the virtual edges of a finite plate. After solving numerically the elastodynamic problem defined in the finite domain, the numerical solution is decomposed into Lamb wave modes. The Lamb wave modes constitute a system of equations, which can be used to determine the scattering coefficients of Lamb waves for the original problem in an infinite plate. The advantage of the mode-exciting method is that a well-developed numerical method such as finite-element (FEM) or boundary element (BEM) can be used in the elastodynamic analysis for the finite region without any modification like coupling with other numerical techniques. In numerical examples, first the error estimation of the mode-exciting method is discussed by considering three types of error indicators. It is shown that among them, the power ratio of nonpropagating modes to propagating modes is the most suitable for the error estimation. Numerical results are then shown for scattering coefficients as a function of nondimensional frequency for edge reflection and crack scattering problems.

A study of the interaction of the S0 Lamb wave with a circular through-thickness hole in a plate is presented. The study is limited to the nondispersive frequency range of this wave, in which the distributions of stress and displacement are simple. This allows a Finite Element analysis to be undertaken using a two-dimensional membrane discretization. Predictions of the direct reflection of the S0 mode and the lateral scattering of the SH0 mode are made for a range of diameters of the hole. At the same time, an analytical solution based on modal superposition is developed, and this is also used to predict the reflection and scattering coefficients. Both sets of predictions are validated by experimental measurements. It is found that the trends of the reflection coefficients for different hole diameters, frequencies and distances from the hole satisfy a simple normalization. On a detailed scale, the functions exhibit undulations which are shown to result from the interference of the direct reflection with secondary reflections which arrive slightly later.

The optimum topology of bimaterial phononic crystal (PhCr) plates with one-dimensional (1D) periodicity to attain maximum relative bandgap width of low order Lamb waves is computationally investigated. The evolution of optimized topology with respect to filling fraction of constituents, alternatively stiff scattering inclusion, is explored. The underlying idea is to develop PhCr plate structures with high specific bandgap efficiency at particular filling fraction, or further with multiscale functionality through gradient of optimized PhCr unitcell all over the lattice array. Multiobjective genetic algorithm (GA) is employed in this research in conjunction with finite element method (FEM) for topology optimization of silicon-tungsten PhCr plate unitcells. A specialized FEM model is developed and verified for dispersion analysis of plate waves and calculation of modal response. Modal band structure of regular PhCr plate unitcells with centric scattering layer is studied as a function of aspect ratio and filling fraction. Topology optimization is then carried out for a few aspect ratios, with and without prescribed symmetry, over various filling fractions. The efficiency of obtained solutions is verified as compared to corresponding regular centric PhCr plate unitcells. Moreover, being inspired by the obtained optimum topologies, definite and easy to produce topologies are proposed with enhanced bandgap efficiency as compared to centric unitcells. Finally a few cases are introduced to evaluate the frequency response of finite PhCr plate structures produced by achieved topologies and also to confirm the reliability of calculated modal band structures. Cases made by consecutive unitcells of different filling fraction are examined in order to attest the bandgap efficiency and multiscale functionality of such graded PhCr plate structures. Refereed/Peer-reviewed

Lamb waves propagating in an infinite plate containing a circular hole, with or without edge cracks, are investigated both theoretically and experimentally in this paper. The theoretical analysis is accomplished by means of a hybrid method called the global local finite element method, in which a bounded region enclosing the hole and the cracks is discretized into finite elements, while the field external to this region is represented analytically in terms of Lamb wave modes. The scattered field is calculated through the application of the boundary conditions at the interface between the discretized region and the unbounded exterior. In the experiments the incident Lamb wave of a specific mode is generated by means of a wedge transducer and the waves scattered by the hole is recorded in conventional contact type transducers located on the plate surface. The measured time histories and amplitude spectra of the transmitted and reflected waves are compared with those calculated from the hybrid model. The agreement between the theoretical and experimental results is found to be excellent in the cases considered. Application of the technique to non-destructive evaluation (NDE) of corrosion and fatigue induced defects in aging structural components is discussed.

This study focuses on the leakage and scattering phenomena of Lamb waves in liquids as the result of the insonification of the end of an immersed solid plate by means of a bounded ultrasonic beam at the Lamb angle. Both acousto-optics measurements and FEM simulations are presented and discussed. It is shown that the observed complex scattered field is composed of the leaking fields of mode-converted backward propagating Lamb waves. The geometrical position of the leakage indicates that the conversion process is completed very locally. On the other hand, it is observed that large zones of the immersion liquid become 'polluted' with scattered ultrasound. An analysis performed in the spatial frequency domain furthermore revealed the presence of a nonlinear interaction between multiple overlapping acoustic fields. Since real structures have limited spatial dimensions, the current results indicate a possible source of misinterpretation during water-coupled non-destructive testing (NDT).