Analytical and experimental analysis of guided waves in an aluminum plate under bending load

Although guided waves offer great potential for monitoring various structures, interpreting signals from piezoelectric sensors remains a challenging task. One main reason is the significant influence of environmental conditions on the wave propagation. A lot of research has already been done on the influence of temperature effects and recently more attention has been shifted towards loads. While previous publications have mainly focused on uni- or bi-directional loads, this publication expands the developed models to include bending loads. After reviewing the analytical basis of acoustoelasticity, the derived equations are expanded to nonhomogeneous elastic bending loads using the partial wave method. The analysis is completed using recent results developed by C. Hakoda and C. J. Lissenden (2018) [1], that gave more physical insight in the propagation of guided waves in various frequency-bands. The focus of the experimental analysis is around the fundamental S0- and A0-Modes of Lamb waves. To validate the analytical results an aluminum plate is instrumented using piezoelectric transducers and loaded with varying bending loads. The experimental results are in good agreement with the analytical theory and demonstrate the influence of bending prestress on guided wave propagation. Based on these results an innovative measurement method for bending loads is developed, that is robust to small temperature changes.

Damage recovery in composite laminates through deep learning from acoustic scattering of guided waves

We propose an innovative deep learning (DL) regression strategy combined with guided wave modes to address inverse acoustic scattering problems effectively. This approach allows for accurate recovery of heterogeneous defect fields at the interfaces of composite laminates. The neural network (NN) model's training process employs stochastic Gaussian fields as output, which are linked to the interfacial defect fields of the physical problem. Our method assumes prior knowledge of the material geometrical properties of the constituent layers. To model the interfaces, we utilize the Quasi-Static Approximation, a technique generating position-dependent interfacial stiffness matrices containing uncoupled normal and tangential springs. We validate our approach by assessing its performance in handling noisy input data and reduced models, as well as accounting model errors at the composite interface. The obtained results show that the proposed method has a remarkable generalization capability, allowing it to recover diverse defect field profiles with accuracy. Moreover, it exhibits robustness concerning noisy data and model errors. Lastly, thanks to the guided wave modes approach, the presented methodology not only maintains its capability to recover heterogeneous defect fields potentially in real-time but also extends the range of inspection to encompass a significantly larger structural area.

Crack length directivity effects on guided-wave acoustic emission: Numerical investigation of radiation patterns

This paper investigates the effect of a finite-sized crack surface on acoustic emission (AE) generated at the crack tip in a thin metallic plate using a 3D time-domain finite element model. Directivity effects on the first arrivals are of particular focus, and the AE is interpreted in terms of a guided mode decomposition. Crack lengths from 0-10 plate thicknesses are studied, in addition to a semi-infinite crack surface, for frequency content in the neighborhood of 0.1-0.4 MHz-mm. Far-field radiation patterns for the fundamental symmetric (S0) and shear horizontal (SH0) guided modes are measured as a function of crack length. The results show an increase in radiation behind the crack tip for both modes and across all considered crack lengths. The surface wave traveling along the crack length appears to be one of the main drivers behind this increase, due to mode conversion after reaching the opposite end of the crack. However, a similar increase is also observed for the semi-infinite crack case, in which there is no mode conversion (the opposite end of the crack is never reached). A radiation offset (RO) metric is introduced to capture this behavior. Parametric studies of the RO across center frequency and bandwidth are presented. Findings suggest that this metric may be of use for AE-based crack length estimation.

Generation of time-independent torque by ultrasonic guided waves

The excitation of acoustic waves by a unidirectional transducer, integrated in a piezoelectric cylindrical tube or disk, can lead to a time-independent torque. This phenomenon, demonstrated earlier in experiments and analyzed with coupling-of mode theory, is explained in detail, starting on the level of lattice dynamics of a piezoelectric crystal. Expressions are derived for the stationary torque in the form of integrals over the volume or surface of the piezoelectric, involving the electric potential and displacement field associated with the acoustic waves generated by the transducer. Simulations have been carried out with the help of the finite element method for a tube made of PZT for two cases: A pre-defined potential on the surface of the tube and metal electrodes buried in the piezoelectric. The displacement field and electric potential of the high-frequency acoustic waves (between 200 and 300 kHz) were computed and used in the evaluation of the integrals. The attenuation due to various loss channels of the acoustic waves in the system has been analyzed in detail, as this plays a crucial role for the efficiency of torque generation. It is conjectured that time-reversal symmetry, present in the absence of attenuation, prohibits the generation of a static torque at least in the linear limit. A qualitative comparison is made between the simulations and earlier experiments. Discrepancies are attributed to lack of knowledge of the relevant material constants of the piezoelectric and to a simplified modeling of the electrode geometry in the cylindrical tube, which was necessary for reasons of numerical accuracy.

Nondestructive corrosion degradation assessment based on asymmetry of guided wave propagation field

The article presents the results of numerical and experimental investigation of guided wave propagation in steel plates subjected to corrosion degradation. The development of novel procedures allowing for the assessment of the corrosion degradation level is crucial in the effective diagnostics of offshore and ship structures that are especially subjected to aggressive environments. The study's main aim is to investigate the influence of surface irregularities on wave propagation characteristics. The paper investigates wavefront asymmetry caused by the non-uniform thickness of damaged specimens. In the first step, the influence of thickness variability on the symmetry of the wave field has been investigated numerically. The corroded plates with variable degrees of degradation have been modeled using the random fields approach. The degree of degradation (DoD) varied from 0% to 40%. In the next step, the developed method was examined during experimental tests performed on specimens subjected to accelerated corrosion degradation. The experimental tests were conducted for intact and for corroded plates characterized by a DoD of 10%. It is demonstrated that the new approach based on wave field analysis can be used in structural state assessment.

A new chevron electromagnetic acoustic transducer design for generating shear horizontal guided wave

Guided wave electromagnetic acoustic transducers (EMATs) have a significant role in non-destructive testing and structural health monitoring. It can generate horizontally polarized shear waves propagating axially or circumferentially to characterize the shape and orientation of pipeline defects. This work proposes a new Chevron pattern-like coil structure design with a periodic permanent magnet (PPM) EMAT configuration. This specific design of the EMAT coil can generate a bi-directional shear horizontal wave (SH-wave) and reduce the side lobes. An optimal Chevron angle of coil wires assists in generating orthogonal propagatingwaveforms. These phenomena lead to the constructive interference of propagating waves and develop a resulting wave along the horizontal direction. A 3D FEM modeling and simulation have been carried out and validated with experimental results. The proposed EMAT results are compared with the conventional racetrack PPM EMAT model, which shows a significant improvement over conventional EMATs. A prototype of this proposed EMAT has been developed. It can be used to inspect surface defects in applications such as fuel transportation pipelines.

Notes on osculations and mode tracing in semi-analytical waveguide modeling

The dispersion curves of (elastic) waveguides frequently exhibit crossings and osculations (also known as veering, repulsion, or avoided crossing). Osculations are regions in the dispersion diagram where curves approach each other arbitrarily closely without ever crossing before veering apart. In semi-analytical (undamped) waveguide models, dispersion curves are obtained as solutions to discretized parameterized Hermitian eigenvalue problems. In the mathematical literature, it is known that such eigencurves can exhibit crossing points only if the corresponding matrix flow (parameter-dependent matrix) is uniformly decomposable. We discuss the implications for the solution of the waveguide problem. In particular, we make use of a simple algorithm recently suggested in the literature for decomposing matrix flows. We also employ a method for mode tracing based on approximating the eigenvalue problem for individual modes by an ordinary differential equation that can be solved by standard procedures.

Debonding growth evaluation in CFRP-reinforced steel structures based on correlation analysis using guided waves

Externally bonded carbon fibre reinforced polymer (CFRP) reinforcement is becoming increasingly popular in the field of structural retrofitting due to its considerable efficiency. However, debonding failure occurs sometimes at the interface between CFRP and steel substrate, which is found to be fatal for the CFRP-reinforced structures. Thus, the bonding condition between two materials should be closely monitored to ensure structural serviceability. A linear guided wave based method employing the correlation analysis is adopted in this paper to monitor the growth of debonding failure generated by fatigue in a CFRP-strengthened steel structure from a relatively small scale (smaller than 20 mm in diameter). The correlation coefficients (CC) between the benchmark signals and the signals after certain cycles of loading are calculated individually. Subsequently, the damage index (DI) is extracted on the basis of CC to illustrate the extent of debonding. Finally, the possible debonding position in the structure is predicted by a probability based imaging method.

Analysis of damage localisation results in GFRP panel for different configurations of air-coupled transducers

In this paper results of the damage assessment of fiber-reinforced composite panels using guided wave propagation phenomenon are presented. For this purpose, non-contact elastic wave generation based on an air-coupled transducer (ACT) is utilised. Elastic wave sensing was based on a scanning laser Doppler vibrometer (SLDV). The problem of ACT slope angle for the effectiveness of elastic wave modes generation is analysed. It was shown that for an excitation frequency of 40 kHz it is possible to generate A₀ wave mode. The authors also investigated the damage sensitivity related to panel coverage area by elastic waves with large energy. An artificial damage in the form of Teflon inserts was utilised. Moreover, the influence of single and multiple acoustic wave sources on artificial damage localisation results was investigated. For this purpose RMS wave energy maps, statistical parameters, and damage indices are utilised. Different locations of ACTs and their influence on damage localisation results are investigated. A damage imaging algorithm based on wavefield irregularity mapping (WIM) has been proposed. In this research low-cost and popular, low-frequency ACT was utilised giving the possibility of realisation of the non-contact damage localisation method.

Directivity of quasi-SH0 modes in cubic anisotropic media

We studied the zeroth order shear horizontal modes (SH0 modes) and the quasi-SH0 modes in cubic-anisotropic plates and proposed a formula to describe the scattering directivity of these guided wave modes in arbitrary directions. The quasi-SH0 waves has many unique advantages. However, their velocity and amplitude are influenced by the material anisotropy and change with incidence orientation. In our finding, when the guided wave incidence orientation coincides with the material symmetry plane, the quasi-SH0 modes' amplitudes generated by a uniform force are approximately equal. Otherwise, the amplitudes are significantly smaller. The formula derived by reciprocity consideration explains this phenomenon. We applied the formula to monocrystalline silicon. The results also show that the quasi-SH0 mode is both velocity non-dispersive and directivity non-dispersive in low-fd (frequency thickness product) state. We established an experimental system based on EMATs and verified the theoretical predictions. This paper completes the theoretical basis for damage reconstruction and acoustic imaging by guided waves in complex structures with cubic anisotropy.

The effects of dispersion on time-of-flight acoustic velocity measurements in a wooden rod

The stiffness of wood can be estimated from the acoustic velocity in the longitudinal direction. Studies have reported that stiffness measurements obtained using time-of-flight acoustic velocity measurements are overestimated compared to those obtained using the acoustic resonance and bending test methods. More research is needed to understand what is causing this phenomenon. In this work, amplitude threshold time-of-flight, resonance, and guided wave measurements are performed on wooden and aluminium rods. Using guided wave theory, it is shown through simulations and experimental results that dispersion causes an overestimation of time-of-flight measurements. This overestimation was able to be mitigated using dispersion compensation. However, other guided wave techniques could potentially be used to obtain improved measurements.

Numerical and experimental investigation of guided ultrasonic wave propagation in non-uniform plates with structural phase variations

The article presents the results of numerical and experimental investigations of guided wave propagation in aluminum plates with variable thickness. The shapes of plate surfaces have been specially designed and manufactured using a CNC milling machine. The shapes of the plates were defined by sinusoidal functions varying in phase shift, which forced the changes in thickness variability alongside the propagation path. The main aim of the study is to analyze the wave propagation characteristics caused by non-uniform thickness. In the first step, the influence of thickness variability on the time course of propagating waves has been analyzed theoretically. The study proves that the wave propagation signals can be determined based on knowledge about the statistical description of the specimen geometry. The histograms of thickness distribution together with the a priori knowledge of the dispersion curves were used to develop an iterative procedure assuming that the signal from the previous step becomes the excitation in the next step. Such an approach allowed for taking into account the complex geometry of the plate and rejecting the assumption about the constant average thickness alongside the propagation path. In consequence, it was possible to predict correctly the signal time course, as well as the time of flight and number of propagating wave modes in specimens with variable thickness. It is demonstrated that theoretical signals predicted in this way coincide well with numerical and experimental results. Moreover, the novel procedure allowed for the correct prediction of the occurrence of higher-order modes.

Propagation of Lamb waves in a metal plate with an abrupt change in thickness using Peridynamics and laser Doppler velocimetry

Plate-like structures can be characterized by a variety of abrupt geometric changes affecting the Lamb wave propagation, similarly to damage occurring in service. Therefore, a deep knowledge of phenomena involved in the interaction between guide waves and discontinuities is required. For this purpose, an experimental investigation is carried out considering an isotropic plate where an abrupt thickness change is present. The fundamental modes excitation is operated by a piezoelectric transducer while the signal sensing in multiple locations, also across the discontinuity, is performed by a scanning laser Doppler vibrometer. The investigation reveals mode conversion and highlights how the effects on the wave propagation depend upon the discontinuity geometrical characteristics. A peridynamics-based model representing the examined problem is also defined and its effectiveness to simulate the observed phenomena is proven.

ASM and finite beam description of the excited leaky Lamb wave fields in a fluid-immersed plate

An angular spectrum method (ASM) full-wave description of stress and energy density in a fluid-immersed plate for the optimization of leaky Lamb wave applications is presented. It models the case when leaky Lamb waves are generated by an external finite transmitter in the immersion fluid, and can calculate the associated stress, energy density, and other field variables within the plate. The normal component of the stress tensor and the energy density are compared against calculations in COMSOL with good agreement, but with some differences due to the two methods. The spatial field of the stress is analyzed using the angular spectrum (plane wave) representation of the stress, which is also used as a reference to exemplify the discrepancies between a pure plane wave approach in leaky Lamb wave applications and the spatial fields that accounts for diffraction and dispersion effects. Comments on the insight that the spatial fields within the plate may provide towards NDT/SHM applications are also given, along with a discussion on why the derivation and implementation of the ASM model is valuable when compared against a benchmarked, ready-to-use software such as COMSOL.

Experiments and modelling of ultrasonic waves in composite plates under varying temperature

Guided wave (GW) structural health monitoring (SHM) systems offer an attractive solution as an in-situ quasi real-time assessment of structural damage, but their sensitivity and efficiency may be impaired under varied environmental and operational conditions. Thus, virtual tests, such as that based on the Finite Element (FE) method, represent a valid approach for simulating and investigating SHM systems, enabling a substantial reduction in experimental campaigns. In this work, GW propagation characteristics in a carbon fibre-reinforced composite plate are studied under a varying temperature condition, representative of the aeronautics application. At first, GW SHM system was physically tested at room temperature (20^°C), and the results were used to calibrate and assess the proposed FE modelling approaches, characterised by different element types and mesh sizes. A temperature independent averaged time compensation factor is proposed to mitigate the numerical data dependency on excitation frequency and propagation angle. Two temperature variations (from 20^°C to -50^°C, and 20^°C to 65^°C) were experimentally and numerically considered to investigate the effect of varying temperature on the GW. For all test cases, the compensated numerical data was compared to the experimental results, and discussed in terms of dispersion curves, focusing on the zero-order symmetric, S₀, and antisymmetric, A₀, modes. Results show that both 2D and 3D FE approaches can accurately predict the changes in GW due to varying temperature, with the group velocity of the A₀ mode being less sensitive to temperature variations.

Full wave simulation of arterial response under acoustic radiation force

With the ultimate goal of estimating arterial viscoelasticity using shear wave elastography, this paper presents a practical methodology to simulate the response of a human carotid artery under acoustic radiation force (ARF). The artery is idealized as a nearly incompressible viscoelastic hollow cylinder submerged in incompressible, inviscid fluid. For this idealization, we develop a multi-step methodology for efficient computation of three-dimensional response under complex ARF excitation, while capturing the fluid-structure interaction between the arterial wall and the surrounding fluid. The specific steps include (a) performing dimensional reduction through semi-analytical finite element formulation, (b) efficient finite element discretization using traditional and recent techniques. The computational efficiency is further enhanced by utilizing (c) modal superposition, followed by, where appropriate, (d) impulse response function. In addition to developing the methodology, convergence analysis is performed for a typical arterial geometry, leading to recommendations on various discretization parameters. At the end, the computational effort is shown to be several orders of magnitude less than the traditional, fully three-dimensional analysis using finite element methods, leading to a practical yet accurate simulation of arterial response under ARF excitations.

Ultrasonic testing of thick and thin Inconel 625 alloys manufactured by laser powder bed fusion

Additive manufacturing of alloys enables low-volume production of functional metallic components with complex geometries. Ultrasonic testing can ensure the quality of these components and detect typical defects generated during laser powder bed fusion (LPBF). However, it is difficult to find a single ultrasonic inspection technique that can detect defects in the large variety of geometries generated using LPBF. In this work, phased array ultrasonic testing (PAUT) is suggested to inspect thick LPBF components, while guided waves are explored for thin curved ones. PAUT is used to detect cylindrical lack of fusion defects in thick LPBF rectangular parts. Practical defects are generated by reducing the laser power at prespecified locations in the samples. The defects' shape and density are verified using optical microscopy and X-ray computed tomography. Partially fused defects down to 0.25 mm in diameter are experimentally detected using a 10 MHz PAUT probe with the total focusing method post-processing. The experimental results are compared to defect images predicted by finite element simulations. For thin components with curved geometry, guided waves are used to detect powder-filled cylindrical defects. The waves are generated using piezoelectric transducers, and the spatiotemporal wavefield is measured using a scanning laser Doppler vibrometer. Using root-mean-square imaging of the wavefield, defects down to 1 mm are clearly detected despite the complex internal features in the samples.

Guided waves-based damage identification in plates through an inverse Bayesian process

The use of guided waves to identify damage has become a popular method due to its robustness and fast execution, as well as the advantage of being able to inspect large areas and detect minor structural defects. When a travelling wave on a plate interacts with a defect, it generates a scattered field that will depend on the defects geometry. By analysing the scattered field, one can thus characterize the type and size of the plate damage. A Bayesian framework based on a guided waves interaction model for damage identification of infinite plate for the first time is presented here. A semi-analytical approach based on the lowest order plate theories is adopted to obtain the scattering features for damage geometries with circular symmetry, resulting in an efficient inversion procedure. Subsequently, ultrasound experiments are performed on a large aluminium plate with a circular indentation to generate wave reflection and transmission coefficients. With the aid of signal processing techniques, the effectiveness and efficiency of the proposed approach are verified. A full finite element model is used to test the damage identification scheme. Finally, the scattering coefficients are reconstructed, reliably matching the experimental results. The framework supports digital twin technology of structural health monitoring.

Damage identification using wave damage interaction coefficients predicted by deep neural networks

The ever-increasing demand for efficiency and cost improvements in lightweight structures with guaranteed safety and reliability is leading to the application of a damage-tolerant design philosophy. Here, accurate knowledge of structural health is critical to avoid catastrophic failures. This knowledge can be obtained by using advanced structural health monitoring (SHM) systems. For thin-walled lightweight structures, methods utilizing guided waves generated by piezoelectric transducers are well suited. The interaction between the guided waves and potential damages can be described by so-called wave damage interaction coefficients (WDICs). These WDICs are unique for each damage and depend solely on its characteristics for a given structure. Therefore, the comparison of known WDICs with estimated ones allows drawing conclusions about the current structural state. In this paper, a novel damage identification method for plate-like structures based on a database of such WDICs is presented. Selected damages are simulated numerically with finite elements to generate WDIC patterns. However, these simulations are computationally highly demanding, thus only a very limited number of damage scenarios can be simulated. This study proposes an innovative technique to substantially enhance the resulting WDIC database by using deep neural networks (DNNs). These DNNs enable smart interpolations and allow not only predicting WDICs for previously unseen damages at low computational costs but also the discovery of knowledge about the complex relationship between damage features and WDIC patterns. A comparison to other machine learning algorithms clearly shows the superior performance of the utilized DNNs for interpolating complex WDIC patterns. The proposed damage identification method is verified using advanced time-domain simulations of a large aluminum plate. A statistical analysis of correct identification rates in a common three-sensor setting is employed for assessing the general performance. It is demonstrated that carefully identified DNNs enable to accurately replicate and interpolate complex WDIC patterns. Furthermore, it is shown that these predicted WDICs allow identifying damage characteristics with high confidence.

Recurrence analysis of friction based dry-couplant ultrasonic Lamb waves in plate-like structures

In this study, the effect of friction on the generation of dry-coupled Lamb waves is experimentally investigated. Recurrence analysis is performed to analyze the complex behavior of friction based dry-coupled Lamb waves. In particular, the effect of the normal force, which is necessary for a stronger dry-coupled Lamb wave generation and the friction, on the transmission of mechanical energy and determinism characteristics of Lamb waves are investigated. The results verify that larger friction coefficient and friction force are crucial for generation and propagation of strong Lamb waves supporting the fact that the main mechanism to transfer mechanical energy using dry-couplant is friction. The sensitivity of Lamb waves to the friction coefficient, highlights the importance of designing specific pads with respect to condition of the surface. Besides, the results show that the normal force and friction coefficient can change the determinism characteristics behavior of multimode Lamb waves. Furthermore, it is shown that the determinism value is sensitive to the friction coefficient and normal force. A similar trend is observed in the determinism values and friction coefficient. In general, a smaller friction coefficient indicates smaller determinism value. Additionally, it is shown that a normal load can change the behavior of a system, as observed from recurrence plots, owing to changes in the Lamb waves trajectories in the phase-space domain. In addition, it is shown that recurrence plots enable the detection of mode transitions in multimode Lamb waves. Recurrence analysis is a complementary tool to frequency domain methods for accurate analysis of multimode Lamb waves behavior.

Ultrasonic guided wave measurement in a wooden rod using shear transducer arrays

Research related to acoustic/ultrasonic guided wave testing in wood is still at an early stage. This paper describes the first study to perform ultrasonic guided wave measurements in a wooden rod using arrays of shear transducers. Enhancement of either longitudinal L(0,1) or torsional T(0,1) wave modes and suppression of other modes was able to be achieved using these arrays. At low frequencies, it was found that the L(0,1) wave mode had a similar speed to that obtained using the traditional resonance and time of flight methods. The torsional T(0,1) wave mode has not been used before for non-destructive testing of wood. Since it is non-dispersive, it would appear to be suitable for wood property estimation and structural health monitoring of wooden structures. These results indicate that ultrasonic guided wave testing techniques have strong potential to be used to provide improved measurement of wood properties and structural health monitoring of wooden structures.

Elastic parameters characterization of multilayered structures by air-coupled ultrasonic transmission and genetic algorithm

This paper describes a non-contact method to characterize isotropic and anisotropic planar multilayer structures using a genetic algorithm. The method is based on the determination of critical angles, where the maxima of the modulus of transmission coefficient of the structure appear, and which correspond to the generation of guided waves. The optimization process minimizes the error between the reference critical angles and associated amplitudes of the transmission coefficient, with the corresponding estimated ones. The estimation of elastic parameters is demonstrated for acrylic and oak plates as well as for a bi-layered structure composed of oak and a thin layer of gesso. It is shown that to obtain satisfactory optimization results, it is necessary for guided modes of higher order than the zero ones to be taken into account. Results also show that some elastic constants such as C₃₃ and C₅₅ retrieved from the transmission coefficient are very sensitive to the optimization.

Superposition model of mode shapes composed of travelling torsional guided waves excited by multiple circular transducer arrays in pipes

In pipe inspection using ultrasonic guided wave technique, the current commercial transmitters are designed for the unidirectional guided wave excitation using multiple circular piezoelectric transducers arrays in the axial direction. However, the source with many individual transducer elements in arrays has difficulty in achieving an axisymmetric loading perfectly for defect detection. Therefore, a quasi-axisymmetric wave is formed due to many undesired wave modes are launched instead of a pure axisymmetric wave at a given excitation frequency. In this paper, a realistic superposition model of axial multiple transducer arrays is proposed. The model has many potential applications; one example is investigating the source influence on the generated quasi-axisymmetric wave effect. The analytical model is employed to achieve the predictions for investigating a transmitter's influence for the unidirectional enhancement of torsional T(0,1) guided wave mode excitation in a pipe inspection system composing of three piezoelectric transducer ring arrays. The excitation function with variable power levels among transducers in arrays is also introduced. The predictive results using the analytical model for the distribution of circumferential displacement amplitudes over time are verified using the finite element method and a CLV-3D laser vibrometry measurement on a 219.1-mm-outer-diameter steel pipe without defect. A comparison between calculated and test results has been analysed quantitatively. The respective results are in good agreement. Thus, predictions for the superposed wavefield can be used to analyse the realistic characterisation of the excitation function in axial multiple transducer arrays. Additionally, a sensitivity analysis for part-circumferential crack detection using the quasi-axisymmetric torsional modes generated is also evaluated using finite element modelling.

Efficient semi-analytical simulation of elastic guided waves in cylinders subject to arbitrary non-symmetric loads

In this paper, we present an approach to model the propagation of high-frequency elastic guided waves in solid or hollow cylinders. This formulation requires only discretization of the radial direction, whereas the circumferential direction is approximated via a truncated Fourier series, and the axial direction is described analytically. The model is extended to allow applying arbitrary non-symmetric loads f(r,θ) on the flat cylinder surface. Efficiency is increased by a proposed methodology to limit the number of Fourier coefficients and by the implementation of hierarchical shape functions to dynamically adjust discretization with respect to frequency. Results are validated against conventional finite element applications, demonstrating the accuracy of the model and a reduction of the computing time by three orders of magnitude. Additionally, we apply a matrix function solution for the scaled boundary finite element method leading to a linear solution in the static case.

Concentric shell gradient index metamaterials for focusing ultrasound in bulk media

Focusing of ultrasound waves is criticalto a number ofclinical andindustrial applications including biomedical and underwater imaging,nondestructive evaluation and material processing. This paper discusses the use of a novel'add-on' gradient refractive index (GRIN) metamaterial structure made ofconcentric shells,to focus ultrasonic waves generated by conventional transducers. Analysis based on the Huygen's principle and numerical simulations is used to design the geometric and material properties of the proposed structure, whose working is demonstrated through experiments. Varying the shell material or thickness is shown to offer an elegant and straightforward way to tailor the focal spot inside the target material. The concentric-shell GRIN lens proposed here has a simple design, and has a potential to be used in dynamic focusing without advanced lenses or electronic steering.

Forced guided waves in linearly elastic plates (I) - An examination of the normal-mode expansion method

Guided waves in a plate can be generated by external loads such as body forces and surface tractions. The region of the plate where the external loads are applied is called the loading zone. Guided waves inside the loading zone are called forced guided waves. The classical normal-mode expansion method developed by Auld and Kino in 1973 has been used widely by numerous researchers and practitioners to study forced guided wave problems in plates, including both elastic and electromagnetic waves. As Part I of this investigation, the current paper shows that the classical normal-mode expansion method of Auld and Kino does not yield the exact elastodynamic solution when applied to forced Lamb waves, because its solution does not satisfy the Hooke's law inside the loading zone. The classical normal-mode expansion method, however, does yield the exact elastodynamic solution when applied to forced horizontally polarized shear waves in that its solution satisfies all the governing equations including the equation of motion, the Hooke's law and the prescribed traction boundary conditions. In Part II, a modified normal mode expansion method will be developed to mitigate the above limitations of the classical normal mode expansion method.

Forced guided waves in linearly elastic plates (II) - A modified normal-mode expansion method

The classical normal-mode expansion method developed by Auld and Kino in 1973 has been used widely by numerous researchers and practitioners to study forced guided waves in plates and layered media, including both elastic and electromagnetic waves. However, it was shown in Part I of this study that, although this method gives the correct solution when applied to horizontally polarized shear waves and electromagnetic waves, it does not yield the correct elastodynamic solution when applied to Lamb waves. To address this shortcoming, we develop in this paper a modified normal-mode expansion method that yields the correct elastodynamic solution in that the solution satisfies all the elastodynamic governing equations and the boundary conditions for forced Lamb waves in a plate. The efficacy of the modified normal-mode expansion method is further confirmed by comparing its solution with the finite element solution. Further, it is showed that when applied to horizontally polarized shear waves, the modified normal-mode expansion method yields numerically the same result as that of the classical normal-mode expansion method. However, the modified normal-mode expansion solution converges much faster.

Investigation of thermo-acoustoelastic guided waves by semi-analytical finite element method

Guided waves are sensitive to variations in propagation environments. Many recent studies have focused on the uniform thermal effect on Lamb waves. However, there is little research on the thermal effect in a more complex situation, such as a nonuniform thermal effect and wave propagation in an arbitrary cross-section. In this study, a thermo-acoustoelastic theory combined with the semi-analytical finite element (TAE-SAFE) method is proposed to investigate both uniform and nonuniform thermal effects on acoustoelastic guided wave propagation. In the TAE-SAFE method, effective thermo-acoustoelastic constants including third-order elastic constants are employed. Then, an acoustoelastic wave equation of the thermal effect is formulated by Hamilton's principle and computed by the semi-analytical finite element (SAFE) method. The phase velocity, group velocity, velocity thermal sensitivity, and displacement mode shape shift can be extracted by the proposed method. To validate this method, numerical results of Lamb waves in an aluminum plate subjected to a uniform thermal effect are compared with the results of a previous theoretical analysis. The results show computational veracity and validity. Two typical cases are investigated: (1) an isotropic aluminum plate under a linear temperature gradient condition; (2) a uniform temperature case in a rail track with a constant irregular cross-section. This study provides an effective numerical method to analyze thermo-acoustoelastic guided wave propagation.

Modeling and numerical study of the influence of imperfect interface properties on the reflection coefficient for isotropic multilayered structures

The microelectronics industry is expressing an increased demand for the development of non-destructive tools and methods for health control and diagnostics in multilayered structures. The purpose of these tools is to detect problems such as delaminations, inclusions and microcracks. The aim of this paper is to study the effect of imperfect interfaces on the wave propagation in multilayered structures. This type of structure represents the typical architecture of many microelectronic components. This study will be based on the calculation of the reflection coefficient and the guided waves dispersion curves. The investigated structure is an isotropic trilayer where two metallic layers are bonded together by an adhesive layer made of an epoxy resin. Comparisons were performed in order to evaluate numerically the influence of several properties of the adhesive layer on the guided waves behavior. In addition, an imperfect viscoelastic interface layer model [1] has been implemented in order to simulate different adherence qualities between the metallic layers.

Design optimization of transducer arrays for uniform distribution of guided wave energy in arbitrarily shaped domains

The use of an array of transducers to excite guided Lamb waves, within a plate or any complex structure, usually leads to a variation in the energy on the propagation direction. In this study, an optimization model is proposed to design an array of transducers to provide uniform energy distribution in a domain of an arbitrary shape. The model is based on finding the optimal placements of the transducers and the optimal time delay for excitation by using a genetic algorithm. The efficiency of the model was tested on an elliptically shaped domain, then on an arbitrarily shaped domain. Both cases showed promising results using various configurations/patterns of transducers. The method was experimentally validated on an aluminium alloy plate for two patterns of transducers including six and eight piezoelectric elements.

Modal pencil method for the radiation of guided wave fields in finite isotropic plates validated by a transient spectral finite element method

Elastic guided waves (GW) can be profitably used in non-destructive evaluation and in structural health monitoring of plate-like structures. Nevertheless, the multi-modal and dispersive behaviour of GW often leads to difficult interpretation of typically measured time-dependent signals. The development of efficient simulation tools appears necessary to better understand complex phenomena involved and to optimize testing configurations. Here, a semi-analytical modal method is proposed to compute GW displacement fields in finite plates radiated by an arbitrary finite-sized source of surface stresses. It takes into account GW reflections and mode conversions at plate boundaries. As far as computation efficiency is concerned, this method is independent of the length of propagation paths, allowing to efficiently address configurations involving long range propagation. Predicted results are given as sums of modal contributions to ease their interpretation. The model is validated by comparing its predictions to those computed by a transient finite-element code.

An ultrasonic guided wave excitation method at constant phase velocity using ultrasonic phased array probes

High-order ultrasonic guided wave modes have recently been attracting interest in a variety of nondestructive testing applications, ranging from thickness gauging to bond characterization. Accurate control of the transmitted ultrasonic guided wave mode is paramount when working at frequencies above the cutoff of the first high-order mode. The high number of modes available makes this range of frequency-thickness products difficult to exploit in practice. Many papers and textbooks have showed that multielement probes, such as comb transducers, are able to target a specific wavelength which depends on the elementary pitch. This method can be enhanced by adding an elementary delay law. However, this method of excitation has major drawbacks as the areas of excitation in a dispersion curves depends on the frequency and the technique is not unidirectional. This paper demonstrate that a conventional phased array transducer for which the elementary pitch is small relative to the targeted wavelength is able to excite high order guided wave modes at a constant phase velocity (independently of the frequency). The aim is to excite different regions of the dispersion curves by controlling the input signal bandwidth and the angle of the generated beam. The paper describes the theoretical background and details the differences between the various methods of excitation of ultrasonic guided waves, especially with the comb transducer method. Finite element simulations are presented to verify the analytical predictions and quantify the unidirectional and diffraction properties of the transmitted beam. Experiments conducted on an aluminum plate show striking agreement with finite element simulations, including the possibility of exciting a single mode in a narrow region at high frequency-thickness products. Experiments conducted on a CFRP plate demonstrates that the method can be adapted to other materials.

Quantitative assessment of compress-type osseointegrated prosthetic implants in human bone using electromechanical impedance spectroscopic methods

Osseointegrated (OI) prostheses are a promising alternative to traditional socket prostheses. They can enhance the quality of life of amputees by avoiding fit and comfort issues commonly associated with sockets. The main structural element of the OI prosthesis is a biocompatible metallic implant that is surgically implanted into the bone of the residual limb. The implant is designed to provide a conducive surface for the host bone to osseointegrate with. The osseointegration process of the implant is difficult to clinically evaluate, leading to conservative postoperative rehabilitation approaches. Elastic stress waves generated in an OI prosthesis have been previously proposed to interrogate the implant-bone interface for quantitative assessment of the osseointegration process. This paper provides a detailed overview of the various elastic stress wave methods previously explored for in situ characterization of OI implants. Specifically, the paper explores the use of electromechanical impedance spectroscopy (EIS) to assess the OI process in compress-type OI prostheses. The EIS approach measures the electrical impedance spectrum of lead zirconate titanate elements bonded to the free end of the implant. The research utilizes both numerical simulation and experimental verification to establish that the electromechanical impedance spectrum is sensitive (between 400 and 460 kHz) to both the degree and location of osseointegration. A baseline-free OI index is proposed to quantify the degree of osseointegration at the implant-bone interface and to assess the stability of the OI implant for clinical decision making.

Air coupled ultrasonic inspection with Lamb waves in plates showing mode conversion

In this paper we demonstrate a non-destructive, non-contact detection method for small defects in thin polymer plates using an air coupled ultrasonic (ACUS) setup. There exist many applications for such methods, e.g. quality control in the manufacturing process or failure prevention by periodical inspections during the lifetime of a product. We demonstrate a setup for the inspection of plates together with signal analysis algorithms to process the measured data, meeting the challenges to handle the dispersive signals and establishing a robust failure criterion. Pressure waves from the transmitter excite different modes of Lamb waves inside the plate. These Lamb waves propagate in the plate and reradiate pressure waves into the air that are then detected by the receiver. Lamb mode conversion is used for defect detection. A numerical model allows the visualization of the propagating waves in the air as well as the Lamb waves inside the plate. Four key parameters of the setup are identified, two angles and two distances. The transmitter and the receiver angles are used to select which Lamb mode (anti-symmetric A₀ or symmetric S₀) is mainly excited and detected, respectively. For the acquisition of the Lamb wave signal the distance from the transmitter to the receiver should be as large as possible but is limited by the attenuation of the signal. Measurements for different values of this distance are essential for signal analysis. The distance between transducer and plate surface should be as small as possible even if it may introduce secondary Lamb waves due to reflections of the pressure wave between transmitter and plate surface. Two algorithms, a model based one and a data driven one, are presented to separate Lamb modes that overlap in time. In these separated signals, the Lamb mode conversion from A₀ to S₀ is shown, allowing a localization of the defect. We conclude that defect detection and localization with Lamb mode conversion is possible with an air coupled ultrasonic setup. Multiple measurements along the propagation direction of the Lamb waves are necessary to allow a thorough signal analysis and visualize the mode conversion.

Inversion algorithm for Lamb-wave-based depth characterization of acoustic emission sources in plate-like structures

An inversion algorithm (termed AEDep) is proposed for estimating the depth of acoustic emission (AE) sources in plate-like structural components. The work is motivated by the need for characterizing early-stage fatigue crack growth in such components. The algorithm achieves depth estimation by automatically extracting the depth-dependent amplitude ratio between the fundamental Lamb modes which comprise the AE signals. A finite element model is designed to study the frequency-dependent forward problem of Lamb wave motion due to a given source, from which the relation between source depth and amplitude ratio is established. Elastodynamic theory is used to validate the model in the frequency domain, as well as to derive a sensor tuning factor which may be incorporated into the solution. The proposed algorithm was tested on two plate-like specimens: a 6061-T6 aluminum plate and a 2025-T6 aluminum aircraft fuselage panel. Validation of the algorithm was achieved by generating controlled AE sources at various depths along the edges of the specimens, in the form of Hsu-Nielsen pencil lead breaks. Good agreement was found in the aluminum plate between the true and estimated source depths. A slight decrease in accuracy was found in the fuselage panel between the true values and their estimations. However, both experimental cases demonstrated the ability to distinguish between sources originating near the mid-plane of a plate-like structure from those near the surface. Lastly, the fast computation of the inversion algorithm shows strong potential for real-time monitoring applications.

Modeling guided wave propagation in functionally graded plates by state-vector formalism and the Legendre polynomial method

A numerical method is presented for the investigation of the propagation characteristic of guided waves in functionally gradient material (FGM) plates. Based on the State-vector formalism and Legendre polynomial method, the typical non-stratified computing of dispersion curves of FGMs is realized, by introducing the univariate nonlinear regression to optimize the arbitrary gradient distribution of material component. Comparing with the conventional Matrix method, the proposed method avoids the exhausting root-locating algorithm of solving the transcendental equation by a single-variable scanning process. This method turns it into an algebraic eigenvalue problem, which mainly depends on the orthogonal completeness and strong recursive property of Legendre polynomial series. It provides a fast and flexible approach to extracting the dispersion curves, displacement distribution and stress profile, simultaneously. Results from chrome-ceramic FGM plate are compared with those from the previous articles to confirm the feasibility and accuracy of the proposed method. Then, this approach is further applied to iron based alumina FGM. The dispersion curves with different gradient function are calculated to illustrate the influence of the gradient variation. Moreover, the influence of the cut-off order of Legendre orthogonal polynomials on the convergence of dispersion curves is also revealed through numerical examples. Utilizing the mapping relationship between the gradient distribution and the propagation characteristics, it gives theoretical support for nondestructive evaluation and quantitative estimation of the structural characteristics of FGM plates.

A closed-form solution to propagation of guided waves in a layered half-space under a time-harmonic load: An application of elastodynamic reciprocity

This article is concerned with the application of reciprocity in computing guided wave motions generated by a time-harmonic load in a layer of uniform thickness joined to a half-space. Explicit expressions for free Rayleigh waves and Love waves propagating in the layered half-space are introduced. Exact solutions of Rayleigh waves and Love waves are derived from reciprocity relations between an actual state - guided waves generated by a time-harmonic line load and a virtual state - an appropriately chosen free wave traveling in the structure. Scattered amplitudes of the wave motions are thus determined. The validation of the reciprocity approach is shown through the computation of the lowest Rayleigh wave mode in the layered half-space, which approaches the calculation of the Rayleigh surface wave in the half-space once the layer thickness approaches zero in the limit.

Long-distance shift of ultrasonic beam using a thin plate with periodic gratings

We achieved the shift of ultrasonic beam over a long distance by guided waves through a brass plate with two groups of periodical gratings on the surface. Using Schlieren imaging, we experimentally observed the propagation of ultrasonic waves through this structure. In addition, simulations were performed using the finite-element method. Both the experimental and simulation results revealed that the shift of ultrasonic beam can be realized in this structure. We further investigated the effect of the shift distance and the size of the gratings on the shift efficiency, and discussed the mechanism. The proposed structure has potential applications in non-destructive evaluation.

In Vivo Measurements of Cortical Thickness and Porosity at the Proximal Third of the Tibia Using Guided Waves: Comparison with Site-Matched Peripheral Quantitative Computed Tomography and Distal High-Resolution Peripheral Quantitative Computed Tomography

The aim of this study was to estimate cortical porosity (Ct.Po) and cortical thickness (Ct.Th) using 500-kHz bi-directional axial transmission (AT). Ct.Th_AT and Ct.Po_AT were obtained at the tibia in 15 patients from a 2-D transverse isotropic free plate model fitted to measured guided wave dispersion curves. The velocities of the first arriving signal (υ_FAS) and A₀ mode (υ_A0) were also determined. Site-matched peripheral quantitative computed tomography (pQCT) provided volumetric cortical bone mineral density (Ct.vBMD_pQCT) and Ct.Th_pQCT. Good agreement was found between Ct.Th_AT and Ct.Th_pQCT (R² = 0.62, root mean square error [RMSE] = 0.39 mm). Ct.vBMD_pQCT correlated with Ct.Po_AT (R² = 0.57), υ_FAS (R² = 0.43) and υ_A0 (R² = 0.28). Furthermore, a significant correlation was found between AT and distal high-resolution pQCT. The measurement ofcortical parameters at the tibia using guided waves might improve the prediction of bone fractures in a cost-effective and radiation-free manner.

Guided acoustic waves at the intersection of interfaces and surfaces

In numerical calculations, guided acoustic waves, localized in two spatial dimensions, have been shown to exist and their properties have been investigated in three different geometries, (i) a half-space consisting of two elastic media with a planar interface inclined to the common surface, (ii) a wedge made of two elastic media with a planar interface, and (iii) the free edge of an elastic layer between two quarter-spaces or two wedge-shaped pieces of a material with elastic properties and density differing from those of the intermediate layer. For the special case of Poisson media forming systems (i) and (ii), the existence ranges of these 1D guided waves in parameter space have been determined and found to strongly depend on the inclination angle between surface and interface in case (i) and the wedge angle in case (ii). In a system of type (ii) made of two materials with strong acoustic mismatch and in systems of type (iii), leaky waves have been found with a high degree of spatial localization of the associated displacements, although the two materials constituting these structures are isotropic. Both the fully guided and the leaky waves analyzed in this work could find applications in non-destructive evaluation of composite structures and should be accounted for in geophysical prospecting, for example. A critical comparison is presented of the two computational approaches employed, namely a semi-analytical finite element scheme and a method based on an expansion of the displacement field in a double series of special functions.

Multi-mode reverse time migration damage imaging using ultrasonic guided waves

The sensitivity of Lamb wave modes to a particular defect or instance of damage is dependent on various factors (e.g., the local strain energy density due to that wave mode). As a result, different modes will be more useful than others for damage detection and quantification, dependent on damage type and location. For example, prior work in the field has shown that out-of-plane modes may have a higher sensitivity than in-plane modes to surface defects in plates. The excitability of a certain data acquisition system and the corresponding resolution for damage imaging also varies with frequency. The aim of the present work was to develop a multi-mode damage imaging technique that enables characterization of damage type and size, general sensitivity to unknown damage types, higher resolution imaging, and detectability regardless of the data acquisition system used. A reverse-time migration (RTM) imaging algorithm was combined with a numerical simulator-the three-dimensional (3D) elastodynamic finite integration technique (EFIT)-to provide multi-mode damage imaging. The approach was applied to two simulated case studies featuring damaged isotropic plates. Sensitivities of damage type to wave mode were investigated by separating the A₀ and S₀ Lamb wave modes obtained from the resultant RTM wavefields.

Guided wave elastography of layered soft tissues

In vivo mechanical characterization of soft biological tissues has broad applications ranging from disease diagnosis to tissue engineering. Shear wave elastography based on the bulk wave theory has been widely used to measure the mechanical properties of soft tissues. Given that most soft tissues basically have layered structures, the dispersive feature of elastic waves should be considered when the thickness of the interested layer is comparable to or smaller than the wavelength. Bearing this fundamental issue in mind, we propose an ultrasound-based guided wave elastography (GWE) method to characterize the mechanical properties of layered soft tissues. The dispersion relations of guided waves in layered structures were derived first, and its explicit expression was achieved. An inverse approach based on the dispersion relation to characterize the mechanical properties of layered soft tissues was then established. Both finite element analysis (FEA) and phantom experiments were carried out to validate the new method. In vivo experiments on forearm skin demonstrate the usefulness of the present method in characterizing layered soft tissues. STATEMENT OF SIGNIFICANCE: Layered soft tissues and artificial soft materials are ubiquitous in both nature and engineering. Imaging their in vivo/in situ mechanical properties finds important applications and remains a great challenge to date. Here, we propose an ultrasound-based guided wave elastography method to in vivo/in situ characterize the elastic properties of layered soft materials. We validate the method via finite element analysis and phantom experiments and further demonstrate its usefulness in practice by performing in vivo measurements on forearm skins. Given that the dispersive feature of elastic waves in layered soft media is considered in our method, it provides the opportunity to assess the intrinsic elastic properties of an individual layer in a non-destructive manner as shown in our experiments.

Ex vivo cortical porosity and thickness predictions at the tibia using full-spectrum ultrasonic guided-wave analysis

The estimation of cortical thickness (Ct.Th) and porosity (Ct.Po) at the tibia using axial transmission ultrasound was successfully validated ex vivo against site-matched micro-computed tomography. The assessment of cortical parameters based on full-spectrum guided-wave analysis might improve the prediction of bone fractures in a cost-effective and radiation-free manner.

PURPOSE

Cortical thickness (Ct.Th) and porosity (Ct.Po) are key parameters for the identification of patients with fragile bones. The main objective of this ex vivo study was to validate the measurement of Ct.Po and Ct.Th at the tibia using a non-ionizing, low-cost, and portable 500-kHz ultrasound axial transmission system. Additional ultrasonic velocities and site-matched reference parameters were included in the study to broaden the analysis.

METHODS

Guided waves were successfully measured ex vivo in 17 human tibiae using a novel 500-kHz bi-directional axial transmission probe. Theoretical dispersion curves of a transverse isotropic free plate model with invariant matrix stiffness were fitted to the experimental dispersion curves in order to estimate Ct.Th and Ct.Po. In addition, the velocities of the first arriving signal (υ_FAS) and A₀ mode (υ_A0) were measured. Reference Ct.Po, Ct.Th, and vBMD were obtained from site-matched micro-computed tomography. Scanning acoustic microscopy (SAM) provided the acoustic impedance of the axial cortical bone matrix.

RESULTS

The best predictions of Ct.Po (R² = 0.83, RMSE = 2.2%) and Ct.Th (R² = 0.92, RMSE = 0.2 mm, one outlier excluded) were obtained from the plate model. The second best predictors of Ct.Po and Ct.Th were vBMD (R² = 0.77, RMSE = 2.6%) and υ_A0 (R² = 0.28, RMSE = 0.67 mm), respectively.

CONCLUSIONS

Ct.Th and Ct.Po were accurately predicted at the human tibia ex vivo using a transverse isotropic free plate model with invariant matrix stiffness. The model-based predictions were not further enhanced when we accounted for variations in axial tissue stiffness as reflected by the acoustic impedance from SAM.

Observation of Guided Acoustic Waves in a Human Skull

Human skull poses a significant barrier for the propagation of ultrasound waves. Development of methods enabling more efficient ultrasound transmission into and from the brain is therefore critical for the advancement of ultrasound-mediated transcranial imaging or actuation techniques. We report on the first observation of guided acoustic waves in the near field of an ex vivo human skull specimen in the frequency range between 0.2 and 1.5MHz. In contrast to what was previously observed for guided wave propagation in thin rodent skulls, the guided wave observed in a higher-frequency regime corresponds to a quasi-Rayleigh wave, confined mostly to the cortical bone layer. The newly discovered near-field properties of the human skull are expected to facilitate the development of more efficient diagnostic and therapeutic techniques based on transcranial ultrasound.

Defect mapping in pipes by ultrasonic wavefield cross-correlation: A synthetic verification

This work presents a reverse-time imaging technique by cross-correlating the forward wavefield with the reverse wavefield for the detection, localization, and sizing of defects in pipelines. The presented technique allows to capture the wavefield reflectivity at the places of ultrasonic wave scattering and reflections. Thus, the method is suitable for detecting pipe defects of either point-like or finite-size types using data from a pulse-echo setup. By using synthetic data generated by 3D spectral element pipe models, we show that the 3D wavefield cross-correlation imaging is capable in the case of cylindrical guided ultrasonic waves. With a ring setup of transducers, we analyze the imaging results obtained from the synthetic single-transducer and all-transducer firings. The presented pipe flaw imaging method is straightforward to carry out using a suitable wave equation solver. Also, the method does not suffer from long iterative runs and numerical convergence issues commonly connected with imaging methods based on either deterministic optimization or statistical inference. The imaging procedure can be fully baseline-free by performing data processing to remove direct arrivals from the ultrasound data.

Sparse representation for Lamb-wave-based damage detection using a dictionary algorithm

Lamb waves are being investigated extensively for structural health monitoring (SHM) because of their characteristics of traveling long distances with little attenuation and sensitivity to minor local damage in structures. However, Lamb waves are dispersive, which results in the complex overlap of waveforms in the damage detection applications of the SHM community. This paper proposes a sparse representation strategy based on an l₁-norm optimization algorithm for guided-Lamb-wave-based inspections. A comprehensive dictionary is designed containing various waveforms under diverse conditions so that the received waveform can be decomposed into a spatial domain for the identification of damage location. Furthermore, the l₁-norm optimization algorithm is employed to pursue the sparse solution related to the physical damage location. The functionality of the created dictionary is validated by both metal beam and composite wind turbine experiments. The results indicate a great potential for the proposed sparse representation using a dictionary algorithm, which provides an effective alternative approach for damage detection.

Higher order longitudinal guided wave modes in axially stressed seven-wire strands

This paper investigates the effect of axial stress on higher order longitudinal guided modes propagating in individual wires of seven-wire strands. Specifically, an acoustoelastic theory for a rod is used to predict the effect of stress on the phase velocity of guided modes in a strand. To this end, the exact acoustoelastic theory for an axially stressed rod is adapted for small deformations. Aside from the exact theory, approximate phase velocity changes (derived from both theory and experiment) are proposed, without the need to solve for dispersion curves. To validate the use of rod theories for strands, a custom-built prestressing bed was designed to apply axial load (up to 50% of yield) to a strand while conducting guided wave measurements. Higher order modes were excited in individual wires, and their phase velocity change under stress is compared to the exact acoustoelastic theory. Furthermore, it is shown that the proposed approximate phase velocity changes derived from theory and experiment only differ by roughly 2% from their exact counterparts. Higher order modes are shown to have stable stress dependence near their peak group velocity, which is beneficial for stress measurement. Additionally, linear stress dependence is observed, which is predicted by rod theories. Due to the unavailability of third order elastic constants for the steel strand, constants for a steel with similar Carbon content (0.6% C Hecla 17) were used as representative values in the theory. Using the Hecla 17 constants, roughly 15% mismatch in the slope of the linear stress dependence was observed when compared to the measurements on a steel strand.

Guided ultrasonic waves for determining effective orthotropic material parameters of continuous-fiber reinforced thermoplastic plates

Ultrasonic methods are widely established in the NDE/NDT community, where they are mostly used for the detection of flaws and structural damage in various components. A different goal, despite the similar technological approach, is non-destructive material characterization, i.e. the determination of parameters like Young's modulus. Only few works on this topic have considered materials with high damping and strong anisotropy, such as continuous-fiber reinforced plastics, but due to the increasing demand in the industry, appropriate methods are needed. In this contribution, we demonstrate the application of laser-induced ultrasonic Lamb waves for the characterization of fiber-reinforced plastic plates, providing effective parameters for a homogeneous, orthotropic material model.

A model based bayesian solution for characterization of complex damage scenarios in aerospace composite structures

Ultrasonic damage detection and characterization is commonly used in nondestructive evaluation (NDE) of aerospace composite components. In recent years there has been an increased development of guided wave based methods. In real materials and structures, these dispersive waves result in complicated behavior in the presence of complex damage scenarios. Model-based characterization methods utilize accurate three dimensional finite element models (FEMs) of guided wave interaction with realistic damage scenarios to aid in defect identification and classification. This work describes an inverse solution for realistic composite damage characterization by comparing the wavenumber-frequency spectra of experimental and simulated ultrasonic inspections. The composite laminate material properties are first verified through a Bayesian solution (Markov chain Monte Carlo), enabling uncertainty quantification surrounding the characterization. A study is undertaken to assess the efficacy of the proposed damage model and comparative metrics between the experimental and simulated output. The FEM is then parameterized with a damage model capable of describing the typical complex damage created by impact events in composites. The damage is characterized through a transdimensional Markov chain Monte Carlo solution, enabling a flexible damage model capable of adapting to the complex damage geometry investigated here. The posterior probability distributions of the individual delamination petals as well as the overall envelope of the damage site are determined.

Efficient simulation of elastic guided waves interacting with notches, adhesive joints, delaminations and inclined edges in plate structures

This paper presents an approach to model transmission and reflection phenomena of elastic guided waves in plates. The formulation is applied to plate structures containing notches, inclined edges, delaminations or (adhesive) joints. For these cases, only the thickness direction of the structure needs to be discretized at several locations, while the direction of propagation is described analytically. Consequently, the number of degrees of freedom is very small. Semi-infinite domains can be modeled, in which case the radiation condition is fulfilled exactly. Traction boundary conditions are introduced on the plate surface without requiring a mesh along the surface. Results are validated against conventional finite element implementations, showing the accuracy of the proposed approach and a reduction of the computational costs by typically 2-3 orders of magnitude.