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In non-destructive evaluation guided wave inspections, the elastic structure to be inspected is often embedded within other elastic media and the ensuing leaky waves are complex and non-trivial to compute; we consider the canonical example of an elastic waveguide surrounded by other elastic materials that demonstrates the fundamental issues with calculating the leaky waves in such systems. Due to the complex wavenumber solutions required to represent them, leaky waves pose significant challenges to existing numerical methods, with methods that spatially discretise the field to retrieve them suffering from the exponential growth of their amplitude far into the surrounding media. We present a spectral collocation method yielding an accurate and efficient identification of these modes, leaking into elastic half-spaces. We discretise the elastic domains and, depending on the exterior bulk wavespeeds, select appropriate mappings of the discretised domain to complex paths, in which the numerical solution decays and the physics of the problem are preserved. By iterating through all possible radiation cases, the full set of dispersion and attenuation curves are successfully retrieved and validated, where possible, against the commercially available software disperse. As an independent validation, dispersion curves are obtained from finite element simulations of time-dependent waves using Fourier analysis. [ABSTRACT FROM AUTHOR]

Guided ultrasonic waves are used for the inspection of multilayered composite aerospace structures. Calculating the corresponding dispersion diagrams is challenging for thick-walled composites with more than 100 layers, such as in modern rocket booster pressure vessels. The Dispersion Calculator (DC) is an open source software for calculating such dispersion diagrams and mode shapes of guided waves. Attenuation caused by viscoelasticity and fluid-loading makes the dispersion curve tracing much more difficult than in the nonattenuated case because the modal solutions are sought in the complex wavenumber plane. The tracing problem is mastered by a reliable algorithm. Whereas leaky Lamb and Scholte waves in coupled and decoupled cases are modeled using the stiffness matrix method, shear horizontal (SH) waves are traced using the transfer matrix method without facing the numerical instability. Through implementation of mode family specific dispersion equations in both matrix techniques for nonattenuated and attenuated cases, symmetric, antisymmetric, and nonsymmetric leaky Lamb, Scholte, and SH waves can be traced separately with better efficiency and robustness. The capabilities of DC are demonstrated by calculating dispersion diagrams and mode shapes for a viscoelastic composite with 400 layers immersed in water. Results are compared against DISPERSE (Imperial College London, London, UK) for selected cases. [ABSTRACT FROM AUTHOR]

The rapidly warming Arctic ocean demands new ways to monitor and characterize changes in sea-ice distribution, thickness, and mechanical properties. Upward-looking sonars mounted on autonomous underwater vehicles offer possibilities for doing so. Numerical simulations were made of the signal received by an upward-looking sonar under a smooth ice sheet using a wavenumber integration code. Demands on sonar frequency and bandwidth for pulse-echo measurements were analyzed. For typical sea-ice physical properties found in the Arctic ocean, even in highly attenuating sea-ice, there is significant information to be extracted from the received acoustic signal. Discrete resonance frequencies in the signal may be related to leaky Lamb waves, and the frequencies are connected to the ratio of the shear wave speed-to-thickness of the ice sheet. The periodicity of the multiple reflections of a pulse-compressed signal may be related to the ratio of compressional wave speed-to- thickness. Decay rates of both types of signals are indicative of the wave attenuation coefficients. Simulations of the acoustic reflection by rough water–ice interfaces were made. Smaller levels of roughness were found to enhance the acoustic signal, while greater levels of roughness are detrimental to the sea-ice characterization process. [ABSTRACT FROM AUTHOR]

A method for the determination of longitudinal and transverse bulk acoustic wave attenuation from measurements of the decay-rate of two independent zero-group-velocity resonances in a couple of matched plates is presented. A linear relation is derived, which links the bulk-wave attenuation coefficients to the decay-rate of plate-resonances. The relation is used to determine the acoustic loss of tungsten at GHz frequencies from noncontact laser-ultrasonic measurements in plates with thicknesses of about 1 µm. The longitudinal and transverse attenuation was found to amount to 1918 m−1 and 7828 m−1 at 2.16 GHz and 3265 m−1 and 12181 m−1 at 2.46 GHz. The presented approach is validated with calculated responses to a thermoelastic source, and the accuracy of the obtained attenuation values is estimated to be in the range of 10%. [ABSTRACT FROM AUTHOR]

This paper numerically investigates the propagation of elastic plate waves along the non-principal directions in a prestretched compressible material described by the Gent model of hyperelasticity. We formulate the elastic tensor and the underlying wave equations in the Lagrangian space by employing the theory of nonlinear elasticity together with the linearized incremental equations. An extension of the Semi-Analytical Finite Element (SAFE) method is discussed for computing the dispersion characteristics of the two fundamental guided wave modes. The predictive capabilities of the numerical framework are established using the previously published data for a weakly nonlinear as well as hyperelastic material models. Using the numerical framework, we then bring out the effects of applied prestretch, orientation of the propagation direction, and material parameters on the dispersion characteristics of the fundamental Lamb modes. A limiting case of the neo-Hookean material model is first considered for elucidating such implicit dependencies, which are further highlighted by considering the strain-stiffening effect captured through the Gent material model. Our results indicate the existence of a threshold prestretch for which the Gent-type material can encounter a snap-through instability; leading to the change in the dispersion characteristics of the fundamental symmetric Lamb mode. [ABSTRACT FROM AUTHOR]

Nonlinear group delay signals with frequency-varying characteristics are common in a wide variety of fields, for instance, structural health monitoring and fault diagnosis. For such applications, the signal is composed of multiple modes, where each mode may overlap in the frequency-domain. The resulting decomposition and forming of time-frequency representations of the nonlinear group delay modes is a challenging task. In this study, the nonlinear group delay signal is modelled in the frequency-domain. Exploiting the sparsity of the signal, we present the nonlinear group delay mode estimation technique, which forms the demodulation dictionary from the group delay. This method can deal with crossed modes and transient impulse signals. Furthermore, an augmented alternating direction multiplier method is introduced to form an efficient implementation. Numerical simulations and experimental data analysis show the effectiveness and advantages of the proposed method. In addition, the included analysis of Lamb waves as well as of a bearing signal show the method's potential for structural health monitoring and fault diagnosis. [ABSTRACT FROM AUTHOR]

Characterization of grain microstructures of metallic materials is crucial to materials science and engineering applications. Unfortunately, the universal electron microscopic methodologies can only capture two-dimensional local observations of the microstructures in a time-consuming destructive way. In this regard, the nonlinear ultrasonic technique shows the potential for efficient and nondestructive microstructure characterization due to its high sensitivity to microstructural features of materials, but is hindered by the ill-posed inverse problem for multiparameter estimation induced by the incomplete understanding of the complicated nonlinear mechanical interaction mechanism. We propose an explainable nonlinearity-aware multilevel wavelet decomposition-multichannel one-dimensional convolutional neural network to hierarchically extracts multilevel time-frequency features of the acoustic nonlinearity and automatically model latent nonlinear dynamics directly from the nonlinear ultrasonic responses. The results demonstrate that the proposed approach establishes the complex mapping between acoustic nonlinearity and microstructural features, thereby determining the lognormal distribution of grain size in metallic materials rather than only average grain size. In the meantime, the integration of the designed nonlinearity-aware network and the quantitative analysis of component importance provides an acceptable physical explainability of the deep learning approach for the nonlinear ultrasonic technique. Our study shows the promise of this technique for real-time in situ evaluation of microstructural evolution in various applications. [ABSTRACT FROM AUTHOR]

Leaky waves are an important class of waves, particularly for guiding waves along structures embedded within another medium; a mismatch in wavespeeds often leads to leakage of energy from the waveguide, or interface, into the medium, which consequently attenuates the guided wave. The accurate and efficient identification of theoretical solutions for leaky waves is a key requirement for the choices of modes and frequencies required for non-destructive evaluation inspection techniques. We choose a typical situation to study: an elastic waveguide with a fluid on either side. Historically, leaky waves are identified via root-finding methods that have issues with conditioning, or numerical methods that struggle with the exponential growth of solutions at infinity. By building upon a spectral collocation method, we show how it can be adjusted to find exponentially growing solutions, i.e., leaky waves, leading to an accurate, fast, and efficient identification of their dispersion properties. The key concept required is a mapping, in the fluid region, that allows for exponential growth of the physical solution at infinity, whilst the mapped numerical setting decays. We illustrate this by studying leaky Lamb waves in an elastic waveguide immersed between two different fluids and verify this using the commercially available software disperse. [ABSTRACT FROM AUTHOR]

A nondestructive method (M) for stress characterization in plate-like structures is proposed. In this method, the acoustoelastic effects (AEEs) on Lamb and shear horizontal guided waves are used to reconstruct a nonuniform multiaxial stress field. The development of M starts by deriving an analytical acoustoelastic model (An-AEM) to predict AEEs induced by a triaxial stress tensor as a function of the stress components, its orientation, the wave propagation direction, and three acoustoelastic coefficients (AECs). The AECs are independent of stress but specific to each mode. The An-AEM allows one to retrieve the three components of the stress tensor and its orientation from AEEs, assuming the stress to be uniform in the plane of the plate and through its thickness. To deal with stress that is nonuniform in the plane, the An-AEM is combined with time-of-flight straight ray tomography to enable stress field reconstruction. Numerical simulation is used to illustrate how such reconstruction can be performed. It is shown that in some cases, stress components can be reconstructed with arbitrary accuracy, and in other cases, the tensorial nature of stress renders the accuracy of its reconstruction dependent on spatial variations of the stress orientation. [ABSTRACT FROM AUTHOR]

In recent years, micro-acoustic devices, such as surface acoustic wave (SAW) devices, and bulk acoustic wave (BAW) devices have been widely used in the areas of Internet of Things and mobile communication. With the increasing demand of information transmission speed, working frequencies of micro-acoustic devices are becoming much higher. To meet the emerging demand, Lamb wave devices with characteristics that are fit for high working frequency come into being. However, Lamb wave devices have more complicated vibrating modes than SAW and BAW devices. Methods used for SAW and BAW devices are no longer suitable for the mode extraction of Lamb wave devices. To solve this difficulty, this paper proposed a method based on machine learning with convolutional neural network to achieve automatic identification. The great ability to handle large amount of images makes it a good option for vibrating mode recognition and extraction. With a pre-trained model, we are able to identify and extract the first two anti-symmetric and symmetric modes of Lamb waves in varisized plate structures. After the successful use of this method in Lamb wave modes automatic extraction, it can be extended to all micro-acoustic devices and all other wave types. The proposed method will further promote the application of the Lamb wave devices. [ABSTRACT FROM AUTHOR]

Transcranial focused ultrasound (FUS) is a noninvasive treatment for brain tumors and neuromodulation. Based on normal incidence, conventional FUS techniques use a focused or an array of ultrasonic transducers to overcome the attenuation and absorption of ultrasound in the skull; however, this remains the main limitation of using FUS. A dual-mode conversion technique based on Lamb waves is proposed to achieve high transmission efficiency. This concept was validated using the finite element analysis (FEA) and experiments based on changes in the incident angle. Aluminum, plexiglass, and a human skull were used as materials with different attenuations. The transmission loss was calculated for each material, and the results were compared with the reflectance function of the Lamb waves. Oblique incidence based on dual-mode conversion exhibited a better transmission efficiency than that of a normal incidence for all of the specimens. The total transmission losses for the materials were 13.7, 15.46, and 3.91 dB less than those associated with the normal incidence. A wedge transducer was designed and fabricated to implement the proposed method. The results demonstrated the potential applicability of the dual-mode conversion technique for the human skull. [ABSTRACT FROM AUTHOR]

Cloaking invisibility is a novel technique that prevents the object from being detected in the background field. The development of new artificial materials and structures promotes the emergence of new achievements in cloaking research. In this work, a broadband square cloaking configuration of elastic wave metamaterial plate is designed and fabricated by the external active control system. The approximate parameters of the flexural wave cloak can be obtained by the coordinate transformation and achieved by alternating layers of the Acrylonitrile Butadiene Styrene (ABS), polydimethylsiloxane (PDMS), and piezoelectric (PZT) patches. With the introduction of active control systems, the square cloak has a wide effective frequency range. The simulation and experimental results show that the square cloak of flexural waves exhibits a good invisible performance in the frequency region of 500–2200 Hz. Compared to the structure without active control systems, the frequency region 2200–2750 Hz is extended for the active cloak. The design and fabrication of the broadband cloak is wished to be helpful during the practical engineering. [ABSTRACT FROM AUTHOR]

An experimental comparison is reported here between two equivalent resonant subwavelength metasurfaces made of long aluminum beams glued closely together on a thin aluminum plate. One metasurface has a random distribution of the resonator beams, and the other has a regular square lattice of pitch 1.5 cm. The random lattice shows the "resonant" behavior of a typical metasurface, with a wide full bandgap for the first A0 Lamb mode. Instead, the regular square lattice combines Fano resonance with Bragg scattering at the edges of the passband, thus creating anisotropy and a pseudo bandgap. Comparisons with numerical simulations are performed, with good agreement with the experimental data. The multimodal response of the beams is also responsible for double negativity in a narrow frequency band, and the event of a pseudo bandgap around this same flexural resonance. In addition, the scattering regimes for both the random and regular metasurfaces are characterized using coherent and incoherent signal analysis. [ABSTRACT FROM AUTHOR]

A theoretical model is derived to extend existing work on the theory of acoustoelasticity in isotropic materials subjected to uniaxial or hydrostatic loadings, up to the case of arbitrary triaxial loading. The model is applied to study guided wave propagation in a plate. The semi-analytical finite element method is adapted to deal with the present theory. Effects of triaxial loading on velocities of Lamb and shear horizontal (SH) modes are studied. They are non-linearly dependent on stress, and this nonlinearity is both frequency-dependent and anisotropic. Velocity changes induced by the effect of stress on the plate thickness are shown to be non-negligible. When a stress is applied, both Lamb and SH modes lose their simple polarization characteristics when they propagate in directions different from the principal directions of stress. The assumption that effects induced by a multiaxial stress equal the sum of effects induced by each of its components independently is tested. Its validity is shown to depend on frequency and propagation direction. Finally, the model is validated by comparing its predictions to theoretical and experimental results of the literature. Its predictions agree very well with measurements and are significantly more accurate than those of existing theories. [ABSTRACT FROM AUTHOR]

Acoustic trapping is a promising technique for aligning particles in two-dimensional arrays, as well as for dynamic manipulation of particles individually or in groups. The actuating principles used in current systems rely on either cavity modes in enclosures or complex arrangements for phase control. Therefore, available systems either require high power inputs and costly peripheral equipment or sacrifice flexibility. This work presents a different concept for acoustic trapping of particles and cells that enables dynamically defined trapping patterns inside a simple and inexpensive setup. Here, dynamic operation and dexterous trapping are realized through the use of a modified piezoelectric transducer in direct contact with the liquid sample. Physical modeling shows how the transducer induces an acoustic force potential where the conventional trapping in the axial direction is supplemented by surface displacement dependent lateral trapping. The lateral field is a horizontal array of pronounced potential minima with frequency-dependent locations. The resulting system enables dynamic arraying of levitated trapping sites at low power and can be manufactured at ultra-low cost, operated using low-cost electronics, and assembled in less than 5 min. We demonstrate dynamic patterning of particles and biological cells and exemplify potential uses of the technique for cell-based sample preparation and cell culture. [ABSTRACT FROM AUTHOR]

The second-harmonic generation of the fundamental antisymmetric Lamb wave at a closed parallel crack in an elastic plate is studied by numerical analysis. The closed crack is modeled as a spring-type interface with quadratic nonlinearity. Based on a perturbation method, the problem of nonlinear Lamb wave scattering is decomposed into two linearized problems, i.e., for the linear reflection/transmission of the incident Lamb wave at the crack and for the generation/radiation of the second-harmonic Lamb waves due to the contact nonlinearity. The reduced problems are solved by the finite element method in the frequency domain. Numerical results demonstrate significant effects of the crack resonance on the linear and nonlinear Lamb wave scattering responses, which appear as sharp peaks/dips in the reflection/transmission spectra and enhanced second-harmonic amplitudes at some frequencies. Two simple frequency selection rules are established which explain the enhanced generation of the second-harmonic Lamb waves. The time-domain analysis is also carried out to supplement the frequency-domain analysis, which confirms that the incident Lamb wave interacts with the crack at some specific frequencies in its bandwidth in a selective manner and enhances the generation of the second-harmonic components. [ABSTRACT FROM AUTHOR]

When investigating the wave propagation and mode conversions in a thin aluminum plate partially immersed in water, a kind of wave packet interaction was observed. It was found that the transmitted ultrasonic signal consists of different wave packets, which contain essential information of different wave types. When the incident angle is very small, the signals can be identified as the major wave packet followed by its tail. The major packet includes the information of the incident wave while the tail is related to the mode conversion and propagation in the plate. When the incident angle increased, the major packet was literally engulfed by its tail, indicating that the directly transmitted incident ultrasound disappeared and more energy was coupled into the plate. The interactions between different wave packets found here reveal the excitation and propagation mechanisms of Lamb waves in plates, which would benefit applications in ultrasonic imaging, signal recognition, underwater acoustic communication, and so on. [ABSTRACT FROM AUTHOR]

During ultrasonic clamp-on flow metering, Lamb waves propagating in the pipe wall may limit the measurement accuracy by introducing absolute errors in the flow estimates. Upon reception, these waves can interfere with the up and downstream waves refracting from the liquid, and disturb the measurement of the transit time difference that is used to obtain the flow speed. Thus, suppression of the generation of Lamb waves might directly increase the accuracy of a clamp-on flow meter. Existing techniques apply to flow meters with single element transducers. This paper considers the application of transducer arrays and presents a method to achieve a predefined amount of suppression of these spurious Lamb waves based on appropriate amplitude weightings of the transducer elements. Finite element simulations of an ultrasonic clamp-on flow measurement setting will be presented to show the effect of array aperture control on the suppression of the Lamb waves in a 1-mm-thick stainless steel pipe wall. Furthermore, a proof-of-principle experiment will be shown that demonstrates a good agreement with the simulations. [ABSTRACT FROM AUTHOR]

Burst wave lithotripsy is a method to noninvasively fragment urinary stones by short pulses of focused ultrasound. In this study, physical mechanisms of stone fracture during burst wave lithotripsy were investigated. Photoelasticity imaging was used to visualize elastic wave propagation in model stones and compare results to numerical calculations. Epoxy and glass stone models were made into rectangular, cylindrical, or irregular geometries and exposed in a degassed water bath to focused ultrasound bursts at different frequencies. A high-speed camera was used to record images of the stone during exposure through a circular polariscope backlit by a monochromatic flash source. Imaging showed the development of periodic stresses in the stone body with a pattern dependent on frequency. These patterns were identified as guided wave modes in cylinders and plates, which formed standing waves upon reflection from the distal surfaces of the stone model, producing specific locations of stress concentration in the models. Measured phase velocities compared favorably to numerically calculated modes dependent on frequency and material. Artificial stones exposed to bursts produced cracks at positions anticipated by this mechanism. These results support guided wave generation and reflection as a mechanism of stone fracture in burst wave lithotripsy. [ABSTRACT FROM AUTHOR]

Elastic waves guided along bars of rectangular cross sections exhibit complex dispersion. This paper studies in-plane modes propagating at low frequencies in thin isotropic rectangular waveguides through experiments and numerical simulations. These modes result from the coupling at the edge between the first order shear horizontal mode SH0 of phase velocity equal to the shear velocity VT and the first order symmetrical Lamb mode S0 of phase velocity equal to the plate velocity VP. In the low frequency domain, the dispersion curves of these modes are close to those of Lamb modes propagating in plates of bulk wave velocities VP and VT. The dispersion curves of backward modes and the associated zero group velocity (ZGV) resonances are measured in a metal tape using noncontact laser ultrasonic techniques. Numerical calculations of in-plane modes in a soft ribbon of Poisson's ratio ν ≈ 0.5 confirm that, due to very low shear velocity, backward waves and ZGV modes exist at frequencies that are hundreds of times lower than ZGV resonances in metal tapes of the same geometry. The results are compared to theoretical dispersion curves calculated using the method provided in Krushynska and Meleshko [J. Acoust. Soc. Am. 129, 1324–1335 (2011)]. [ABSTRACT FROM AUTHOR]

Love waves are of great importance in geophysics, electronics, and engineering. Despite intensive studies on high-frequency Love waves for delay lines and chemical/biomedical sensors, moderate-frequency and low-frequency Love waves have seldom been investigated. Here, Love waves in a 2-mm-thick Plexiglas plate bonded on a 50-mm-thick aluminum block were successfully excited and received by using d24 and d15 shear mode PZT wafers. A d31 mode PZT wafer was also employed as the sensor, and results show that no Rayleigh-Lamb type waves were generated. The group velocity curve of the excited Love wave from 120 to 525 kHz matches the theoretical curve well. This work could promote applications of Love waves in many engineering fields. [ABSTRACT FROM AUTHOR]

An accurate and numerically inexpensive method is presented to calculate the reflection of in-plane waves at the free surface of an elastic substrate supporting a periodic array of plates. The method is based on the expansions of the elastic fields on the pseudo-periodic modes in the substrate and on the Lamb modes in the plates. These expansions involve unknown amplitudes which are determined by simple matrix inversion when accounting for the boundary conditions at the surface of the substrate and at the free edges of the plates. Exemplifying results are reported in a wide range of frequency covering two resonances of the plates which are analyzed: a flexural resonance of slender bodies and the quasi-resonance of the so-called edge mode. The convergence of the method is inspected quantitatively; it is shown that it is good in view of the fact that the stress is singular at the corners of the plates in contact with the substrate. In particular, the scattering coefficients converge as 1 / N s 3 / 2 with N s the truncation of the expansions. [ABSTRACT FROM AUTHOR]

In a reverberant cavity, when a noise field is sufficiently diffuse, the correlation of the signal measured by two sensors provides an estimation of the Green's function (GF) between them. Here, the convergence of this passive estimation in the case of elastic waves on thin plates is studied. A statistical approach is proposed, which relates the similarity between the cross correlation and the GF to the structural properties of the plate and the number of uncorrelated sources. The analysis is sustained by experimental results obtained on an aluminum plate. This study allows us to evaluate the efficiency of passive structural health monitoring of plate-like structures based on noise correlation. Finally, a most interesting finding shows an absolute upper bound of the signal-to-noise ratio for GF quality reconstruction: 4 N s / 5 , independently of the plate properties. [ABSTRACT FROM AUTHOR]

Optical breakdown of water is used as a sound source to excite a broadband set of leaky Lamb waves in submerged aluminum plates. The source is shown to simultaneously excite guided modes spanning 0.1–5 MHz in frequency and 0–0.8 mm−1 in wavenumber. The measured response overlaps well with dispersion curves for Lamb waves in the plates, revealing strong coupling to both symmetric and antisymmetric modes. The strongest responses arise when a mode's phase velocity approximately equals the plate's compressional wave velocity. These results are shown to arise from an interplay of the sensing geometry, guided wave speeds, and signal processing. Finally, implications for non-contact sensing are discussed. [ABSTRACT FROM AUTHOR]

In this work, a design of integrating ultrasonic transduction with live cell imaging chamber is introduced. The principle of a metal-incident-glass-output acoustic path was used to deliver a uniform energy profile into the imaging/incubation chamber in the form of leaky Lamb waves. The design was applied to examine living mouse mammary gland epithelial cells (EpH4). Significant changes in intracellular activities were observed even at a very low energy intensity level (1 MHz, ISATA = 1 mW/cm2, continuous wave). Live imaging with ultrasonic stimulation provides a different paradigm to interrogate cellular mechanosensitive responses in real time. [ABSTRACT FROM AUTHOR]

Lamb waves are elastodynamic guided waves in plates and are used for non-destructive evaluation, sensors, and material characterization. These applications rely on the knowledge of the dispersion characteristics, i.e., the frequency-dependent wavenumbers. The interaction of a plate with an adjacent fluid leads to a nonlinear differential eigenvalue problem with a square root term describing exchange of energy with the surrounding medium, e.g., via acoustic radiation. In this contribution, a spectral collocation scheme is applied to discretize the differential eigenvalue problem. A change of variable is performed to obtain an equivalent polynomial eigenvalue problem of fourth order, which is linear in state-space and can reliably be solved using modern numerical methods. Traditionally, the leaky Lamb wave problem has been solved by finding the roots of the characteristic equations, a numerically ill-conditioned problem. In contrast to root-finding, the approach described in this paper is inherently able to find all modes and naturally handles complex wavenumbers. The full phase velocity dispersion diagram and attenuation curves are presented and are shown to be in excellent agreement with solutions of the characteristic equation as well as computations made with a perturbation method. The procedure is applicable to anisotropic, viscoelastic, inhomogeneous, and layered plates coupled to an inviscid fluid. [ABSTRACT FROM AUTHOR]

The reflection and transmission characteristics of Lamb waves at an adhesive single lap joint of plates are examined theoretically by the hybrid finite element method. The adhesive joint is modeled by a linear spring-type interface, which is characterized by normal and tangential stiffnesses. For the incidence of the lowest-order antisymmetric (A0) Lamb mode in a low frequency range, it is shown that the reflection and transmission coefficients of the A0 mode take local maxima and minima at multiple frequencies. This behavior results from the interference of waves originating from the lowest-order antisymmetric guided wave mode in the overlap region. The peak frequencies of the transmission coefficient increase monotonically with increasing tangential stiffness, but are almost invariant with the normal stiffness of the adhesive joint. Furthermore, time-domain numerical simulation using the finite element method is carried out to discuss the theoretical results. As a result, for the A0 mode incidence, the reflection and transmission waveforms of the A0 mode from the lap joint are found to show long-oscillation tails. The spectral analysis for the obtained waveforms shows that these tails are necessary to identify the frequencies at which the reflection and transmission coefficients take local maxima and minima. [ABSTRACT FROM AUTHOR]

In this paper, the effect of a large pre-stress on the propagation of small amplitude Lamb waves in an incompressible elastic plate is investigated. Using the theory of incremental elasticity, the dispersion equations, which give the phase velocity of the symmetric and anti-symmetric wave modes as a function of the wavenumber, plate thickness, and pre-stress state, are derived for a general strain energy function. By considering the fourth-order strain energy function of incompressible isotropic elasticity, the correction to the phase velocity due to the pre-stress is obtained implicitly to the second order in the pre-strain/stress, and depends on the second, third, and fourth-order elastic constants. Numerical results are presented to show the dependence of the phase velocity of the Lamb wave modes upon the applied stress. These are compared to the first-order correction, and agree well with the limiting and asymptotic values obtained previously. It is envisaged that the present results may well find important practical applications in various guided wave based ultrasonic techniques utilising gels and rubber-like materials. [ABSTRACT FROM AUTHOR]

Leaky Lamb waves have the potential to be used to perform non-destructive testing on a set of several parallel and immersed plates. Short-time Fourier transform and two-dimensional Fourier transform have both been successfully used to measure the propagation properties: phase and group velocity, and leaky attenuation. Experimental measurements were validated by comparison between theory, experimentation and finite-element simulations (using comsol multiphysics® software) in the case of one immersed plate in water. These signal processing techniques proved to be efficient in the case of multi-modal propagation. They were applied to two immersed plates to identify the leaky Lamb mode generated in the second plate. Dispersion curves of the system composed by two immersed and parallel plates are computed. When plates have the same thickness, leaky Lamb modes propagate from the first to the second plate without any mode change, with the apparent attenuation being weaker in the second plate. Considering that the second plate is continuously supplied in energy by the first one, an energy-based model is proposed herein to estimate the apparent attenuation in the second plate. Despite our extremely simplifying assumption, this model proved to be in good agreement with both finite-element modelling and experimentation. [ABSTRACT FROM AUTHOR]

Recently, a perturbation approach was adopted for the non-collinear mixing of plate waves in an isotropic elastic plate with quadratic nonlinearity by Ishii, Biwa, and Adachi [J. Sound Vib. 419, 390–404 (2018)] and a resonance condition was derived theoretically, namely, that a significant scattered plate wave is generated when its frequency and wavevector coincide with the sum/difference of those of its primary waves. However, that analysis assumed monochromatic plane waves that interacted everywhere in the plate. To apply the non-collinear mixing of plate waves to nondestructive evaluation of plate-like structures, the influence of the spatial and temporal finiteness of the primary waves on the generation of the scattered wave must be elucidated. To that end, the present study conducts three-dimensional dynamic finite-element analyses on the mixing of lowest-order antisymmetric Rayleigh–Lamb waves that have finite beam widths and time durations. The generation of scattered lowest-order symmetric Rayleigh–Lamb and shear horizontal waves with sum frequencies is discussed for various beam widths, intersection angles, and primary frequencies. The resonance condition derived originally for monochromatic plane waves in the aforementioned study is found to be valid even when the wave interaction is allowed only within limited space and time. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Acoustoelastic techniques have been recently used to characterize the state of prestress in structures such as plates. The velocity of guided wave modes propagating through plates is sensitive to the magnitude and orientation of the initial state of stress. Dispersion curves for phase velocities of plate guided waves can be computed using the superposition of partial bulk waves (SPBW) method. Here, a semi-analytical finite element (SAFE) method is formulated for the acoustoelastic problem of guided waves in weakly nonlinear elastic plates. The SAFE formulation is shown to provide phase velocity dispersion curve results identical with those provided by the SPBW method for the problem of a plate under a uniaxial and uniform tensile stress. Analytical phase and group velocity dispersion curves are also obtained for a plate with an initial prestress gradient through its thickness using the SAFE method. The magnitude of the prestress gradient is shown to have a significant effect on phase and group velocities of the fundamental and first order Lamb modes, only in certain frequency-thickness regimes. [ABSTRACT FROM AUTHOR]

Monocrystalline silicon wafers are widely used in the photovoltaic industry for solar panels with high conversion efficiency. Guided ultrasonic waves offer the potential to efficiently detect micro-cracks in the thin wafers. Previous studies of ultrasonic wave propagation in silicon focused on effects of material anisotropy on bulk ultrasonic waves, but the dependence of the wave propagation characteristics on the material anisotropy is not well understood for Lamb waves. The phase slowness and beam skewing of the two fundamental Lamb wave modes A0 and S0 were investigated. Experimental measurements using contact wedge transducer excitation and laser measurement were conducted. Good agreement was found between the theoretically calculated angular dependency of the phase slowness and measurements for different propagation directions relative to the crystal orientation. Significant wave skew and beam widening was observed experimentally due to the anisotropy, especially for the S0 mode. Explicit finite element simulations were conducted to visualize and quantify the guided wave beam skew. Good agreement was found for the A0 mode, but a systematic discrepancy was observed for the S0 mode. These effects need to be considered for the non-destructive testing of wafers using guided waves. [ABSTRACT FROM AUTHOR]

High order Lamb waves are investigated for the effects of stress on both symmetrical and anti-symmetrical modes in an aluminum plate for wave propagation and load parallel. Data are compared with those for the case of load and measurement axis perpendicular. It is the S1 mode which exhibits significantly higher sensitivity to stress than other Lamb modes. For aluminum the use of the S1 mode for stress measurement is found to be about six times more sensitive, than bulk waves, for the load-measurement axes parallel case and this compares with about ten times for the case of load-measurement axes perpendicular. [ABSTRACT FROM AUTHOR]

In this letter, an experimental and numerical study of the influence of symmetric resonators on Lamb waves that propagate in a thin metallic plate is reported. The resonators consist of a set of small, closely packed rods that pass through the plate from side to side to create a locally resonant metamaterial. Adjusting the symmetry of these rods creates degenerate flexural resonances that can be tuned to couple only with a given Lamb mode that is either symmetric (S0) or anti-symmetric (A0). This approach offers promising perspectives in the development of metamaterials for elastic waves that involve non-scalar interactions. [ABSTRACT FROM AUTHOR]

Ultrasonic Lamb waves are a widely used research tool for nondestructive structural health monitoring. They travel long distances with little attenuation, enabling the interrogation of large areas. To analyze Lamb wave propagation data, it is often important to know precisely how they propagate. Yet, since wave propagation is influenced by many factors, including material properties, temperature, and other varying conditions, acquiring this knowledge is a significant challenge. In prior work, this information has been recovered by reconstructing Lamb wave dispersion curves with sparse wavenumber analysis. While effective, sparse wavenumber analysis requires a large number of sensors and is sensitive to noise in the data. In this paper, it extended and significantly improved by constraining the reconstructed dispersion curves to be continuous across frequencies. To enforce this constraint, it is included explicitly in a sparse optimization formulation, and by including in the reconstruction an edge detection step to remove outliers, and by using variational Bayesian Gaussian mixture models to predict missing values. The method is validated with simulation and experimental data. Significant improved performance is demonstrated over the original sparse wavenumber analysis approach in reconstructing the dispersion curves, in synthesizing noise-removed signals, in reducing the number of measurements, and in localizing damage. [ABSTRACT FROM AUTHOR]

The present article investigates the propagation of Rayleigh waves along a horizontal semi-infinite crack, and its interaction with the crack tip. Finite element analysis was used to simulate wave propagation and study the interaction. An incident Rayleigh wave diffracts as bulk waves into the half-space upon interaction with the crack tip. It was observed that the diffracted bulk modes can interact with the half-space boundary, and mode converts into a Rayleigh wave traveling along the boundary. A qualitative analysis was performed to determine the effect of crack depth using transmission, reflection, and scattering coefficients. Moreover, the possibility of Lamb wave generation also arises since the crack face and boundary form a stress-free plate section. The source of the “turning” Lamb modes was also identified from the observations. The characteristics of the transmitted Rayleigh wave were also explored, and a certain degree of mode coupling between Rayleigh and shear waves was observed when the crack tip was farther away from the boundary. [ABSTRACT FROM AUTHOR]

Modeling and experiments are used to investigate Lamb wave propagation in the direction perpendicular to an applied stress. Sensitivity, in terms of changes in velocity, for both symmetrical and anti-symmetrical modes was determined. Codes were developed based on analytical expressions for waves in loaded plates and they were used to give wave dispersion curves. The experimental system used a pair of compression wave transducers on variable angle wedges, with set separation, and variable frequency tone burst excitation, on an aluminum plate 0.16 cm thick with uniaxial applied loads. The loads, which were up to 600 le, were measured using strain gages. Model results and experimental data are in good agreement. It was found that the change in Lamb wave velocity, due to the acoustoelastic effect, for the S1 mode exhibits about ten times more sensitive, in terms of velocity change, than the traditional bulk wave measurements, and those performed using the fundamental Lamb modes. The data presented demonstrate the potential for the use of higher order Lamb modes for online industrial stress measurement in plate, and that the higher sensitivity seen offers potential for improved measurement systems. [ABSTRACT FROM AUTHOR]

Optimization of Lamb modes induced by laser can be achieved by adjusting the spatial source distribution to the mode wavelength (λ). The excitability of Zero-Group Velocity (ZGV) resonances in isotropic plates is investigated both theoretically and experimentally for axially symmetric sources. Optimal parameters and amplitude gains are derived analytically for spot and annular sources of either Gaussian or rectangular energy profiles. For a Gaussian spot source, the optimal radius is found to be λZGV/π. Annular sources increase the amplitude by at least a factor of 3 compared to the optimal Gaussian source. Rectangular energy profiles provide higher gain than Gaussian ones. These predictions are confirmed by semi-analytical simulation of the thermoelastic generation of Lamb waves, including the effect of material attenuation. Experimentally, Gaussian ring sources of controlled width and radius are produced with an axicon-lens system. Measured optimal geometric parameters obtained for Gaussian and annular beams are in good agreement with theoretical predictions. A ZGV resonance amplification factor of 2.1 is obtained with the Gaussian ring. Such source should facilitate the inspection of highly attenuating plates made of low ablation threshold materials like composites. [ABSTRACT FROM AUTHOR]

The propagation speed of ultrasonic waves in pre-stressed media can be evaluated either at the natural or initial frames of reference. In this paper general equations that can be applied to the partial wave technique are presented in order to obtain the dispersion spectra of acoustoelastic Lamb waves in anisotropic plates in either frame of reference. Employing these equations, dispersion curves for the fundamental modes in a pre-stressed transversely isotropic aluminum plate were numerically obtained in both reference frames under longitudinal and transverse loading with the material transverse axis along each of the Cartesian directions, as well as the propagation along a non-principal direction. Results confirm that due to the material natural anisotropy, the speed variation depends not only on the pre-stress direction but also on the material orientation as well as on the polarization of the propagating mode. Similar to bulk waves, the relationship between the speed at the natural and initial frames is a function of the load direction. [ABSTRACT FROM AUTHOR]

This paper presents an inexpensive but accurate analytical method to calculate the scattering of straight-crested Lamb waves from cracks parallel to the plate surface. The same method is applicable for the disbond problem. In this method, the scatter field is expanded in terms of complex Lamb wave modes with unknown amplitudes. These unknown amplitudes are obtained from the boundary conditions using vector projection utilizing the power expression. The process works by projecting the stress conditions onto the displacement eigen-spaces of complex Lamb wave modes and vice versa. The authors call this technique “complex modes expansion with vector projection” (CMEP). The CMEP approach is versatile and can be readily applied to corrosion, cracks, or disbonds. In this paper, the CMEP method is applied to a horizontal crack in a plate. For verification of the results the authors compared them with the results obtained by using the finite element method (FEM) and literature. The FEM analysis was conducted in the frequency domain with non-reflecting boundaries. It was found that CMEP results correspond very well with FEM results over a wide frequency-thickness range up to 1.5MHz mm with CMEP being orders of magnitude faster than FEM. [ABSTRACT FROM AUTHOR]

The paper presents a perturbation approach for calculating amplitude-dependent Lamb wave dispersion in nonlinear plates. Nonlinear dispersion relationships are derived in closed form using a hyperelastic stress-strain constitutive relationship the Green-Lagrange strain measure and the partial wave technique integrated with a Lindstedt-Poincaré perturbation approach. Solvability conditions are derived using an operator formalism with inner product projections applied against solutions to the adjoint problem. When applied to the first- and second-order problems these solvability conditions lead to amplitude-dependent nonlinear dispersion corrections for frequency as a function of wavenumber. Numerical simulations verify the predicted dispersion shifts for an example nonlinear plate. The analysis and identification of amplitude-dependent nonlinear Lamb wave dispersion complements recent research focusing on higher harmonic generation and internally resonant waves which require precise dispersion relationships for frequency-wavenumber matching. [ABSTRACT FROM AUTHOR]

The paper studies the interaction of Lamb waves with the free edge of a plate. The reflection coefficients of a Lamb mode at a plate free edge are calculated using a semi-analytical method, as a function of frequency and angle of incidence. The conversion between forward and backward Lamb modes is thoroughly investigated. It is shown that at the zero-group velocity (ZGV) frequency, the forward S1 Lamb mode fully converts into the backward S2b Lamb mode at normal incidence. Besides, this conversion is very efficient over most of the angular spectrum and remains dominant at frequencies just above the ZGV-point. This effect is observed experimentally on a Duralumin plate. First, the S1 Lamb mode is selectively generated using a transducer array, second the S2b mode is excited using a single circular transducer. The normal displacement field is probed with an interferometer. The free edge is shown to retro-focus the incident wave at different depths depending on the wave number mismatch between the forward and backward propagating modes. In the vicinity of the ZGV-point, wave numbers coincide and the wave is retro-reflected on the source. In this frequency range, the free edge acts as a perfect phase conjugating mirror. [ABSTRACT FROM AUTHOR]

The intersections between Lamb mode dispersion curves of free isotropic plates at real values of frequency and wave number are examined for the full allowed range of Poisson's ratio r. The generic intersections between the dispersion curves for symmetric and anti-symmetric branches are classified into three types. Type F intersections are conditioned by the two additional real solutions of Rayleigh's cubic equation that occur for r < 0:26308. Types I and II intersections occur for all values of r, and are distinguished by the vanishing or divergence of the tangent functions in the defining equations for the Lamb modes. A brief discussion is provided of intersections between branches of like symmetry and additional intersections between unlike symmetry branches that occur for special values of r. [ABSTRACT FROM AUTHOR]

A method is proposed to evaluate in a non-contact way the phase velocity dispersion curves of circumferential waves around a shell of arbitrary shape immersed in a fluid. No assumptions are made about the thickness or the material of the shell. A geometrical model is derived to describe the shape of the radiated wavefronts in the surrounding fluid, and predict the positions of its centers of curvature. Then the time-reversal principle is applied to recover these positions and to calculate the phase velocity of the circumferential waves. Numerical finite-difference simulations are performed to evaluate the method on a circular and on an elliptic thin shell. Different dispersion curves can be recovered with an error of less than 10%. [ABSTRACT FROM AUTHOR]

Material stiffness and plate thickness are the two key parameters when performing quality assurance/ quality control on pavement structures. In order to estimate the plate thickness non-destructively, the Impact Echo (IE) method can be utilized to extract the thickness resonance frequency. An alternative to IE for estimating the thickness resonance frequency of a concrete plate, and to subsequently enable thickness determination, is presented in this paper. The thickness resonance is often revealed as a sharp peak in the frequency spectrum when contact receivers are used in seismic testing. Due to a low signal-to-noise ratio, IE is not ideal when using non-contact microphone receivers. In studying the complex Lamb wave dispersion curves at a frequency infinitesimally higher than the thickness frequency, it is seen that two counter-directed waves occur at the same frequency but with phase velocities in opposite directions. Results show that it is possible to detect the wave traveling with a negative phase velocity using both accelerometers and air-coupled microphones as receivers. This alternative technique can possibly be used in non-contact scanning measurements based on aircoupled microphones. [ABSTRACT FROM AUTHOR]

Zero-Group Velocity (ZGV) Lamb waves are studied in a structure composed of two plates bonded by an adhesive layer. The dispersion curves are calculated for a Duralumin/epoxy/Duralumin sample, where the adhesion is modeled by a normal and a tangential spring at both interfaces. Several ZGV modes are identified and their frequency dependence on interfacial stiffnesses and on the bonding layer thickness is numerically studied. Then, experiments achieved with laser ultrasonic techniques are presented. Local resonances are measured using a superimposed source and probe. Knowing the thicknesses and elastic constants of the Duralumin and epoxy layers, the comparison between theoretical and experimental ZGV resonances leads to an evaluation of the interfacial stiffnesses. A good agreement with theoretical dispersion curves confirms the identification of the resonances and the parameter estimations. This non-contact technique is promising for the local evaluation of bonded structures. [ABSTRACT FROM AUTHOR]

This paper presents a method for measuring circumferential Lamb waves propagating on a cylindrically curved thin plate. The measurement is carried out using a wideband and line-focused poly(vinylidene fluoride) transducer along with a defocusing waveform measurement method. After synthesizing the acquired waveforms, interference patterns can be obtained and a cross correlation method is developed to accurately extract the wave velocity as a function of wave frequency. Using three stainless steel thin plates of different thicknesses (100, 150, and 300 µm) and a radius of curvature of 10mm, dispersion curves for several fundamental and higher order modes of circumferential Lamb waves are simultaneously determined. Theoretical dispersion curves are also calculated and compared with their experimental counterparts. Very good agreements are observed, which concludes the measurement accuracy of this measurement method. [ABSTRACT FROM AUTHOR]

The excitability of zero group velocity (ZGV) Lamb waves using a pulsed laser source is investigated experimentally and through numerical simulation. Experimentally, a laser based ultrasonic technique is used to find the optical spot size on the sample surface that allows an optimal coupling of the optical energy into the ZGV mode. Numerical simulations, using the time domain finite differences technique, are carried out to model the thermoelastic generation process by laser irradiation and the propagation of the generated acoustic waves. The experimental results are in good agreement with the numerical predictions. The experimentally and numerically obtained responses of the plate are investigated by a short-time Fourier transform. The responses show that the source diameter does not affect the fundamental behavior of the temporal decay of the ZGV mode. [ABSTRACT FROM AUTHOR]

This paper presents a quantitative study of conversion of evanescent Lamb waves into propagating in isotropic plates. The conversion is substantiated by prescribing time-harmonic Lamb displacements/tractions through a narrow aperture at an edge of a semi-infinite plate. Complex-valued dispersion and group velocity curves are employed to characterize the conversion process. The amplitude coefficient of the propagating Lamb modes converted from evanescent is quantified based on the complex reciprocity theorem via a finite element analysis. The power flow generated into the plate can be separated into radiative and reactive parts made on the basis of propagating and evanescent Lamb waves, where propagating Lamb waves are theoretically proved to radiate pure real power flow, and evanescent Lamb waves carry reactive pure imaginary power flow. The propagating power conversion efficiency is then defined to quantitatively describe the conversion. The conversion efficiency is strongly frequency dependent and can be significant. With the converted propagating waves from evanescent, sensors at far-field can recapture some localized damage information that is generally possessed in evanescent waves and may have potential application in structural health monitoring. [ABSTRACT FROM AUTHOR]