Leaky Lamb Waves Research Articles

On the cutoff, reappearance, and persistence of subsonic leaky A0 Lamb waves

Abstract Subsonic leaky A0 Lamb waves, whose phase speeds are lower than the fluid’s sound speed, exhibit several peculiar behaviours. In this work, we investigate three such behaviours: Cutoff, where the A0 branch cuts off at some point in the subsonic domain, reappearance, where the cut-off A0 branch reappears at lower frequencies, and persistence, where the A0 branch is never cut off at all. From the literature, we take the case of a 1 mm thick aluminium plate immersed in air of varying density. We then analyse its exact leaky A0 wave solutions by means of a sound radiation model that takes energy conservation into account. This analysis explains these peculiar behaviours by connecting them with the conditions that allow sound-radiating subsonic leaky A0 Lamb waves.

A combined inspection technique for debonding defects in CFRP-strengthened steel structures based on leaky Lamb wave and low-power vibrothermography

A combined inspection technique for debonding defects in CFRP-strengthened steel structures based on leaky Lamb wave and low-power vibrothermography

A new methodology of non-destructive testing in a set of two parallel immersed plates using time reversal process and leaky Lamb waves

Ultrasound has been identified as a suitable method for inspecting complex structures (such as nuclear reactors), as it can propagate through both liquids and steel elements to be inspected. Leaky Lamb waves have been extensively researched to detect damages in plate-shaped structures, which are waves that reemit bulk waves towards the surrounding fluid. An imaging method based on the time reversal of Lamb waves has been applied in preliminary work to detect the edge of a single immersed plate and a machined notch. In this study, the frequency-domain topological energy method is applied to a set of two parallel immersed plates to succeed in accurately localizing defects represented by the edges of the plates. Firstly, the behaviour of leaky Lamb waves is briefly addressed. A 2D-STFT (two-dimensional Short Time Fourier Transform) is then used to separate the different Lamb modes, which is a powerful tool for tracking the modes involved in the propagation over time. The Fast Topological Imaging Method (FTIM), which allows for faster computations with less data storage, is applied to the case of Lamb waves in a set of parallel plates. Lamb modes can be identified then selected to improve the analysis of the obtained images. An original methodology is proposed based on spots (maxima) analysis for interpreting the results of this topological energy and identifying the edges of the two plates. This process could be applied, in the same manner, to other scattering defects in ultrasound non-destructive testing of plates.

Computing leaky Lamb waves for waveguides between elastic half-spaces using spectral collocation.

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.

The higher order leaky Lamb wave sensitivity of a notch in a fluid-immersed plate

We present an ultrasonic method of detecting cracks in pipelines based on using normally incident transducers in a pitch-catch setup, which can only excite Lamb modes of higher order than the fundamental modes A0 and S0 commonly used in crack detection applications. By excitation and measurements of the Lamb modes S1, S2, and A3, in a steel plate immersed in fluid with and without a notch (to emulate a crack), the performance of the modes towards crack detection is quantified by assessing whether it returns a high leaky component and whether the notch has a large impact on the leaky component. In order to narrow the scope of measurements necessary to investigate notch sensitivity for different system parameters, and to potentially optimize the system setup, we present a computationally efficient theoretical model based on angular spectrum method (ASM) and the theoretical sensitivity kernel formulation from the field of seismology that accounts for a scatterer in the wave path between the transmitter and receiver. The model is compared against measurements, which show that the frequency components of the S2 mode has both the largest leaky frequency component in the given setup and the largest sensitivity at a frequency close to the maximum leaky frequency such that a difference caused by the notch is easily measured. By using the measurements and the validation calculation as baseline reference, we calculate the expected S2 mode sensitivity and leaky components for larger plate thicknesses and larger standoffs, which exemplifies how the model can be applied in measurement system design and optimization.

Classification of solutions for guided waves in fluid-loaded viscoelastic composites with large numbers of layers.

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.

Simulation of acoustic reflection and backscatter from arctic sea-ice

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.

Modelling acoustic radiation from vibrating surfaces around coincidence: Radiation into fluids

It is well-known that vibrating surfaces generate sound waves in adjacent fluids. According to the classical radiation model, the nature of these waves depends on whether the vibration’s phase speed cv is above (supersonic) or below (subsonic) the fluid sound speed cf. The transition between these two domains is known as coincidence. In the supersonic domain, the sound wave radiates into the fluid. In the subsonic domain, the classical model states that the wave becomes evanescent and clings to the surface. In the last 30 years, however, several articles on leaky guided waves have reported radiating waves in the subsonic domain, which is at odds with the classical model. In this article, we investigate an enhanced model for sound radiation near and below coincidence. Unlike the classical model, this model fully respects conservation of energy by balancing the radiated power with power lost from the guided wave underlying the vibration. The model takes into account that this power loss and the consequent attenuation of the surface vibration result in an inhomogeneous radiated sound wave — an effect that cannot be neglected near coincidence. We successfully validate the model against exact solutions for leaky A0 Lamb waves around coincidence. The model can also be used as a perturbation method to predict the attenuation of leaky A0 waves from the properties of free A0 waves, giving more accurate estimates than existing perturbation methods. We further investigate subsonic leaky A0 waves using the enhanced model. Thereby we, for example, explain the peculiar reappearance or persistence of the leaky A0 wave at lower frequencies, an effect brought to attention by previous theoretical studies.

Simulation of acoustic reflection from Arctic ice

The acoustic reflection from an ice sheet in the arctic, as observed by an upward looking sonar, is simulated. The reflection from a smooth ice sheet is modeled using OASES, using material properties that may be found in the published literature. Depending on the bandwidth of the signal, specular reflections from the top and bottom of the ice, as well as one or more resonances that are identified as leaky Lamb waves should be detectable. If the speed of the Lamb wave is faster than the speed of sound in water, it will leak energy back into the water. The leaky Lamb wave has a characteristic resonant frequency that is a function of the ice thickness and shear speed. The reflection and backscatter from a rough ice sheet is modeled using SPECFEM2D. Scattering from a rough interface may obscure the expected signals, depending on the severity of the roughness. [Work supported by ONR, Ocean Acoustics Program.]

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.

Air-Coupled Ultrasound Sealing Integrity Inspection Using Leaky Lamb Waves in a Simplified Model of a Lithium-Ion Pouch Battery: Feasibility Study.

Inspecting the sealing integrity of lead tabs is an important means of ensuring the reliability and safety of pouch-type lithium-ion (Li-ion) batteries with a thin multi-layered aluminum (Al) laminated film. This paper presents a new air-coupled ultrasonic non-destructive testing (NDT) inspection method based on leaky Lamb wave transmission; and reception for evaluating the sealing integrity between the lead tab and the Al pouch film. The proposed method uses the critical incidence angle between the air and the layer with the fastest Lamb wave velocity to maximize the signal-to-noise ratio in the through-transmission mode. To determine the critical incidence angle, phantom experiments with two test pieces (i.e., an Al tab and an Al tab sealed with an Al pouch film) are conducted. In addition, 2D scans are performed at various incidence angles for an inhouse pouch-type Li-ion battery with a 1-mm-wide foreign material inserted as a defect. At the critical incidence angle (i.e., 22°), the proposed air-coupled ultrasonic NDT method in through-transmission mode successfully identifies the shape and location of the defect through c-scan image reconstruction. These preliminary results indicate that the proposed air-coupled ultrasonic NDT method with leaky Lamb waves can be used to inspect the sealing integrity of Li-ion pouch batteries in dry test conditions.

Structural health monitoring of partially immersed metallic plates using nonlinear guided wave mixing

Metallic plates are important structural components of many liquid containment structures, such as liquid storage tanks and sewer pipes. Time-dependent loads can result in fatigue and degradation of the metallic material. Nonlinear guided wave mixing has been demonstrated to be sensitive to microstructural change at the early stage of material degradation. Previous studies have been carried out using the nonlinear guided wave mixing technique on various structures in gaseous environments. However, its application to structures immersed in liquid has not been explored. This paper numerically and experimentally investigates the nonlinear guided wave mixing in an aluminum plate loaded with water on one side. Experiments are carried out with an empty metal tank and the tank filled with water, respectively. The results show that cumulative generation of harmonics at the sum frequency due to the material nonlinearity of the partially immersed plate can be achieved by mixing the fundamental leaky symmetrical Lamb (leaky S0) waves at two different frequencies. Under the same experimental conditions, the amplitudes of the guided wave signals and the values of the relative nonlinearity parameters on the partially immersed plate are different from their counterparts on the plate without water. Finally, numerical simulations are performed with the material nonlinearity of the test plate simulated by the Murnaghan constitutive model. The numerical results reveal that both the second harmonics and the combination harmonics are sensitive to the material nonlinearity of the plate loaded with water on one side.

Leaky wave characterisation using spectral methods.

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.

Study on leaky Lamb waves in functionally graded composites loaded by asymmetric fluids

The present work aims at contributing to the investigation of a numerical method to describe the leaky Lamb waves, which propagate along the functionally graded composite plates when undergoing asymmetric fluids. The motions are considered under the two-dimensional plane strain assumption. In some respects, the proposed numerical scheme is an extension of the spectral collection method calculating the Lamb waves in a vacuum plate (stress-free on the surfaces). However, the proposed scheme implements differently because the displacement field here is influenced by both vertical heterogeneous and loaded fluids. The solution procedure relies on a linearization algorithm using a high dimensional state space, which permits the transformation of the nonlinear eigenvalue problem to the polynomial eigenvalue problem. Two comparisons are given to validate the effectiveness and support the method. Finally, results on specific examples (functionally graded composite plate immersed in the same and different fluids) are discussed to study leaky Lamb waves' propagating properties.

Interaction of three-dimensional acoustic beam with fluid-loaded solid plate: Axial near- to far-field transmission at normal beam incidence

Axial radiation from leaky Lamb waves propagating in a 6.05 mm water-immersed steel plate being excited by a sound beam normally incident to the plate, is investigated as a function of axial distance, z, and frequency, f, over the 350–1000 kHz frequency band of the S2, A2, and A3 Lamb modes in the plate. For certain leaky Lamb modes, prior literature has revealed complex characteristics in the transmitted pressure field close to the plate, caused by diffraction due to the finite angular spectrum of the incident beam. The present work extends earlier work by bringing insight into the changes of these field characteristics in the near- and far-field of the transmitted beam, over the frequency band of leaky Lamb modes, for normal beam incidence to the plate. A baffled piston source in a full-wave angular spectrum propagation model is used to analyze the phenomena involved. Maxima and minima that can not be described with plane wave theory are observed in the frequency spectrum of the axial pressure transfer function through the plate. At very long ranges the normalized transmitted sound beam tends to attain characteristics of the plate’s plane-wave transmission coefficient, for two of the leaky Lamb modes. Near-field interference phenomena not described in prior literature are identified. For the leaky Lamb mode associated with a backward-wave branch close to the fundamental thickness-extensional resonance in the plate, TE1, the axial near-field is shown to extend to very far ranges. Supplementary measurements add confidence to the simulation results and findings. Besides of their fundamental significance in the study and understanding of sound beams transmitted through a fluid-immersed solid plate, the results are of importance e.g. in immersion applications where material characterization is made using fluid-coupled ultrasonic transducers in a through-thickness resonant transmission setup, such as plate thickness or material properties measurements.

Arterial Stiffness Probed by Dynamic Ultrasound Elastography Characterizes Waveform of Blood Pressure.

The clinical and economic burdens of cardiovascular diseases pose a global challenge. Growing evidence suggests an early assessment of arterial stiffness can provide insights into the pathogenesis of cardiovascular diseases. However, it remains difficult to quantitatively characterize local arterial stiffness in vivo. Here we utilize guided axial waves continuously excited and detected by ultrasound to probe local blood pressures and mechanical properties of common carotid arteries simultaneously. In a pilot study of 17 healthy volunteers, we observe a ∼20 % variation in the group velocities of the guided axial waves (5.16 ± 0.55 m/s in systole and 4.31 ± 0.49 m/s in diastole) induced by the variation of the blood pressures. A linear relationship between the square of group velocity and blood pressure is revealed by the experiments and finite element analysis, which enables us to measure the waveform of the blood pressures by the group velocities. Furthermore, we propose a wavelet analysis-based method to extract the dispersion relations of the guided axial waves. We then determined the shear modulus by fitting the dispersion relations in diastole with the leaky Lamb wave model. The average shear modulus of all the volunteers is 166.3 ± 32.8 kPa. No gender differences are found. This study shows the group velocity and dispersion relation of the guided axial waves can be utilized to probe blood pressure and arterial stiffness locally in a noninvasive manner and thus promising for early diagnosis of cardiovascular diseases.

Early damage detection of metallic plates with one side exposed to water using the second harmonic generation of ultrasonic guided waves

Metallic plates are the main structural components in a wide range of thin-walled structures under extreme operational conditions, such as nuclear cooling pipes, pressure vessels, rocket fuel tanks, and submarine hulls. These structures operate in extreme environments and are subjected to transient and repetitive loads. Real-time health monitoring of these structures is indispensable because they are vulnerable to fatigue and corrosion damage. Second harmonic generation is one of the reliable damage detection approaches to evaluate microstructural evolution and has been successfully applied to characterize initial damage on different structures in gaseous environments. However, there have been very limited studies on the second harmonics generation on the structures submerged in liquid. This paper experimentally and numerically investigates the feasibility of using second harmonic generation to evaluate the material degradation of metallic plates with one side exposed to water. The fundamental leaky symmetric Lamb wave mode (leaky S0) at low frequencies is selected because it has low-attenuation and weakly dispersive features, enabling approximate internal resonance. The experimental results show that the second harmonics of leaky S0 waves grow linearly with the propagation distance. The growth rate of the relative nonlinearity parameter (β′) can be related to the material nonlinearity of the one-side water-immersed plate. In addition, this study proposes a three-dimensional (3D) finite element (FE) model to simulate the generation of second harmonics in the one-side water-immersed plate. The material properties of the plate are modeled by the Murnaghan strain energy function. The Murnaghan constants of aluminum that describe the material nonlinearity at different fatigue levels are obtained from a previous experimental study. The simulation results demonstrate that the values of β′ change significantly with the material properties of the one-side water-immersed plates in the initial stages of fatigue damage. Thus, it can be concluded that the second harmonic generation techniques can be used for early damage detection of metallic plates with one side exposed to water.

Edge and Notch Detection in a Plate Using Time Reversal Process of Leaky Lamb Waves

Leaky Lamb waves are proven effective to carry out nondestructive testing especially on parallel and immersed plates. To detect and localize defects in such a set, this work associates for the first time the topological energy method and leaky Lamb waves. This methodology is applied in a single immersed plate to validate its application. Firstly, Lamb mode A1 is generated in the plate, and the reflected waves on the defect are measured. A first case is examined where the edge is considered as a defect to be localized. Then, measurements are taken on a plate where a notch is machined. The measurements are time reversed and reinjected in a finite-element simulation. The results are then correlated with the direct problem of the topological energy method that is also simulated. In both cases, the defects are precisely localized on the energy images. This work is the preliminary step to an application of the topological energy method to a set of two parallel and immersed plates where the research defect is located in the second plate.

Leaky Lamb wave–based resin impregnation monitoring with noninvasive and integrated piezoelectric sensor network

The propagation characteristics of leaky Lamb wave (LLW) when the rigid mold is loaded with water or viscous resin by one side are calculated numerically and verified experimentally, and the amplitude of A0 mode decreases linearly with the increase of liquid layer thickness. Then the valid applications of LLW in two- and three-dimensional resin flow monitoring of hand lay-up and VARI processes are carried out. The amplitude of A0 mode shows a downward trend in resin impregnation of both in-plane and through-thick directions, and the dry spots of different sizes could be identified. The amplitude and energy of received signals would decrease with the increase of resin coverage and the benchmark model of A0 mode is established and validated. The new wide sensing range measurement methods are proposed to effectively monitor the two- and three-dimensional resin flow front by the PZT sensor network in both noninvasive and integrated ways.

Investigation of transcranial ultrasound delivery via Lamb wave mode conversion leveraging a transducer pair

Cranial Lamb waves have been recently proposed for the non-invasive identification of the mechanical properties of the cranial bone, the evaluation of its acoustic radiation characteristics, and the estimation of the elastic and transmission properties of cranial sutures. Few works have focused on the so-called Lamb mode conversion phenomenon for transcranial ultrasound delivery, in which an attempt was made to control the focal point within the brain for incident acoustic beams beyond the critical angle. In our study, we further investigate this problem by overcoming some of the limitations of previous works, which are mainly related to the use of simplified geometries and material properties. To this end, we experimentally and numerically investigate leaky Lamb waves in immersed cranial bones by adopting a two-step strategy. In the first step, the dispersion properties of leaky Lamb waves are retrieved in the 0–500 kHz range along the mechanical properties of the cranial bone layers. The material data are then used to determine, via numerical simulations, the range of frequencies in which Lamb mode conversion can be effectively exploited for transcranial focusing purposes. Finally, we experimentally validate the numerical findings by means of an immersed setup that utilizes a pair of ultrasonic transducers.