Leaky Lamb Waves Research Articles

Excitation of leaky lamb waves in cranial bone using a phased array transducer in a concave therapeutic configuration

Ultrasonic therapeutic transducers that consist of large numbers of unfocused, low power elements have begun to replace single, focused, high power elements. This allows the operator to use phased array techniques to change the focal position in the tissue during therapy. In transcranial therapy, this phased array configuration is essential to reduce local heating at the highly attenuating bone. Recently, Dual Mode Ultrasound Arrays (DMUAs) have been developed which leverage existing elements for imaging during therapy. DMUAs have the benefit of both the therapeutic and imaging systems being co-registered. This improves upon the existing approach of using a separate ultrasound system for guidance, as the acoustic beam path is the same for both. Unfortunately, the highly reflective nature of bone means that DMUAs have not been applied to transcranial therapy. However the recent near-field observation of lamb waves in cranial bone opens the possibility for DMUAs to be applied to a guided wave scan of the skull. This would allow co-registration of the bone’s ultrasonic properties with the therapeutic axis which would facilitate adaptive beamforming. In this work, a beamforming scheme for the excitation of guided waves in cranial bone using a therapeutic phased array is described and demonstrated experimentally.

Unusual energy properties of leaky backward Lamb waves in a submerged plate

It is found that leaky backward Lamb waves, i.e. waves with negative energy-flux velocity, propagating in a plate submerged in a liquid possess extraordinary energy properties distinguishing them from any other type of waves in isotropic media. Namely, the total time-averaged energy flux along the waveguide axis is equal to zero for these waves due to opposite directions of the longitudinal energy fluxes in the adjacent media. This property gives rise to the fundamental question of how to define and calculate correctly the energy velocity in such an unusual case. The procedure of calculation based on incomplete integration of the energy flux density over the plate thickness alone is applied. The derivative of the angular frequency with respect to the wave vector, usually referred to as the group velocity, happens to be close to the energy velocity defined by this mean in that part of the frequency range where the backward mode exists in the free plate. The existence region of the backward mode is formally increased for the submerged plate in comparison to the free plate as a result of the liquid-induced hybridization of propagating and nonpropagating (evanescent) Lamb modes. It is shown that the Rayleigh's principle (i.e. equipartition of total time-averaged kinetic and potential energies for time-harmonic acoustic fields) is violated due to the leakage of Lamb waves, in spite of considering nondissipative media.

Improved Method for Obtaining Characteristic Equation of Leaky Lamb Waves in a Multilayered Medium Containing Liquid

Improved Method for Obtaining Characteristic Equation of Leaky Lamb Waves in a Multilayered Medium Containing Liquid

Rough interfaces and ultrasonic imaging logging behind casing

Ultrasonic leaky Lamb waves are sensitive to defects and debonding in multilayer media. In this study, we use the finite-difference method to simulate the response of flexural waves in the presence of defects owing to casing corrosion and rough fluctuations at the cement-formation interface. The ultrasonic obliquely incidence could effectively stimulate the flexural waves. The defects owing to casing corrosion change the amplitude of the earlyarrival flexural wave, which gradually decrease with increasing defect thickness on the exterior walls and is the lowest when the defect length and wavelength were comparable. The scattering at the defects decreases the energy of flexural waves in the casing that leaks directly to fluids. For rough cement-formation interface, the early-arrival flexural waves do not change, whereas the late-arrival flexural waves have reduced amplitude owing to the scattering at rough interface.

Effect of pressurization on helical guided wave energy velocity in fluid-filled pipes

The effect of pressurization stresses on helical guided waves in a thin-walled fluid-filled pipe is studied by modeling leaky Lamb waves in a stressed plate bordered by fluid. Fluid pressurization produces hoop and longitudinal stresses in a thin-walled pipe, which corresponds to biaxial in-plane stress in a plate waveguide model. The effect of stress on guided wave propagation is accounted for through nonlinear elasticity and finite deformation theory. Emphasis is placed on the stress dependence of the energy velocity of the guided wave modes. For this purpose, an expression for the energy velocity of leaky Lamb waves in a stressed plate is derived. Theoretical results are presented for the mode, frequency, and directional dependent variations in energy velocity with respect to stress. An experimental setup is designed for measuring variations in helical wave energy velocity in a thin-walled water-filled steel pipe at different levels of pressure. Good agreement is achieved between the experimental variations in energy velocity for the helical guided waves and the theoretical leaky Lamb wave solutions.

Simulation and modeling of ultrasonic pitch-catch through-tubing logging

Cased petroleum wells must be logged to determine the bonding and hydraulic isolation properties of the sealing material and to determine the structural integrity status. Although ultrasonic pitch-catch logging in single-casing geometries has been widely studied and is commercially available, this is not the case for logging in double-casing geometries despite its increasing importance in plug and abandonment operations. It is therefore important to investigate whether existing logging tools can be used in such geometries. Using a finite-element model of a double-casing geometry with a two-receiver pitch-catch setup, we have simulated through-tubing logging, with fluid between the two casings. We found that there appears a cascade of leaky Lamb wave packets on both casings, linked by leaked wavefronts. By varying the geometry and materials in the model, we have examined the effect on the pulse received from the second wave packet on the inner casing, sometimes known as the third interface echo. The amplitude of this pulse was found to contain information on the bonded material in the outer annulus. Much stronger amplitude variations were found with two equally thick casings than with a significant thickness difference; relative thickness differences of up to one-third were simulated. Finally, we have developed a simple mathematical model of the wave packets’ time evolution to encapsulate and validate our understanding of the wave packet cascade. This model shows a more complex time evolution in the later wave packets than the exponentially attenuated primary packet, which is currently used for single-casing logging. This indicates that tools with more than two receivers, which could measure wave packets’ amplitude at more than two points along their time evolution, would be able to draw more information from these later packets. The model was validated against simulations, finding good agreement when the underlying assumptions of the model were satisfied.

Comparison of Slowness Profiles of Lamb Wave with Elastic Moduli and Crystal Structure in Single Crystalline Silicon Wafers

Single crystalline silicon wafers having (100), (110), and (111) directions are employed as specimens for obtaining slowness profiles. Leaky Lamb waves (LLW) from immersed wafers were detected by varying the incident angles of the specimens and rotating the specimens. From an analysis of LLW signals for different propagation directions and phase velocities of each specimen, slowness profiles were obtained, which showed a unique symmetry with different symmetric axes. Slowness profiles were compared with elastic moduli of each wafer. They showed the same symmetries as crystal structures. In addition, slowness profiles showed expected patterns and values that can be inferred from elastic moduli. This implies that slowness profiles can be used to examine crystal structures of anisotropic solids.

The effects of air gap reflections during air-coupled leaky Lamb wave inspection of thin plates

Air-coupled ultrasonic inspection using leaky Lamb waves offers attractive possibilities for non-contact testing of plate materials and structures. A common method uses an air-coupled pitch–catch configuration, which comprises a transmitter and a receiver positioned at oblique angles to a thin plate. It is well known that the angle of incidence of the ultrasonic bulk wave in the air can be used to preferentially generate specific Lamb wave modes in the plate in a non-contact manner, depending on the plate dimensions and material properties. Multiple reflections of the ultrasonic waves in the air gap between the transmitter and the plate can produce additional delayed waves entering the plate at angles of incidence that are different to those of the original bulk wave source. Similarly, multiple reflections of the leaky Lamb waves in the air gap between the plate and an inclined receiver may then have different angles of incidence and propagation delays when arriving at the receiver and hence the signal analysis may become complex, potentially leading to confusion in the identification of the wave modes. To obtain a better understanding of the generation, propagation and detection of leaky Lamb waves and the effects of reflected waves within the air gaps, a multiphysics model using finite element methods was established. This model facilitated the visualisation of the propagation of the reflected waves between the transducers and the plate, the subsequent generation of additional Lamb wave signals within the plate itself, their leakage into the adjacent air, and the reflections of the leaky waves in the air gap between the plate and receiver. Multiple simulations were performed to evaluate the propagation and reflection of signals produced at different transducer incidence angles. Experimental measurements in air were in good agreement with simulation, which verified that the multiphysics model can provide a convenient and accurate way to interpret the signals in air-coupled ultrasonic inspection using leaky Lamb waves.

Guided ultrasonic wave testing of an immersed plate with hidden defects

This paper presents the results of an experimental study in which guided ultrasonic waves are used for the contactless nondestructive testing of a plate immersed in water. In the experiment, narrowband leaky Lamb waves are generated using a focused transducer and are detected with an array of five immersion sensors arranged in a semicircle. The ultrasonic signals are processed to extract a few damage-sensitive features from the time and frequency domains. These features are then fed to an artificial neural network to identify the presence of hidden defects, i.e., defects devised on the surface of the plate not facing the probing system. We find that the noncontact inspection system and the signal processing technique enable the classification of the plate health with a success rate >75%.

Transient analysis of leaky Lamb waves with a semi-analytical finite element method

We previously formulated a semi-analytical finite element technique for Lamb waves in a plate surrounded by fluids and investigated the dispersion curves and wave structures for leaky Lamb waves. Herein, this technique is extended to the calculation of transient responses both in a plate and in fluids for dynamic loading on the plate surface. To gain fundamental insights into guided wave inspection for a water-filled pipe or tank, guided waves generated upon transient loading of a flat plate water-loaded on one side were analyzed. The results show that a quasi-Scholte mode propagating at the plate-water interface is useful for the long-range inspection of a water-loaded plate because of its non-attenuation and minimal dispersion; moreover, this mode has superior generation efficiency in the low-frequency range, while it is localized near the plate-water interface at higher frequencies.

Outlier Analysis and Artificial Neural Network for the Noncontact Nondestructive Evaluation of Immersed Plates

We present an experimental study where guided ultrasonic waves were used for the noncontact nondestructive evaluation of an aluminum plate immersed in water. Broadband leaky Lamb waves were generated using a pulsed laser and were detected with an array of immersion transducers arranged in a semicircle. The signals were processed to extract some features from the time, frequency, and joint time-frequency domains. These features were then fed to an unsupervised learning algorithm based on the outlier analysis to detect the presence of damage, and to a supervised learning algorithm based on artificial neural networks to classify the types of defect. We found that the hybrid laser-immersion transducers system and both learning algorithms enable the detection of the defects and their classification with good success rate.

Concentration Measurement in Bubbly Liquids - A Matter of Times

Leaky Lamb waves in an acoustic cavity can be utilized for the measurement of temperature, density and sound velocity of an enclosed liquid. If the sensitivity of these variables to a change of predefined components in a liquid mixture is high enough, an online concentration measurement can be utilized as well. Gas bubbles can influence the measurable times-of-flight which can be disadvantageous for the concentration measurement. This paper will show how simultaneous group and phase velocity measurements can be used to calculate the sound velocity and the concentration in pure liquids, even if gas bubbles are interspersed.

Visualization of Leaky Ultrasonic Lamb Wave Experiments in Multilayer Structures

Leaky ultrasonic Lamb waves propagating in liquid-filled steel pipes are widely used by the oilfield service industry in wellbores to measure the acoustic properties of the material located outside the pipe. Typically, the annular region between the steel pipe and the geological formation is cemented to provide mechanical integrity and to ensure hydraulic isolation between different geological layers in the well. We present results from an experimental study along spatial and temporal dimensions to visualize the propagating waveforms of such measurements for liquid or solid annular materialsbehind the steel pipe. Our measurements focus on the lowest-order flexural waves. These radiate energy into neighboring layers if the flexural phase speed is supersonic with respect to the bulk compressional- or shear-wave phase speeds of the adjacent media. In the case of a compressional phase speed higher than the flexural phase speed, the resulting flexural mode attenuation is then strongly reduced. Several annular materials with compressional velocities higher and lower than the flexural phase speed were investigated to demonstrate this effect. Finally, the propagation of compact flexural-wave packets along the steel pipe was recorded, and the results were compared with computed modal dispersion and attenuation curves.

J0420203 半解析的有限要素法による漏洩ラム波の過渡応答解析

J0420203 半解析的有限要素法による漏洩ラム波の過渡応答解析

Propagation of waves in micropolar generalized thermoelastic materials with two temperatures bordered with layers or half-spaces of inviscid liquid

The aim of the present paper is to study the propagation of Lamb waves in micropolar generalized thermoelastic solids with two temperatures bordered with layers or half-spaces of inviscid liquid subjected to stress-free boundary conditions in the context of Green and Lindsay (G-L) theory. The secular equations for governing the symmetric and skew-symmetric leaky and nonleaky Lamb wave modes of propagation are derived. The computer simulated results with respect to phase velocity, attenuation coefficient, amplitudes of dilatation, microrotation vector and heat flux in case of symmetric and skew-symmetric modes have been depicted graphically. Moreover, some particular cases of interest have also been discussed.

On the use of an array of ultrasonic immersion transducers for the nondestructive testing of immersed plates

This paper presents the results of an experimental study in which guided ultrasonic waves were used for the nondestructive evaluation of an aluminium plate immersed in water. Leaky Lamb waves were generated using a spherical focused transducer, and detected by five immersion transducers arranged in a semi-circular array. The signals were processed to extract seven damage-sensitive features from the time, frequency and joint time–frequency domains. These features were then fed to an unsupervised learning algorithm based on the outlier analysis to identify the presence of defects artificially devised on the plate. We found that the array of immersion transducers and the signal processing technique enable the detection of the defects with a success rate close to 95%.

Elastic Properties Inversion of an Isotropic Plate by Hybrid Particle Swarm-Based-Simulated Annealing Optimization Technique from Leaky Lamb Wave Measurements Using Acoustic Microscopy

This paper presents a new method for the inversion of elastic properties of an isotropic thin plate by line-focus acoustic microscopy. Over 10 modes of the leaky Lamb waves of a 380 \(\upmu \)m thick aluminum plate were extracted by the \(V(f\),\(z)\) measurement. The inversion method of hybrid particle swarm-based-simulated annealing (PS-B-SA) optimization induces an objective function dependent on the determinant of the coefficient matrix of the dispersive characteristic equation. PS-B-SA allows considerable flexibility in parametric inversion problem and seeks the global rather than the local minimum. An alternative image display method combined with the objective function will be used to show the dispersion curves and to demonstrate the principles of the PS-B-SA optimization algorithm. The elastic properties (Young’s modulus \(E\), shear modulus \(G\), Poisson’s ratio \(\nu \)) and thickness (2\(h)\) of the specimen are determined by the inversion of the dispersion curves. Inversed parameters by particle swarm optimization algorithm are compared with the PS-B-SA results to show the validity and stability of the hybrid method. Agreement between the inversed material parameters and the reported data is shown to be excellent.

Effects of source and cavity depths on wave fields in layered media

Abstract The multiple modes of Rayleigh waves (R-waves) or leaky Lamb waves (L-waves) may be present in the activated and/or the back-scattered wave fields. The presence of these waves in the wave fields is related to the source and the cavity depths. Two types of layered media are used to investigate the influences of the source and the cavity depths. One is the layered half space where the half space is stiffer than all the overlying layers; the other is the pavement system where there is significant velocity contrast between layers and the shear velocity of layers decreases with the layer depth. The discrete displacement expressions developed for spherical point sources are used to study the effects of the source depth on the excitability and the propagation behavior of R-waves or leaky L-waves. In layered half spaces, the multiple modes of R-waves can be activated by the sources within a certain depth. The effective phase velocity of these activated modes is derived. In pavement systems, the leaky L-waves can be activated by the sources at any depth. The discrete displacement expressions of the scattered waves are derived and used to evaluate the effects of the cavity depth on the presence of R-waves or the leaky L-waves in the back-scattered wave field.

Calculation of leaky Lamb waves with a semi-analytical finite element method

A semi-analytical finite element method (SAFE) has been widely used for calculating dispersion curves and mode shapes of guided waves as well as transient waves in a bar like structures. Although guided wave inspection is often conducted for water-loaded plates and pipes, most of the SAFE techniques have not been extended to a plate with leaky media. This study describes leaky Lamb wave calculation with the SAFE. We formulated a new solution using a feature that a single Lamb wave mode generates a harmonic plane wave in leaky media. Dispersion curves obtained with the SAFE agreed well with the previous theoretical studies, which represents that the SAFE calculation was conducted with sufficient accuracy. Moreover, we discussed dispersion curves, attenuation curves, and displacement distributions for total transmission modes and leaky plate modes in a single side and both two side water-loaded plate.

Imaging Defects in a Plate with Full Non-Contact Scanning Laser Source Technique

Previously, we used contact receiving transducers in the scanning laser source (SLS) technique for imaging defects on a plate in order to achieve a high signal-to-noise (SN) ratio. Herein, we developed a fast non-contact defect imaging technique that employs the SLS technique for in-line product inspection. Leaky Lamb waves from a plate were detected with a sufficiently large SN ratio by using low-frequency air-coupled transducers. Spurious images caused by reflected waves in the plate were removed by synthesizing images from multiple receivers. Defect images were compared for different repetition frequencies of laser emission. Images were found to be distorted at high repetition frequencies (2/3kHz) owing to reverberations in the plate. [doi:10.2320/matertrans.I-M2014817]