Showing papers on "Lamb waves published in 1987"

Estimation of the thickness of thin metal sheet using laser generated ultrasound

Abstract: A noncontacting technique has been developed to measure the thickness of thin metal sheet by using a pulsed laser to generate both symmetric and antisymmetric Lamb waves. These have been detected with a laser interferometer. Analysis of the waveforms allows an estimation of the sheet thickness and accuracies to within 2% are attainable on sheets as thin as 27 μm.

Applied seismic wave theory

Abstract: Introduction. I. Capita Selecta from Vector Analysis. Scalar product, gradient, curl and divergence. Theorem of Stokes, theorem of Gauss and Green's theorem. II. One-Dimensional Discrete Spectral Analysis. The delta pulse and discrete functions. Fourier series of periodic time functions. Fourier integral of transients. Relationship between the discrete property and periodicity. Sampling and aliasing in time and frequency. Matrix formulations. Decomposition of a broad band experiment into monochromatic simulations. III. Multi-Dimensional Discrete Spectral Analysis. Basic theory. Spatial aliasing. Two-dimensional spectral analysis and plane wave decomposition. Extensions to three dimensions. IV. Vibrations. Basic concepts. Free vibrations. Forced vibrations. Coupled systems. From vibrations to waves. V. Acoustic Waves. Derivation of the acoustic wave equation. One-way versions of the acoustic wave equation. Plane waves. Spherical waves. Cylindrical waves. Principle of numerical modeling with the acoustic wave equation. VI. Elastic Waves. Compressional waves in homogeneous isotropic solids. Shear waves in homogeneous isotropic solids. Derivation of the elastic wave equation. One-way versions of the elastic wave equation. Principle of numerical modeling with the elastic wave equation. VII. Boundary Conditions. Reflection and transmission coefficients for acoustic boundaries. Reflection in terms of convolution. The fluid-solid boundary. Reflection and transmission coefficients for elastic boundaries. Summary. VIII. Kirchhoff and Rayleigh Integrals. Derivation of the Kirchhoff integral for homogeneous media. Derivation of the Rayleigh integrals for homogeneous media. Rayleigh integrals in terms of convolution. Transformation of Rayleigh integrals to the wave number domain. Kirchhoff and Rayleigh integrals for inhomogeneous fluid-like media. Rayleigh integrals as one-way versions of the Kirchhoff integral. Discrete version of the Kirchhoff integral. Discrete versions of the Rayleigh integrals. Summary. IX. Directivity Properties of Wave Fields. Fraunhofer approximations in terms of the Fourier integral. Directivity patterns. Far field expressions of scattered wave fields. Summary. X. Forward and Inverse Problems. Principle of one-way forward wave field extrapolation. Principle of one-way inverse wave field extrapolation. Principle of two-way techniques. Example. Summary. (Each chapter includes an introduction and references). Appendices. Subject Index.

Resonance theory of elastic waves ultrasonically scattered from an elastic sphere

Abstract: The interaction of elastic waves incident on an elastic spherical inhomogeneity is studied in detail, particularly in the resonance scattering regime. Incident and scattered compression and shear waves in lossless elastic media separate into three modes: a p mode for the compression wave, and s and t modes for the shear wave. A description of how the acoustic energy redistributes among these modes during the scattering process is contained in the scattering matrix that we separate here into background and resonance portions for the two extreme cases of a nearly soft and a nearly rigid elastic sphere. This produces farfield scattering amplitudes which are a superposition of a background contribution felt to contain reflected and Franz‐type circumferential waves and a resonance contribution that seems to contain refracted, Rayleigh, and whispering gallery waves. Limiting cases (a fluid sphere in an elastic medium, an elastic sphere in a liquid medium, and a fluid sphere in a fluid medium) are extracted from...

Lamb and creeping waves around submerged spherical shells resonantly excited by sound scattering

Abstract: Acoustic wave scattering by spherical shells in water in the resonance region is studied. The interaction is studied classically and by the resonance scattering theory (RST). The connection between internal resonances and the Lamb waves excited in the shell is analyzed. Conditions are derived that govern the propagation of Lamb waves in a spherical shell when it is fluid‐loaded or in vacuo. These general conditions reduce to the usual conditions for Lamb waves in plates, in the large radii limit. The connection is established between the outer scattering problem and the internal vibrational problem that excites the shell resonances, and it is demonstrated that the creeping‐wave series that synthesizes the Franz waves around the shell, can be obtained quite simply without the use of the Watson–Sommerfeld Method (WSM).All that is required is suitable one‐term expansions of the denominators of the scattering amplitudes. This eliminates the need for the cumbersome excursions through the complex angular moment...

Principle of prestack migration based on the full elastic two-way wave equation

Abstract: The acoustic approximation in seismic migration is not allowed when the effects of wave conversion cannot be neglected, as is often the case in data with large offsets. Hence, seismic migration should ideally be founded on the full elastic wave equation, which describes compressional as well as shear waves in solid media (such as rock layers, in which shear stresses may play an important role). In order to cope with conversions between those wave types, the full elastic wave equation should be expressed in terms of the particle velocity and the traction, because these field quantities are continuous across layer boundaries where the main interaction takes place. Therefore, the full elastic wave equation should be expressed as a matrix differential equation, in which a matrix operator acts on a full wave vector which contains both the particle velocity and the traction. The solution of this equation yields another matrix operator. This full elastic two‐way wave field extrapolation operator describes the re...

Lamb waves in unsupported thin films: A Brillouin-scattering study.

Abstract: Using Brillouin scattering we have succeeded in observing the normal modes of vibration of unsupported films in a region where the dispersion relationship is quadratic. Extremely low-lying excitations were observed in thin films with thicknesses as small as 200 A\r{}. Contrary to what has been found in work on supported films, we are able to extract information on a number of the elastic moduli because the measured velocities in very thin films do not depend on the properties of the substrate. This technique should be a valuable addition to the tools which can be used in the study of materials in thin-film form.

Existence of Negative Group Velocities in Lamb Waves

Abstract: It is known only fragmentarily that negative group velocities exist in some lower modes of Lamb waves whose phase velocities are very high This paper reveals numerically that the existence of negative group velocities depends not only on the frequency-thickness product but also on Poisson's ratio σ of the plate material Negative group velocities exist in S1 mode for σ<045, and in A2 mode for σ<031 In addition, S3, S4, S6 and A5 modes exhibit negative group velocities in respective narrow ranges of σ

Measurement of Ultrasonic Wavespeeds in Off-Axis Directions of Composite Materials

Abstract: The relationship of NDE with structural analysis is to provide quantitative information about material mechanical properties. For a composite structure (such as a rocket motor case) which is designed to handle in-plane loading, NDE should, ideally, provide information about the in-plane stiffness and strength properties of the structural material [1]. Because acoustic wave propagation depends on material elastic properties as well as being sensitive to material inhomogeneities, ultrasonic NDE has been nominated as a viable means of satisfying the needs of structural analytical modeling [2]. To address the need to detect in-plane properties, leaky Lamb wave [3,4] and non-normal incidence transmission [1] methods are being developed, for example. Development of composite ultrasonic NDE techniques, which are sensitive to material mechanical properties in the plane of a structure, required an understanding of acoustic wave propagation in anisotropic media. If a wave is introduced into the structure wall with an oblique angle of incidence less than critical angle, the refracted wave will travel in a non-principal or off-axis direction of the composite material. As a result, the wave energy will not generally travel in a direction normal to its phase fronts as it would in an isotropic medium. The acoustic wave energy or wave group propagates at a deviation angle, ψ, with respect to the phase front normal [5,6] as shown in Fig. 1. The deviation angle should be considered when measuring acoustic phase velocities from which the stiffnesses are calculated. The following sections discuss the effect of the group velocity propagation direction upon phase velocity measurements of quasi-longitudinal and quasi-shear waves propagating in non-principal directions in principal planes of orthotropic composite materials. Experimental results are shown for unidirectional graphite composite material samples.

Analysis of performance of leaky lamb wave transducer operating at liquid-solid interface

Abstract: The propagation characteristics of a leaky Lamb wave transducer built from a thin piezoelectric plate with interdigital electrodes are numerically analyzed under the condition of operating at a liquid-solid interface. The phase velocity, electromechanical coupling constant, and efficiency for acoustic beam radiation into water are given as a function of the product of the frequency and the substrate thickness. Numerical results are well confirmed experimentally.

A Single Transducer Broadband Technique for Leaky Lamb Wave Detection

Abstract: The introduction of advanced composite materials into many of the new generation aircraft and spacecraft has given rise to a significant increase in all aspects of operational capability These materials come in many forms; organic and non-organic, fibrous and particulate, and endless combinations of the above which not only give enhanced strength characteristics, but deliver them in very specific design directions The more common uses are in both primary and secondary aircraft structures, however, considerable effort is also being put into designing composite materials for use in hostile environments such as those destined for use as jet engine turbine blades

Signal Processing of Leaky Lamb Wave Data for Defect Imaging in Composite Laminates

Abstract: Inspection of composite laminates with Leaky Lamb waves (LLW) has been shown to hold promise of improved reliability and increased sensitivity to important defects [1]. Conventional scanning with the LLW has the possible disadvantage that the method is sensitive not only to internal structure, but also to small variations in plate thickness, which are indistinguishable from elastic property changes. To circumvent this potentially irrelevant sensitivity, a technique has been developed [2] whereby such variations can be selectively ignored, while retaining sensitivity to important defects or material property variations. The method consists of applying frequency modulation to the usual tone burst RF signal and exploiting detailed knowledge of the Lamb wave spectrum of composites [3] to discriminate between significant defects or property changes and small thickness variations in the plate. The current work extends and expands this analog signal processing scheme by performing the analysis on digitized data, permitting a much more general and flexible approach which will be described.

Lamb wave graphic tablet

Abstract: A graphic sensor based on the measurement of the propagation time of an acoustic wave train is described. Lamb waves are launched in a plate of ordinary glass by piezoelectric bars bonded to the edges of the plate. They are detected at their arrival under the tip of the drawing pencil by a small piezoelectric disc placed in the pencil body. The useful area of the tablet is 19×27 cm2; the resolution is about 0.2 mm.

Bifurcation, stability and symmetry of nonlinear waves

Abstract: The bifurcation of wave-like spatio-temporal structures due to a hard-mode instability at non-zero wave number is investigated for a simple class of driven systems in one space dimension. We find generically a bifurcation of two branches of waves, travelling waves and standing waves, characterized by nontrivial subgroups of the symmetry group of the system. If both branches are supercritical, the wave with the larger amplitude is found to be stable. In all other cases, both waves are unstable for small amplitudes. At the common boundary of the stability regions of the two wave types in parameter space we find a bifurcation of a branch of modulated waves involving two independent frequencies, connecting the branches of travelling waves and standing waves.

Ultrasonic nondestructive evaluation of fibre-reinforced composite materials — a review

Abstract: This paper reviews various ultrasonic nondestructive evaluation techniques applicable to fibre-reinforced composites. The techniques are briefly described and key references are cited. Methods to evaluate the reduced stiffness of composites due to micro-damage are described. Results show that for composites through-the-thickness attenuation increases and stiffness does not change due to transverse cracks, but in-plane stiffness and attenuation changes are substantial and can be measured by the Lamb wave techniques.

Surface sound waves in ferroelastics near phase transitions

Abstract: Surface waves characteristics in vicinity of ferroelastic phase transitions has been investigated both theoretically and experimentally. It is shown that the softening of one of the elastic moduli (or their combination) leads to a modification of the structure and to reduction in the velocity of Rayleigh and Lamb waves. Elastic and piezoelectric anomalies near the phase transition lead to a modification of the Guljaev-Bleustein waves. The Rayleigh waves in the rochelle salt were investigated experimentally. Near the upper Curie point the phase velocity reduction, localization depth increase and relative increase of shear displacement component were observed. These results correspond to the theoretical calculation.

Nondestructive Evaluation of Composite Laminates by Leaky Lamb Waves Using a Bubbler Device

Abstract: The application of Leaky Lamb waves (LLW) to nondestructive testing in field conditions was studied using a bubbler device. To reduce the sensitivity of LLW modes to surface curvature, the dispersion curve of LLW in graphite/epoxy laminates was used in the design of the bubbler. The results are described and discussed.

The influence of constraints on the properties of acceleration waves in isotropic thermoelastic media

Abstract: The properties of acceleration waves are investigated for situations in which the waves propagate in isotropic heat-conducting elastic media subject to arbitrary sets of constraints. Conditions under which waves may exist in the presence of constraints are investigated for classes of constraints broad enough to encompass all those encountered in practice. Attention is focussed on principal waves, and results are presented for the growth of the amplitudes of such waves first for fronts of arbitrary curvature, and subsequently by specialisation for plane, cylindrical and spherical waves travelling in material which has undergone one-dimensional plane deformation, cylindrically symmetric and spherically symmetric deformation, respectively.

Non-destructive evaluation of matrix cracks in fiber-reinforced composites by leaky lamb waves

Abstract: Leaky Lamb waves have been used for the non-destructive evaluation of fiber-reinforced composites. Two fundamental acoustic properties of the Lamb waves, namely, the wavespeed and attenuation have been measured. Stiffness is deduced from the wavespeed. The damage mode selected for this study is matrix cracking. Matrix cracks are introduced in the cross-ply laminate by static loading. Wavespeed and attenuation are measured after each damage state. As expected, the in-plane stiffness decreases and the attenuation increases as the damage increases. It was observed that the stiffness reduction was dependent on the stacking sequence while the attenuation was dependent on the scattering cross-section of the cracks, k1a.

Reflection of Bounded Acoustic Beams from a Layered Solid

Abstract: It is well known that when a bounded beam of acoustic waves is incident on a fluid-solid interface at certain critical angles, the reflected beam is significantly distorted and displaced due to the interference between specularly and nonspecularly reflected waves. Measurement and analysis of the reflected field can be used to estimate certain near surface elastic properties of the solid by means of several alternative nondestructive experimental arrangements [1,2]. In most of these experiments the interface generated leaky waves play a significant role. Thus a good understanding of the interface phenomena is a prerequisite to the design of experiments for their practical applications.