Showing papers on "Lamb waves published in 1989"

Free Wave Propagation in Plates of General Anisotropic Media

Abstract: The propagation of Lamb waves in plates has been the subject of numerous investigations since their postulation by Lamb in 1916 [1,2]. Most of the work in existence deals with various aspects of these guided waves in plates of isotropic materials. Comparatively speaking a limited number of results has appeared in which Lamb or horizontaly polarized SH wave propagation in anisotropic plates has been considered in any detail. For Lamb waves, theoretical analyses have been reported in plates of cubic [3,4], transversely isotropic [5,6], and orthotropic [7,9] media.

Elastic Wave Field Extrapolation: Redatuming of Single- and Multi-Component Seismic Data

Abstract: Introduction. I. Acoustic Waves. Introduction. Acoustic wave equation. Spherical wave solutions of the acoustic two-way wave equation. Plane wave solutions of the acoustic two-way wave equation. References. II. Elastic Waves. Introduction. Elastic wave equation. Spherical wave solutions of the elastic two-way wave equation. Plane wave solutions of the elastic two-way wave equation. References. III. Acoustic Two-Way and One-Way Wave Equations. Introduction. Acoustic wave equations for horizontally layered media. Acoustic wave equations for arbitrarily inhomogeneous media. References. IV. Elastic Two-Way and One-Way Wave Equations. Introduction. Elastic wave equations for horizontally layered media. Elastic wave equations for arbitrarily inhomogeneous media. References. V. Acoustic Forward Wave Field Extrapolation. Introduction. Acoustic reciprocity theorems. Acoustic representation theorems. Acoustic two-way and one-way Rayleigh integrals. Acoustic forward wave field extrapolation operators. References. VI. Elastic Forward Wave Field Extrapolation. Introduction. Elastic reciprocity theorems. Elastic representation theorems. Elastic two-way and one-way Rayleigh integrals. Elastic forward wave extrapolation operators. References. VII. Acoustic Inverse Wave Field Extrapolation in Low Contrast Media. Introduction. Acoustic inverse wave field extrapolation in laterally invariant media. Acoustic inverse wave field extrapolation in arbitrarily inhomogeneous media. References. VIII. Elastic Inverse Wave Field Extrapolation in Low Contrast Media. Introduction. Elastic inverse wave field extrapolation in homogeneous isotropic media. Elastic inverse wave field extrapolation in arbitrarily inhomogeneous anisotropic media. References. IX. Acoustic Inverse Wave Field Extrapolation in High Contrast Media. Introduction. Recursive acoustic inverse wave field extrapolation. Iterative acoustic inverse wave field extrapolation. X. Elastic Wave Field Extrapolation in High Contrast Media. Introduction. Recursive elastic inverse wave field extrapolation. Iterative elastic inverse wave field extrapolation. XI. Acoustic Redatuming of Single-Component Seismic Data. Introduction. Forward model for single-component seismic data. Surface related acoustic pre-processing. Acoustic redatuming. References. XII. Elastic Redatuming of Multi-Component Seismic Data. Introduction. Forward model for multi-component seismic data. Surface related elastic pre-processing. Elastic redatuming. References. Appendices. A. Matrix Notation. B. Interactions of One-Way Acoustic Wave Fields. C. Interactions of One-Way Elastic Wave Fields. Index.

Leaky Lamb waves in an anisotropic plate. I: An exact solution and experiments

Abstract: The propagation of leaky Lamb waves in a plate consisting of a general balanced symmetric composite material is considered. The problem has been examined both analytically as well as experimentally. An exact solution for the dispersion equation was obtained. Numerical results for complex‐valued wavenumber were obtained for an isotropic material (aluminum) and a (0/903)s graphite/epoxy laminate. Excellent agreement for the isotropic case and a satisfactory agreement for the anisotropic case between the theory and experiment were observed.

A laser study of transient Lamb waves in thin materials

Abstract: A method is described by which transient ultrasonic Lamb waves may be generated and detected within thin materials, using laser techniques. The material is thin enough that only the two lowest‐order modes of Lamb waves need be considered. These are the a0 mode, which is dispersive in the thin plate limit, and the s0 mode, which is not. Signal processing techniques were used to determine the dispersion characteristics of the a0 mode, and the velocity of the s0 mode, in both aluminum and metallic glass samples. From these measurements, it was possible to estimate both the thickness of the samples and their elastic constants. The errors involved in such a measurement are discussed.

Sensitivity of Near-Surface Shear-Wave Velocity Determination From Rayleigh And Love Waves

Abstract: Rayleigh and Love waves recorded on seismic-shot gathers can be used to determine the thickness and shear-wave velocity of shallow subsurface layers. After the data are transformed into the k-f domain, the dispersion curve for each of the phases can be picked from maxima on the contour plot. This dispersion curve is then inverted for the velocities and depths. Different frequencies in the dispersion curve yield information about different depths. The fundamental mode has proven to be of greater use than higher modes. Both Rayleigh and Love waves are easily inverted. However, the Love waves seem to yield information in a lower portion of the spectrum than the Rayleigh modes. Three examples are given from field experiments conducted near Canton, Texas.

Nonlinear generation of elastic waves in granite and sandstone: Continuous wave and travel time observations

Abstract: Beams generated by nonlinear interaction have proved useful as low-frequency, highly directional sources in water and may ultimately find application in geophysical exploration. For nonlinear elastic waves to be used as seismic sources they must be detected as discrete arrivals; measuring travel times of pulsed, nonlinear beams is a necessary first step toward that end. In this paper we discuss two new observations of the interaction of nonlinear elastic waves in both crystalline rock and sandstone. We show that observed travel times of pulsed waves agreed with predicted times for the case where two P wave pulses interacted to produce an S wave pulse. The travel time measurement was difficult to obtain because conversion efficiency is low. In extending our continuous wave experiments to sandstone we also satisfied three criteria previously verified in crystalline quartz norite and in granite to demonstrate nonlinear interaction: (1) the frequency of the nonlinear-generated signal equalled the difference frequency f1–f2 when two P waves interacted to produce an S wave, (2) the amplitude of the signal was proportional to the amplitude product of the primary waves, and (3) in the case of intersecting P waves the trajectory of the nonlinear beam matched that predicted by nonlinear elasticity theory.

Marginally dispersive ultrasonic waveguides

Abstract: Methods and apparatus for ultrasonically measuring selected physical parameters of a test material or structure are achieved by selecting and configuring waveguides for transmitting extensional, longitudinal, shear, Rayleigh and Lamb waves into media in a marginally dispersive manner. Marginally dispersive transmission is defined by specific criteria of velocity and waveguide diameter. Methods and apparatus for acoustically isolating the waveguides to permit leakage are included, as well as a method of extension to flexural mode conversion to launch flexural waves into a medium.

Observations and modeling of the backscattering of short tone bursts from a spherical shell: Lamb wave echoes, glory, and axial reverberations

Abstract: Tone bursts having durations of 3 or 4 cycles were incident on an air‐filled stainless steel shell in water. The resulting sequence of echoes included a specular reflection and echoes radiated by Lamb waves on the shell. Echo structure was studied for ka of 24 to 75, where a denotes the outer radius; b/a=0.838, where b denotes the inner radius. The amplitudes of Lamb wave echoes were modeled using an elastic generalization of the geometrical theory of diffraction (GTD) [P. L. Marston, J. Acoust. Soc. Am. 83, 25–37 (1988)]. The required Lamb wave parameters (the phase velocity cl and damping βl ) were found by the Sommerfeld–Watson method; an efficient numerical method for the computation of the required complex root νl is described. The echoes were identified by comparing arrival times with predictions; bursts reflected from a solid tungsten carbide sphere were used for a reference amplitude. Measurements with ka=24 of the largest Lamb wave echo (which was due to a flexural wave) were made at various back...

Measurement of in-plane and out-of-plane ultrasonic displacements by optical heterodyne interferometry

Abstract: An heterodyne optical probe, which permits one to measure out-of-plane and in-plane displacements at the surface of a specimen excited by ultrasound is presented. The principles at the basis of the two modes of operation are explained and the sensitivities for in-plane and out-of-plane detection are analyzed. The optical layout of the probe and the schematic of its demodulation circuitry are presented. Its accuracy is tested with Rayleigh surface waves. Examples of application to laser-generated Rayleigh and Lamb waves are also presented.

The acoustic scattering by a submerged, spherical shell. I: The bifurcation of the dispersion curve for the spherical antisymmetric Lamb wave

Abstract: The acoustic scattering by thin‐walled, evacuated, elastic spherical shells immersed in water is studied. The analytic structure of the scattering amplitude in the complex‐k plane is directly analyzed using Cauchy’s residue theorem, and dispersion curves are presented for the lowest elastic modes of the fluid‐loaded shell. It is found that fluid loading has a profound effect on the vacuum dynamical characteristics of the shell; the spherical equivalent of the first antisymmetric, flat‐plate Lamb wave for the fluid‐loaded shell bifurcates into two distinct modes near the frequency that the vacuum dispersion curve transitions from a subsonic to a supersonic phase velocity. By way of contrast, the spherical equivalent of the first symmetric Lamb wave is essentially unaffected. The salient features of the free‐field scattering process are also analyzed in terms of the resonance excitation of these modes.

Onset of nonlinear waves on falling films

Abstract: Steady waves on a thin liquid film flowing down an inclined plane are analyzed near the critical Reynolds number. A second‐order bifurcation analysis of an interface equation, which is valid to third order in the long‐wave expansion, reveals two sets of waves near criticality. One set travels faster than twice the interfacial velocity, while the other set is symmetrically slower for the vertical film. Each set contains two families of shocks, one family of periodic waves, and a single solitary wave. Local analytical estimates of the velocity, amplitude, and wavelength are obtained for all waves. These estimates are favorably compared to numerical solutions of the steady waves and to experimental data near criticality. An interesting result is that naturally excited waves with wavelengths close to the maximum growing linear mode should not be studied with a local analysis near the neutral curve. Instead, they are better approximated by a Melnikov perturbation of the solitary wave solution.

On the topology of the complex wave spectrum in a fluid‐coupled elastic layer

Abstract: The behavior of the complex leaky Lamb wave (LLW) spectrum of a plate immersed in a fluid has been studied as a function of the ratio of fluid‐to‐solid densities. It has been shown that widely accepted assumptions concerning the similarities between the classical Lamb wave spectrum and the LLW spectrum are not valid as the fluid density approaches that of the solid. Recent experimental and theoretical results demonstrate that there is a strong anomaly in the reflectance of composite plates in water. This anomaly is related to the details of the complex LLW spectrum. The spectrum is composed of both the familiar propagating Lamb wave branches and the mostly imaginary, nonpropagating branches. From the character of the complex spectrum, it is demonstrated that topological changes in the fundamental symmetric mode are related to its nearness to the first complex branch of the spectrum. Increasing the fluid–solid density ratio leads to interaction between these modes and to mutual interchange between portions of their branches. As the density ratio increases from zero to infinity, the complex spectrum is gradually transformed from a classical Lamb wave spectrum to one appropriate for a plate with zero normal surface displacements.

Effect of switching a magnetoplasma medium on a traveling wave: longitudinal propagation

Abstract: The interaction of electromagnetic radiation with a time-switched magnetoplasma is considered. It is shown that for longitudinal propagation within the so-called radio approximation (neglecting ion motion), the original wave splits into three waves whose frequencies are different from that of the incident wave. One of the waves is strongly influenced by the static magnetic field, and its frequency can be controlled by the strength of this field. Numerical results are presented for the cases of right-hand and left-hand circular polarization of the incident waves. >

Lamb waves and fluid‐borne waves on water‐loaded, air‐filled thin spherical shells

Abstract: The results of a recent study of fluid‐borne waves on plates with one‐sided fluid loading [M. Talmant, Ph.D. thesis, University of Paris VII (1987)] allow the prediction of the corresponding waves and their resonances (as well as of the Lamb‐wave resonances) on thin submerged spherical shells. Similar fluid waves and the ensuing ‘‘bifurcation’’ in the dispersion curves of the first antisymmetric vibration mode on cylindrical shells were previously described [J. V. Subrahmanyam, Ph.D. thesis, Catholic University of America (1983); J. L. Rousselot, Acustica 58, 291 (1985)] and the fluid waves were observed by Talmant et al. [J. Acoust. Soc. Am. 84, 681–688 (1988)]. The resonances predicted by the plate model for spherical shells are confirmed here by comparison with scattering cross‐section calculations using surface integral equation radiation and scattering (SIERRAS) and T‐matrix codes.

Scattering and Attenuation of Elastic Waves in Random Media

Abstract: In seismic exploration, elastic waves are sent to investigate subsurface geology. However, the transmission and interpretation of the elastic wave propagation is complicated by various factors. One major reason is that the earth can be a very complex medium. Nevertheless, in this paper, we model some terrestrial material as an elastic medium consisting of randomly distributed inclusions with a considerable concentration. The waves incident on such an inhomogeneous medium undergo multiple scattering due to the presence of inclusions. Consequently, the wave energy is redistributed thereby reducing the amplitude of the coherent wave.

Propagation of acoustic surface waves in periodic structures

Abstract: This review covers the propagation of acoustic surface waves (ASW) in periodic structures. The authors discuss the main types of ASW: Rayleigh waves, Gulyaev?Bleustein waves, Love waves. Shear surface waves which can propagate along a periodically uneven surface of an elastic solid are described in detail. The authors rigorously treat the Bragg reflection of ASW from periodic arrays of grooves on the substrate for the cases of normal, oblique, and side incidence. Reciprocal conversion effects between bulk and surface waves in an array whose period is close to the ASW wavelength are discussed, together with such related effects as the interaction between Rayleigh waves and Lamb modes, acoustic wave transmission through a gap in a piezoelectric material, etc. Laser excitation of ASW and magnetostatic wave propagation in periodic structures are also reviewed.

Long wavelength approximation for Lamb wave characterization of composite laminates

Abstract: A simple method for measuring Lamb wave phase velocities is used to obtain data for the lowest symmetric Lamb mode (S0) and the lowest antisymmetric Lamb mode (A0) for composite laminates. The experimental data are compared with the results from an approximate theory for the lowest Lamb modes in the low frequency, long wavelength region for a unidirectional laminate, a symmetric cross-ply laminate, a symmetric quasi-isotropic laminate and an aluminum plate. There is good correlation between the data and the results from the approximate theory, which suggests that the approximate theory works well in the low frequency, long wavelength region in these cases. Also, this experimental procedure of measuring phase velocities of the lowest symmetric and antisymmetric modes can be used to characterize laminated composite plates with and without damage since each material and stacking sequence gives distinct lowest symmetric and antisymmetric curves.

Sensor device using lamb elastic waves for detecting the presence of a liquid at a predetermined level

Abstract: The sensor device for detecting the presence or absence of a liquid (2) at predetermined level (N) in a tank (1) comprises a transmitter transducer (51; 51'; 61), a receiver transducer (52, 52', 62), and electronic means (100) for processing the signals applied to the transmission transducer and delivered by the receiver transducer. In the vicinity of the predetermined level (N) of the tank (1), the device includes a detection plate (50; 50', 60) having at least one face (58) which comes into contact with the liquid (2) when the liquid reaches that level. The detection plate carries the transmitter transducer which is disposed for locally generating Lamb waves in the plate, and the plate also carries the receiver transducer which is disposed for detecting the presence or the absence of Lamb waves transmitted along the plate. The receiver transducer is connected to a high gain amplifier whose output is connected to the transmitter transducer so as to form an oscillating closed loop, with oscillations in the loop being interrupted when the liquid reaches the predetermined level (N).

Propagation characteristics of plate waves in a Z-cut X-propagation LiTaO3 thin plate

Abstract: This paper describes the numerical analysis and experimental verification of the behavior of plate waves in a Z-cut X-propagation LiTaO3 thin plate. With the product of the frequency and the substrate thickness as a parameter, the phase velocity, mechanical displacement and electromechanical coupling coefficient are obtained. the Lamb waves of zeroth-order antisymmetric mode (AO) and symmetric mode (SO) are coupled more tightly than the Rayleigh mode. the SO mode SH wave is a tightly coupled mode comparable to the piezoelectric plate, and is of low dispersion. the results of an experimental verification in an LiTaO3 of 100 μ thick agreed well with the theoretical data in the frequency range below 50 MHz. These results are effective in designing the plate wave devices.

Calculation of Wave Propagation in Composite Materials Using the LAMB Wave Concept

Abstract: Over recent years the development of the use of composite materials has led to growing activity in the nondestructive testing field.Widely known techniques such as acoustic emission and ultra-sound have found a new field of application here and new techniques such as acousto-ultrasonics which have recently appeared have shown some interesting results in detecting defects in composite structures.However, acoustic emission for defect localisation and acousto-ultrasonics have sometimes shown a lack of reliability; very little is known about theoretical aspects of wave propagation in these materials, nor about the interaction existing in the material between acoustic waves and defects as the wave propagates.On the basis of some assumptions, theoretical calculations have been made on the prop agation of a steady wave in unidirectional composite plates and compared successfully to experimental results found in the literature.

A high efficiency Lamb wave lens for subsurface imaging

Abstract: A conventional scanning acoustic microscope lens excites all the possible modes of acoustic waves in the solid structure under examination. The excited leaky modes contribute significantly to the high contrast obtained in the images, but because all such modes exist simultaneously, the interpretation of the images is not straightforward. A new lens geometry that can be used with acoustic microscopes to image layered solid structures is proposed. This new lens can efficiently focus the acoustic waves in only one of the Lamb wave modes of the layered solid. The images obtained are easy to interpret, and the subsurface sensitivity is high. >

Single Mode Lamb Wave Inspection of Composite Laminates

Abstract: Flaw detection in composite plates presents a very difficult problem Conventional echoscopic techniques are not feasible because the back-scattered signal from a possible defect is usually overshadowed by much stronger reflections from the walls of the thin plate and by additional scattering from inherent inhomogeneities such as imbedded fibers and alternating plies Single or double transmission attenuation measurements offer a convenient, but rather insensitive alternative Fig 1 shows the schematic diagrams of the conventional normal incidence and the oblique incidence so-called Lamb wave inspection techniques At normal incidence, we can use a focused transducer of very good lateral resolution, but the sensitivity might be rather low when the defect exhibits a very small scattering cross-section from this particular direction of interrogation This occurs, for instance, in the case of weak porosity when the defects tend to be concentrated in a thin layer parallel with the plies, or as is shown in Fig 1, in the case of transverse cracks In such cases, oblique incidence inspection can be expected to give better sensitivity since Lamb modes propagating parallel to the plate are more attenuated At the same time, the lateral resolution will be inherently lower, therefore the ultrasonic contrast must be carefully optimized on a case-by-case basis

The propagation of time harmonic RAyleigh-Lamb waves in a bimaterial plate

Abstract: The time harmonic elastodynamic response of two semi-infinite elastic plates of dissimilar material properties perfectly bonded along their lateral faces is studied. The wave field in either half-plate can be written as a superposition of the so-called Rayleigh–Lamb eigenmodes of an infinite plate. The interaction of a time harmonic incident wave with the interface results in reflected and transmitted fields that contain contributions from all of the real, imaginary, and complex eigenmodes of an infinite plate. Attention is focused on the distribution of energy among the various reflected and transmitted eigenmodes over a range of frequencies. The fundamental symmetric and the fundamental antisymmetric Lamb modes are each used as input excitations. Such excitations can be approximately realized in experiments. It is assumed that the solution of such a canonical problem will facilitate the solution of problems with complicated time-dependent sources.

Phase velocity of Lamb waves on a spherical shell: Approximate dependence on curvature from kinematics

Abstract: The phase velocity cl along the outer surface of a thick shell for Lamb waves may be calculated as a function of frequency by use of Watson transform methods. For thick shells, this cl is offset from Lamb’s result for a flat plate of the same thickness h. This discrepancy may be removed by distinguishing the velocity along the outer surface (of radius a) from the velocity along a curve corresponding to the average radius [a−(h/2)] for the shell. The resulting expression in h/a facilitates an improved approximation of cl from Lamb’s analysis. The approximations may be useful in scattering calculations for cases where cl exceeds the speed of sound in the surrounding fluid.

Remote sensing of the thickness of hollow cylinders from optical excitation and detection of Lamb waves

Abstract: The probe is a laser beam focused on a point diametrically opposite to the source. Each optical pulse launches acoustic waves that propagate in the form of a slightly dispersive symmetric mode and of a strongly dispersive antisymmetric mode (Lamb waves). At low frequencies the instantaneous-phase phi is a linear function of 1/t. The slope of the curve phi (1/t) for large times, i.e. for low frequencies, provides the thickness of the hollow cylinder. Experiments have been carried out with a YAG laser (pulse of 80 ns. 8 mJ, source length of 15 mm), a heterodyne interferometric probe, and hollow cylinders in duraluminum of inner diameter 20 mm and nominal thicknesses 0.16, 0.45, and 0.98 mm. >

Method and apparatus for measuring parameters of solid phase of slurries

Abstract: A method for measuring parameters of solid phase of slurries having the following steps: forming ultrasonic oscillations and emitting them into a fluid under study, forming the Lamb waves and directing them into a wall of a vessel containing the fluid under study, forming acoustic currents and radiation pressure of sonic radiation in the fluid under study, and measuring amplitude and length of pulses of ultrasonic oscillations that pass through the fluid under study and the Lamb waves that pass through a predetermined distance along the wall of the vessel containing the fluid under study without and with the action of the acoustic currents and radiation pressure of sonic radiation, the values of which are used for the assessment of concentration of solid phase of the fluid under study. An apparatus for carrying out the method has two measurement channels each having a logarithmic converter, a subtraction unit and a division unit.