Showing papers on "Lamb waves published in 1985"

Plane waves in linear elastic materials with voids

Abstract: The behavior of plane harmonic waves in a linear elastic material with voids is analyzed. There are two dilational waves in this theory, one is predominantly the dilational wave of classical linear elasticity and the other is predominantly a wave carrying a change in the void volume fraction. Both waves are found to attenuate in their direction of propagation, to be dispersive and dissipative. At large frequencies the predominantly elastic wave propagates with the classical elastic dilational wave speed, but at low frequencies it propagates at a speed less than the classical speed. It makes a smooth but relatively distinct transition between these wave speeds in a relatively narrow range of frequency, the same range of frequency in which the specific loss has a relatively sharp peak. Dispersion curves and graphs of specific loss are given for four particular, but hypothetical, materials, corresponding to four cases of the solution.

Wave formation on a vertical falling liquid film

Abstract: The method of integral relations is used to derive a nonlinear two-wave equation for long waves on the surface of vertical falling liquid films. This equation is valid within a range of moderate Reynolds numbers and and be reduced in some cases to other well-known equations. The theoretical results for the fastest growing waves are compared with the experimental results concerning velocities, wave numbers, and growth rates of the waves in the inception region. The validity of the theoretical assumptions is also confirmed by direct measurements of instantaneous velocity profiles in a wave liquid film. The results of the experimental investigation concerning nonlinear stationary waves and the evolution of initial solitary disturbances are presented.

Leaky Lamb waves in fibrous composite laminates

Abstract: Results of experimental measurements and theoretical calculations on ultrasonic leaky Lamb‐wave propagation in fiber‐reinforced, unidirectional composite laminates are presented. With the Lamb wave vector oriented parallel to the fiber direction, dispersion curves of phase velocity versus frequency and plate thickness have been constructed from measurements of ultrasonic reflection from fluid‐loaded composite plates. The experimental results are supported by a theoretical model of Lamb‐wave propagation in the composite plate. The model begins with an approximate calculation of the effective, homogeneous, transversely isotropic elastic behavior of a unidirectional composite laminate in the long‐wavelength limit, using a two‐step procedure based on alternating layered media. This intermediate continuum result is then incorporated into a calculation of the ultrasonic reflection coefficient of a fluid‐loaded anisotropic plate, which is assumed to approximate the fibrous composite laminate. Good quantitative agreement with the model is found if the fiber volume fraction is taken to be an adjustable parameter. However, not all portions of the dispersion curves predicted by the model can be observed in the data. It is conjectured that relative differences in mode coupling account for this discrepancy.

A perturbation theory for the acoustoelastic effect of surface waves

Abstract: The acoustoelastic effect for surface and plate waves propagating in nonuniformly stressed media is analyzed. The theory is based on our earlier perturbation theory and normal mode technique which was used for volume waves. As with the earlier treatment, a Lagrangian description of the motion of the particles in an elastic medium is used. The results are applied to analyze the acoustoelastic effect for Rayleigh waves and Lamb waves in nonuniformly stressed media.

Use of Rayleigh Waves in Liquefaction Studies

Abstract: The Spectral-Analysis-of-Surface-Waves method is a new seismic method for efficient determination of shear wave velocity in situ. Vertical impacts applied to the ground surface are used to generate Rayleigh waves with different frequencies. Propagation of the waves is monitored with surface receivers located known distances apart. By employing waveform analysis techniques, the variation of Rayleigh wave velocity with frequency is calculated. With inversion, shear wave velocity, shear modulus and layering of the site are determined. Several case studies where liquefaction occurred are presented. In each case, the shear wave velocities of the liquefiable layer were less than 450 fps.

Analysis and computation for nonlinear elastic surface waves of permanent form

Abstract: Linear elastic surface waves are nondispersive. All wavelengths travel at the Rayleigh wave speed c R. This absence of frequency dispersion means that nonlinear waves of permanent form cannot be determined as a small perturbation from a sinusoidal wavetrain. By representing the general Rayleigh wave of the linear theory in terms of a pair of conjugate harmonic functions, waves which propagate without distortion are characterized as those having surface elevation profiles which satisfy a certain nonlinear functional equation. In the small-strain limit, this reduces to a quadratic functional equation. Methods for the analysis of this equation are presented for both periodic and nonperiodic waveforms. For periodic waveforms, the infinite system of quadratic equations for the Fourier coefficients of the profile is solved numerically in the case of a certain ‘harmonic’ elastic material. Two distinct families of profiles having phase speed differing from the linearized Rayleigh wave speed are found. Additionally, two families of exceptional waveforms are found, describing profiles which travel at the Rayleigh wave speed.

Optical monitoring of photoacoustic pulse propagation in silicon wafers

Abstract: We demonstrate a new optical and noncontact method for direct and fast detection of photoacoustic pulse propagation in thin silicon wafers. A probe beam deflection technique is used to monitor both longitudinal and Lamb wave propagations from which information on the elastic constants and the sample orientation can be obtained. Results obtained for wafers of different orientations and doping levels are compared with previous contact measurements.

Scattering of a Rayleigh Wave by an Elastic Quarter Space

Abstract: We study the two-dimensional, steady-state problem of the scattering of waves in a homogeneous, isotropic, linear-elastic quarter space. We derive decoupled equations for the Fourier transforms of the normal and tangential displacements on the free surfaces. For incidence of a Rayleigh surface wave, we plot the amplitudes and phases of the surface waves reflected and transmitted by the corner. These curves were obtained numerically.

Gaussian beams for surface waves in laterally slowly-varying media

Abstract: Summary. Asymptotic ray theory is applied to surface waves in a medium where the lateral variations of structure are very smooth. Using ray-centred coordinates, parabolic equations are obtained for lateral variations while vertical structural variations at a given point are specified by eigenfunctions of normal mode theory as for the laterally homogeneous case. Final results on wavefields close to a ray can be expressed by formulations similar to those for elastic body waves in 2-D laterally heterogeneous media, except that the vertical dependence is described by eigenfunctions of ‘local’ Love or Rayleigh waves. The transport equation is written in terms of geometrical-ray spreading, group velocity and an energy integral. For the horizontal components there are both principal and additional components to describe the curvature of rays along the surface, as in the case of elastic body waves. The vertical component is decoupled from the horizontal components. With complex parameters the solutions for the dynamic ray tracing system correspond to Gaussian beams: the amplitude distribution is bell-shaped along the direction perpendicular to the ray and the solution is regular everywhere, even at caustics. Most of the characteristics of Gaussian beams for 2-D elastic body waves are also applicable to the surface wave case. At each frequency the solution may be regarded as a set of eigenfunctions propagating over a 2-D surface according to the phase velocity mapping.

Longitudinal resonance in surface acoustic phonons

Abstract: A detailed study of the longitudinal surface resonance of leaky wave in the acoustic spectrum of solids is carried out. The authors study the lineshape of the resonance in the power spectrum of both isotropic and anisotropic solids. The physical meaning of the new mode is investigated in connection with the reflection coefficients of bulk waves at the free surface and with the amplitude of vibration of Lamb waves.

Evolution of atmospheric spectrum by processes of wave‐wave interaction

Abstract: Previous work has shown that a primary gravity wave of sufficient amplitude will always decay through resonant wave-wave interactions with two secondary gravity waves. The interaction among the resonant trio can be reasonably rapid and may be an important process responsible for energy exchange among gravity waves of different wavelengths in the atmosphere. By taking statistical ensemble averages to the interaction equations we obtain an hierarchy of moment equations, the closure condition of which can be effected by making a random phase approximation. The obtained kinetic equation is Boltzmann-like and describes the time evolution of wave action. The nonlinear kinetic equation is impossible to solve in general except numerically, but the equation is drastically simplified in three limiting cases identified as elastic scattering, parametric subharmonic instability, and induced diffusion processes. Through elastic scattering, an upgoing wave is scattered into a downgoing wave by interacting resonantly with a vertical shear. This process is thus responsible for making the atmospheric spectrum vertically symmetric if it is not so initially. The parametric subharmonic instability process is responsible for transferring energetic large-scale waves to small-scale waves at one-half the frequency. The induced diffusion process is responsible for time evolution of small-scale waves by a three-wave process involving two nearly identical waves of small scales interacting resonantly with a large-scale vertical shear. The rapidity with which these three processes take place in the atmosphere and their implication in the atmospheric spectrum are investigated and discussed.

Ultrasonic transducer of monolithic array type

Abstract: On the front face of a piezoelectric plate, electrodes split into an array form are disposed. Thus, there is provided a transducer of monolithic array type having an array of transducer elements operating independently, without cutting the piezoelectric plate. On the rear face of the piezoelectric plate, a plurality of grooves are formed to attenuate the Lamb wave propagating in the face direction while being reflected at the front face and the rear face.

Acoustic Lamb wave‐electric field nonlinear interaction in YZ LiNbO3 plates

Abstract: The nonlinear electroacoustic effect has been investigated for acoustic Lamb wave propagation in a YZ LiNbO3 plate under a uniform bias electric field. A theoretical model is briefly outlined, which shows how the effect can be interpreted in terms of second and third order material constants. The strength of the nonlinear interaction has been experimentally evaluated through measurements of the change in phase velocity of Lamb modes produced by the bias field. The experiments were performed in the frequency range 8–33 MHz on most of the Lamb modes excited in a 1.25‐mm‐thick plate by an interdigital transducer with a periodicity λ=0.396 mm. The results evidence a strong dependence of the nonlinear effect on the order and symmetry of the analyzed modes.

Theory of ultrasonic resonances in a viscoelastic layer

Abstract: We present a resonance theory for the acoustic transmission and reflection coefficients of an elastic plate imbedded in a fluid medium, which includes the effects of plate viscosity. This formulation provides a direct means for determining the material parameters of the plate from the measured acoustic resonances of the Rayleigh and Lamb waves in the plate (i.e., their positions in frequency or angle, their widths, and their heights) which are given in our formalism by explicit analytic expressions that depend on the material parameters. Viscosity is seen to manifest itself in a decrease of the resonance peaks and in a broadening and frequency dependence of the resonance widths, which may be used to determine the frequency‐dependent loss factor of the plate.

On Rayleigh Waves and Related Propagating Acoustic Waves

Abstract: The propagation of mechanical disturbances in gases, fluids and solids has been studied for many centuries, and has attracted the attention of such celebrated physicists as Newton, Poisson, Hooke, Stokes and Maxwell. Although never enjoying the significance or popularity of electromagnetic wave propagation, it received increased interest in the late eighteenth and early nineteenth centuries with the investigations of RAYLEIGH [1], LOVE [2], STONELEY [3] and others into seismic wave propagation. It was during the course of such studies that exactly one hundred years ago Lord Rayleigh showed theoretically that a mechanical disturbance can propagate unperturbed on the surface of a semi-infinite isotropic solid, in many respects like waves on the sea. Rayleigh conjectured that such surface waves would be especially significant in seismic wave propagation because, unlike bulk acoustic waves, they would only diffract on the surface, not into the volume of the earth. In this conjecture he was partly correct, but it was shown later by LOVE [2] that surface waves arising from the layered structure of the earth’s surface (and having a different particle motion, as discussed later) are probably more important in this respect. A number of other studies have been undertaken over the years in an attempt to define the modes of propagation of specific mechanical structures, such as the work of Pochhamner and Chree on cylindrical bars, and of STONELEY [3] on the waves that can propagate at a plane boundary between two solids.

Land applications of shear waves

Abstract: Shear waves were discussed in terms of raypaths in the first article of this series. They may also be viewed as wavefronts. An excellent and brief tutorial treatment of compressional waves (P) and shear waves (S) is offered by R. Garotta in the brochure Land seismic shear waves produced by CGG (Technical Series No: 507.78.05). Garotta begins by stating that homogeneous and isotropic solids can transmit two types (see Figure 1) of elastic waves, compressional and shear, and provides a mathematical proof that their respective propagation velocities are different.

Liquid level gauge

Abstract: An ultrasonic liquid level gauge 10 comprises two solid surfaces 42 and 50 in opposed relationship, and a plane reflecting surface 32 supported between the surfaces so as to be slightly below the liquid level 18 in use. A Lamb wave is caused to propagate down one surface 42, undergoing mode conversion to compression waves in the liquid 16 which reflect off the reflecting surface 32 onto the other surface 50, undergoing mode conversion to a Lamb wave propagating up the other surface 50. The reflecting surface 32 may be supported by a float 30, and the solid surfaces 42 and 50 may be opposite walls of a rectangular tube 12.

Signal Analysis of Leaky Lamb Wave Spectra for NDE of Composites

Abstract: A new way to analyze signals of leaky Lamb wave (LLW) spectra to perform nondestructive evaluation of fiber reinforced composite laminates has been investigated. Coupling to the Lamb waves is accomplished by mode conversion of an incident compressional wave in a fluid surrounding the plate, where a second transducer in the fluid detects the LLW. NDE applications of this excitation have been studied in graphite-epoxy plates using swept frequency RF tone bursts in the range of 0.5 to 10. MHz. To prevent insignificant spatial variations in either fiber volume fraction or plate thickness from obscuring the detection of important defects, a new scheme has been devised to analyze the ultrasonic reflection signals from the plate. Examples of two-transducer LLW C-scans of composite plates with seeded defects are presented, demonstrating improved discrimination and sensitivity of the new signal handling method.

Nonlinear effects on transverse shear waves in an elastic medium

Abstract: The effect of second- and third-order nonlinearities on transverse shear waves in an elastic medium is examined. It is found that waveform distortion and shock development occur on a length scale which is an order of magnitude greater than for longitudinal waves. Explicit solutions for modulated traveling waves are obtained.

A note on the influence of the elasticity on wave propagation in an acoustic/elastic coupled medium

Abstract: Comparisons of the laboratory physical modeling experiment and the finite element numerical simulation of the physical modeling experiment of wave propagation in an acoustic/elastic coupled medium, reveal that the finite element numerical simulation of the physical modeling experiment, when an elastic medium is modeled as an acoustic medium, is definitely inferior than that, when an elastic medium is modeled actually as an elastic medium. The elasticity of an acoustic/elastic coupled medium, as expected, has a pronounced influence on the shear wave conversion and propagation; in turn, the characteristics of wave forms and arrival events involve both the compressional and shear waves. These findings may bear significant implications of whether the elastic property of the ocean bottom plays an important role in the long range sound transmission in oceans.

Lamb-wave electroacoustic voltage sensor

Abstract: The effect of a bias electric field on the phase velocity of Lamb waves propagating in a piezoelectric plate has been investigated in order to develop an electroacoustic voltage sensor. Experiments were performed on YX and YZ LiNbO3 Lamb‐wave delay lines, used as the stabilizing element in the feedback loop of an oscillator, by measuring the fractional frequency change produced by a bias electric field normal to the plate surfaces. The results obtained have shown that Lamb‐wave sensors can exhibit a higher sensitivity and a better linearity than the corresponding Rayleigh‐wave devices.

Lamb wave reflection at plate edges

Abstract: The changing of modes taking place in Lamb wave reflected from the limiting edge of a plate is taken into consideration by evaluating the coupling of the single shear and longitudinal components, through Snell’s law. Acousto‐optical probing of the acoustic field is used for studying the effect in isotropic plates, in the range of a few megahertz.

Stacking investigations of higher‐order mantle Rayleigh waves

Abstract: We present the initial results of an ongoing study of higher-order mantle overtones of Rayleigh waves. The main problem is to separate overtone branches (3R,4R,5R), traveling with identical group velocities at similar frequencies. Global stacking is used, both for traveling waves and normal modes, with dispersion results in generally excellent agreement with both theoretical models and values published for a well-separated part of the 3R branch.

Scattering of rayleigh waves in an elastic three-quarter space

Abstract: This study investigates the generation of waves, due to the incidence of Rayleigh waves upon the corner of an elastic three-quarter space. Incident Rayleigh waves travel along one surface of the elastic three-quarter space. Integral equations are derived by use of the Fourier transform technique, and are solved by deforming the integration paths into paths along which the integrands vary smoothly in magnitude. Expressions for the energy flux of Rayleigh waves along two free surfaces and for scattered body waves, were obtained. Partition of energy flux and directivity of the scattered P and S waves are discussed. The agreement between our theory and the experiment made by another investigator is considerably good. Substantial amounts of energy of incident Rayleigh waves are scattered away in the form of S waves, in the same direction as incident Rayleigh waves. Another interesting and important feature is the fact that, just around the corner of the elastic medium, the dilatational and distortional parts of waves are very large in magnitude. In other words, a kind of trapping of these waves occurs around the corner. These two kinds of waves are out of phase and the resultant waves are small in magnitude, due to the result of cancelling.