Influence of a structurally damaged surface layer of the hexagonal crystal on the dispersion and attenuation of Rayleigh surface acoustic waves

Analytical expressions for the dispersion of the phase velocity and the inverse attenuation length of Rayleigh waves are derived with allowance made for a thin (as compared to the length of the surface wave) isotropic damaged surface layer that is contiguous with vacuum and located on the surface of a hexagonal crystal with the sixfold axis perpendicular to the surface. It is demonstrated that, in the limit of long wavelengths (as compared to the characteristic inhomogeneity size), which is of greatest interest for experimenters, the change in the dispersion of the phase velocity of Rayleigh waves is proportional to the second power of the frequency, whereas the inverse attenuation length of Rayleigh waves is proportional to the fifth power of the frequency. The inverse attenuation length of the Rayleigh wave is calculated numerically. The calculation method previously proposed by one of the authors (Kosachev, 1998) is generalized to the case of an isotropic damaged layer on an anisotropic (hexagonal) substrate.     

Scattering of a Rayleigh surface acoustic wave by a small-size inhomogeneity in a solid half-space

We use the Born approximation of the perturbation method to solve the problem of scattering of a harmonic Rayleigh surface acoustic wave by a weak-contrast inhomogeneity that is small compared with the wavelength and is located in a solid half-space near its boundary. The material of the inhomogeneity differs from the material of the half-space only in its density. The Rayleigh wave incident on the inhomogeneity is excited by a monochromatic surface force source acting normally to the half-space boundary. We derive expressions for the displacement fields in the scattered spherical compressional and shear (SV- and SH-polarized) waves. Scattering of the Rayleigh wave into a Rayleigh wave is studied in detail. We find expressions for the vertical and horizontal components of the displacement vector in the scattered Rayleigh wave as well as its radiated power. It is shown that the field of the scattered surface wave is mainly formed by vertical oscillations of the inhomogeneity in the field of the incident wave. In this case, the radiated power for the scattered Rayleigh wave formed by vertical motion of the inhomogeneity in the incident-wave field depends on the depth of the inhomogeneity as the fourth power of the function describing the well-known depth dependence of the vertical displacements in the Rayleigh surface wave. Correspondingly, the dependence of the radiated power for the scattered Rayleigh wave formed by horizontal motion of the inhomogeneity depends on its location depth as the fourth power of the depth dependence of the horizontal displacements in the Rayleigh surface wave. We perform calculations of the ratio between the powers of the scattered and incident Rayleigh waves for different ratios between the velocities of the compressional and shear waves in a solid. It is shown that the radiated power for the scattered surface wave decreases sharply with increasing depth of the subsurface-inhomogeneity location. Thus, the scattering of a Rayleigh wave into a Rayleigh wave is fairly efficient only when the location depth of the inhomogeneity does not exceed about one-third of the wavelength of the shear wave in an elastic medium.     

Effect of the structurally damaged surface layer of an isotropic solid on Rayleigh wave dispersion and damping

The effect of the structurally damaged isotropic surface layer on the free surface of an isotropic solid on the Rayleigh wave propagation has been considered. The phase velocity dispersion and inverse Rayleigh wave decay length in the second order of vanishing with respect to the ratio of the structurally damaged layer thickness to the wavelength have been obtained in an analytical form. For the dispersion and the inverse wave decay length, the long-wave limit has been studied when the wavelength is much larger than the characteristic size of layer inhomogeneity. The inverse decay length has been calculated numerically.     

Experimental study of surface wave propagation in strongly heterogeneous media

In the present paper, the propagation of Rayleigh waves in a strongly heterogeneous medium is discussed. Scattering of stress waves is a difficult scientific problem. Specifically, the interaction of surface waves with distributed inhomogeneity seems highly complicated due to the existence of two displacement components. Rayleigh waves undergo significant attenuation and velocity change depending on the frequency and the inhomogeneity content. The aim of this study is to highlight the dispersive behavior of concrete, especially when damaged, and increase the experimental data in an area where the work is limited.     

A new method for reconstructing medium inhomogeneities using Rayleigh waves: Case studies

The problem of reconstructing local low-contrast inhomogeneities in the Earth’s surface layers by means of coherent Rayleigh surface waves is considered. It is shown that analysis of the frequency characteristics of shear projections in this wave on the surface allows construction of the function of inhomogeneity distribution in a specified depth range. The results from seismoacoustic reconstruction of inhomogeneities correlate with data obtained using standard geophysical methods and are confirmed by direct observations.     

Combining Brillouin spectroscopy and laser-SAW technique for elastic property characterization of thick DLC films

Surface Brillouin spectroscopy (SBS) has been widely used for elastic property characterization of thin films. For films thicker than 500 nm, however, the wavelength of surface acoustic wave in the frequency range available for SBS is smaller than film thickness, and the SBS measures only the Rayleigh wave of the film. The laser-SAW technique, on the other hand, measures only the low-frequency portion of the surface acoustic wave dispersion and can estimate only one elastic modulus of the film (typically Young's modulus). In this work, we have combined the two methods to determine both Young's modulus and Poisson's ratio of a diamond-like carbon (DLC) film. It was found that reasonable estimates can be obtained for the longitudinal wave velocity, shear wave velocity, and Young's modulus of the film. The Poisson's ratio, however, still has a relatively large measurement error.     

Rayleigh wave propagation along the boundary of a non-Newtonian fluid-saturated porous medium

The Frenkel-Biot theory is used to study the reflection of elastic waves from the boundary of a non-Newtonian (Maxwell) fluid-saturated porous medium. The velocity and attenuation of a Rayleigh surface wave propagating along the boundary of the medium are determined. Two models of a fluid-saturated porous medium are used for calculation: with pore channels of a fixed diameter and with a lognormal distribution of pore channels in size. The results of calculations show that, when the fluid in the porous medium is characterized by a small Deborah number (i.e., exhibits non-Newtonian properties), the velocity of Rayleigh waves exhibits a considerable frequency dispersion. The results also suggest that, in principle, it is possible to estimate the Deborah number from the measured frequency dispersion of the Rayleigh wave velocity.     

Coating thickness affects surface stress measurement of brush electro-plating nickel coating using Rayleigh wave approach

A surface ultrasonic wave approach was presented for measuring surface stress of brush electro-plating nickel coating specimen, and the influence of coating thickness on surface stress measurement was discussed. In this research, two Rayleigh wave transducers with 5 MHz frequency were employed to collect Rayleigh wave signals of coating specimen with different static tensile stresses and different coating thickness. The difference in time of flight between two Rayleigh wave signals was determined based on normalized cross correlation function. The influence of stress on propagation velocity of Rayleigh wave and the relationship between the difference in time of flight and tensile stress that corresponded to different coating thickness were discussed. Results indicate that inhomogeneous deformation of coating affects the relationship between the difference in time of flight and tensile stress, velocity of Rayleigh wave propagating in coating specimen increases with coating thickness increasing, and the variation rate reduces of difference in time of flight with tensile stress increasing as coating thickness increases.     

Rayleigh wave at the boundary of an inhomogeneous nonlinear viscoelastic half-space

In the approximation of weak nonlinearity and weak viscosity of the medium, we obtain an equation describing the spectral density of the particle horizontal velocity for a Rayleigh wave propagating along the boundary of a half-space. The coefficients of nonlinear interaction between the wave harmonics are found on the assumption that the third-order elastic moduli arbitrarily depend on the depth. We find expressions for the complex correction to the wave frequency due to small relaxation corrections to the elastic moduli and small variations in the medium density, which arbitrarily depend on the depth as well. The imaginary part of this correction to the frequency determines the decay of the linear Rayleigh wave due to small relaxation corrections to the elastic moduli arbitrarily dependent on the depth. Using numerical simulation (with allowance for the interaction of 500 harmonics), we study distortions of an initially harmonic Rayleigh wave for a particular dependence of variations in the nonlinear moduli on the depth. An integral equation is derived for the nonlinear elastic moduli as functions of the depth. It is shown that for independent spatio-temporal distributions of the viscous moduli, functions determining the dependence of the viscosity on the depth are described by an analogous integral equation. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 50, No. 3, pp. 212–226, March 2007.     

Eigenfunction expansion method to characterize Rayleigh wave propagation in orthotropic medium with phase lags

ABSTRACT

The present paper deals with the propagation of Rayleigh surface waves in homogeneous, orthotropic thermoelastic half space in the context of three-phase lag model of thermoelasticity. A vector matrix differential equation is formed by employing normal mode analysis to the considered equations which is then solved by eigenfunction expansion method. The frequency equations for different cases are derived and the path of surface particles during Rayleigh wave propagation is found elliptical. Effect of phase lags on phase velocity, attenuation coefficient, and specific loss are presented graphically with respect to frequency as well as wave number.     

Simulation on laser-induced surface acoustic wave on isotropic cylinders by finite element method

Based on the thermoelastic theory, a finite element model is developed to simulate the process of laser inducing ultrasonic field in isotropic cylinders, which can take the temperature dependence of thermal parameters into account. Using the finite element model, we have simulated the ultrasonic fields induced by a pulse laser line source impacting on the generatrix of aluminum cylinders with different diameters. And the intact waveforms of surface acoustic wave (SAW including cylindrical Rayleigh and Whispering gallery (WG) modes) are presented, which are in very good agreement with the calculated and experimental waveforms in other literatures. Furthermore, the dispersion properties of cylindrical Rayleigh waves are analyzed by the method of phase spectral analysis, and the results show that with the increasing frequency, the phase velocity of cylindrical Rayleigh wave rapidly increases to the maximum value, and then gradually decreases to that of plane Rayleigh wave. With the diameter of cylinder decreasing, the maximum value of phase velocity and the corresponding frequency increase.     

Analysis of Laser-generated Rayleigh wave on viscoelastic materials

In order to understand the viscoelasticity of material, this research has been conducted to study the propagation characteristics of viscoelastic Rayleigh wave theoretically. A model is presented for the pulsed laser generation of ultrasound on viscoelastic medium surface. Referred to the Kelvin model, the frequency equation and the normal displacement of viscoelastic Rayleigh wave were derived, the influence of the viscoelastic modulus on dispersion and attenuation was discussed. From the theoretical calculation, it is shown that the effect of viscoelasticity on the attenuation of Rayleigh wave is more than that on its dispersion. In the case of a weak viscosity, the attenuation of viscoelastic Rayleigh wave is directly proportional to viscosity modulus; the effect of shear viscosity on the attenuation is much more than that of bulk viscosity. The transient response of viscoelastic Rayleigh wave was also simulated using Laplace and Hankel inversion transform, which are showed in good agreement with the theoretic predictions. The model provides a useful tool for the determination of viscoelastic parameters of medium.     

Pulsed Rayleigh wave scattered at a surface crack

This paper investigates Rayleigh wave interaction with machined slots on flat aluminium blocks to simulate surface breaking cracks. Using a finite element method, Rayleigh wave scattering by narrow slots of varied depth ranging from 0.5 mm to 20 mm is calculated. Pulsed wideband Rayleigh waves with a centre frequency of 590 kHz and -6 dB bandwidth of 520 kHz is considered. Reflection and transmission coefficients are calculated and compare well with the published literature. We and other workers have reported enhancement of the measured amplitude or particle velocity of an apparent Rayleigh wave close to a surface defect. In this paper, it is found that the predicted enhancement of in-plane components of particle velocities close to a crack is significantly higher than that of the out-of-plane components of particle velocities which appears to be mainly due to the mode-converted surface skimming longitudinal wave from the crack that has mainly in-plane components near the sample surface. The enhancement of the in-plane particle velocity will be observed regardless of the type of in-plane sensitive ultrasonic detector used. The explanation of the discrepancy of the reflection and transmission coefficients obtained by pulsed and narrow band or pseudo continuous Rayleigh waves is discussed. The later-arriving Rayleigh waves from reverberation along the inside of the crack surface are observed, as has been previously reported by other workers, and this may also be used to gauge slot depth.     

Study of Rayleigh type surface wave in the initial stressed irregular bottom of ocean due to point source

Rayleigh type surface wave propagation in the irregular bottom of ocean model which is the interface of homogeneous liquid layer over laying an irregular boundary of homogeneous orthotropic half space under initial stresses has been discussed in this paper. Three different dispersion equations are obtained in the form of simple equation using and not using Perturbation technique. Some special cases have been considered. The effect of irregularity, initial stressed, point source, and depth of liquid layer on the propagation of Rayleigh waves has been analyzed and results of numerical discussion have been presented graphically for three different dispersion equations. Mainly the graphs are shown the variation of phase velocity with wave number in different cases.     

Imaging of surface acoustic waves

A new experimental method has been devised that directly determines the group velocities of surface acoustic waves. A point source and a point detector are employed to measure the ultrasonic transmission across a solid surface as a continuous function of the propagation direction. Results for single pulses give the times-of-flight for both Rayleigh surface waves (RSW's) and pseudo-surface-waves (PSW's). Calculations and measurements of the group velocities of the surface waves on silicon show some unanticipated behavior: fluid loading qualitiatively changes the group velocity curves for both RSW and PSW. In particular, the RSW branch gains an additional component which we denote here as an induced Rayleigh wave (IRW). If a wave train is employed in the experiment, the analog of phonon focusing is observed for the ultrasonic waves, modified by internal-diffraction effects. Systematic measurements of the wave intensities on silicon as a function of propagation distance are consistent with expected acoustic losses into the surrounding water: the attenuation length of a wave depends on the mode and frequency. A survey of surface-wave images on other crystals is included in this study.     

航空透明件表面波声弹效应

表面波作为超声波的一种特殊形式,由于其传播特性,使得通过改变频率检测距物体表面不同深度处的;初邕应力成为可能,因此,各种产表面波声弹理论与实验技术的研究不断受到重视。本文从弹性波和有限变形理论出发,推导了表面波在有初始应力的各同性弹性体中传播时,物体表面应力与超声波传播速度之间的一般关系。对作为收音机坐舱的航空透年ＹＢ－３有机玻璃试件进行了声弹性实验。同时还给出了由实验数据回归的三次多项式声弹公式     

Elastic constants of a plate from impact-echo resonance and Rayleigh wave velocity

A new method is proposed for calculating the dynamic elastic constants of an isotropic plate from measurements of the impact-echo resonance and Rayleigh wave velocity. Poisson's ratio is shown to be a single-valued function of the ratio between thickness frequency and Rayleigh wave velocity. This dependence is derived theoretically from the condition of resonance at the minimum frequency of the first-order symmetric Lamb mode. A finite element model is developed to determine how this frequency varies with Poisson's ratio. The results obtained by modal analysis and the power-spectral density technique are in good agreement with those calculated as the solution of the S1 Lamb mode equation. The method is verified by impact-echo tests on concrete and methacrylate plates. A laser interferometer is used to detect the vibration. Thickness frequencies are accurately identified by applying the multicross-spectral density to the signals detected at several points close to the impact point. In a separate experiment, Rayleigh waves are generated by the mediator technique. The wave velocities are determined from the arrival times of the surface wave at several points. Finally, the main sources of uncertainty are evaluated.     

Scattering of Rayleigh waves by a statistical inhomogeneity of the mass density

The problem of the scattering of a Rayleigh wave by a surface inhomogeneity of the mass density of an isotropic solid is solved in the Born approximation of perturbation theory. The inhomogeneity is statistical with a Gaussian correlation function in the plane parallel to the surface and is deterministic with an exponentially decaying dependence on the coordinate perpendicular to the surface. Expressions are derived for the displacement fields in the scattered longitudinal (P), transverse (SV and SH), and Rayleigh (R) waves at large distances from the inhomogeneity. The Rayleigh wave energy scattering coefficients are calculated as functions of the wavelength λ, the correlation length a of the inhomogeneity, the depth d of the defective layer, and the Poisson ratio of the medium, σ. The angular distribution of the scattered Rayleigh wave energy is determined. Asymptotic expressions are obtained for the scattering coefficient in various limiting cases with respect to the parameters a/λ and λ/d. The relation between the energies in the scattered P, SV, SH, and R waves is established. The resulting equations are used to calculate the scattering coefficients numerically over a wide range of variation of the parameters a/λ, λ/d, and σ; the results are presented in the form of graphs and a table. A physical pattern of the scattering process is constructed and used as a basis for interpreting the results of the study. Fiz. Tverd. Tela (St. Petersburg) 39, 267–274 (February 1997)     

Two-dimensional modeling of wave propagation in materials with hysteretic nonlinearity

A multiscale model for the two-dimensional nonlinear wave propagation in a locally microdamaged medium is presented, and numerical simulations are analyzed in view of nondestructive testing applications. The multiscale model uses a statistical distribution of hysterons and upscales their microscopic stress-strain relations to a mesoscopic level. Macroscopic observations are then predicted by finite integration techniques. The influence of a small region with hysteretic nonlinearity on the generation of harmonics is investigated, and numerical results for different amplitudes of the input signal and different analysis techniques of the response signal are presented. Second, a study is conducted on the interaction of a Rayleigh wave with a microdamaged zone with hysteretic nonlinearity at the surface of an otherwise linear body, and the influence of the microdamaged zone on the surface wave velocity and on the generation of harmonics is examined. It is found that the effect of hysteresis on the Rayleigh wave propagation can be barely seen in the surface wave velocity measurement, but shows up nicely in the wave spectrum. The potential of a nonlinearity based depth profiling technique is explored by evaluating the nonlinear responses at different frequencies for a vertically stratified medium with spatially varying hysteresis properties.     

Diffraction of homogeneous and inhomogeneous plane waves on a doubly corrugated liquid/solid interface

This paper extends the theory of the diffraction of sound on 1D corrugated surfaces to 2D corrugated surfaces. Such surfaces, that are egg crate shaped, diffract incoming sound into all polar directions, which is fundamentally different from 1D corrugated surfaces. A theoretical justification is given for extending the classical grating equation to the case of incident inhomogeneous waves, for 1D corrugated surfaces as well as for 2D corrugated surfaces. Even though the present paper presents a theory which is valid for all angles of incidence, special attention is given to the particular case of the stimulation of surface waves by normal incident sound. The most interesting conclusion is that, depending on the frequency and the incident inhomogeneity, Scholte-Stoneley waves and leaky Rayleigh waves can be generated in different directions. This effect might be of particular interest in the development of surface acoustic wave devices and the basic idea of this steering effect can be of importance for planar actuators.