Ray representation of longitudinal lateral waves in acoustic microscopy

For object materials having a large enough Rayleigh velocity, the V(z) (where V is the output voltage and z is the defocus distance) variation is mainly due to interference between the fields of the geometrically reflected wave and the leaky Rayleigh wave. However, for materials, such as organic compounds, having a low Rayleigh velocity, the leaky Rayleigh wave is not excited. For this case, the lateral wave resulting from propagation along the surface of the longitudinal wave plays a significant role in determining the V(z) dependence. The effect of the lateral wave contribution on V(z) is studied. Ray optics is to derive an expression giving the influence of the longitudinal lateral wave. Good agreement is found between the theory and measurements for z not near zero. Because of the ease with which the longitudinal wave velocity can be obtained from V(z), one can conveniently determine the elastic constant c(11 ) of isotropic materials using the acoustic microscope.     

Propagation properties of longitudinal leaky surface waves on lithium tetraborate

Theoretical and experimental results of longitudinal leaky surface waves with a higher phase velocity than that of ordinary leaky surface waves and a low propagation loss on lithium tetraborate (LBO) are investigated in detail. They propagate along the surface with a phase velocity close to that of longitudinal bulk wave, slightly radiating two kinds of shear bulk waves (or one shear bulk wave in the case that one of two shear wave terms is uncoupled) into the solid. Most surface components of the mode consist of a longitudinal wave term and an electromagnetic wave term. The detailed propagation properties of the longitudinal leaky surface waves on LBO with the Euler angles (phi, theta, 90 degrees ) are investigated theoretically and experimentally. The (011) cut of LBO was found to be desirable for higher frequency SAW devices. One of the reasons why that mode on LBO has a low propagation loss is also discussed.     

Wave analysis of the acoustic material signature for the line focus microscope

A model is presented for the computation of the acoustic material signature for a line focus scanning acoustic microscope, based on a boundary element calculation and an electromechanical reciprocity identity. This identity is used to relate the voltage at the terminals of the microscope's transducer to the acoustic wavefields at the interface between the specimen and the coupling fluid. A Gaussian beam, launched in the buffer rod, is tracked through the lens and its matching layer. A model for the matching layer that is convenient for use with the boundary element technique is presented. The wavefields scattered from the surface of the specimen, including the leaky Rayleigh wave, are then calculated. Knowing the wavefields incident on and scattered from the specimen, the acoustic signature is calculated using the reciprocity relation. Results are presented for a defect free halfspace, and are compared with those of an analytical model and an experimental measurement.     

Behavior of Rayleigh surface waves in an anisotropic media lying over a prestressed orthotropic half-space

The present paper discusses the propagation of Rayleigh waves in an anisotropic layer with finite thickness lying over a prestressed orthotropic half-space. An anisotropic media and orthotropic media are supposed for the upper layer and lower half-space, respectively. Dispersion equation and displacement components are computed in a compact form considering the case that the displacement and stress are continuous at the interface and stress vanishes on a free surface. Graphs are sketched to represent the effect of density, initial stress and height of the layer on wave velocity. The graphs are also configured to exhibit the mode of propagation of Rayleigh waves. This paper is an attempt to explain the nature of Rayleigh waves mathematically.     

Waves in a rotating elastic solid

Wave propagation in a uniformly rotating elastic solid is discussed based on displacement equations in a moving frame. The time-harmonic Green’s dyadic for a point body force is obtained in closed form. It is reconfirmed that two quasi dilatational and shear waves are coupled to each other, and the deformation decomposition into the dilatation and rotation is not possible for the rotating solid. Further, it is also confirmed that the velocity of the Rayleigh surface wave depends not only on the rotational velocity but also on its direction and that the Rayleigh wave vanishes when the rotational velocity approaches the Rayleigh wave velocity of the immovable solid.     

Two-dimensional wave propagation in a micropolar thermo-elastic layer with stretch

This paper deals with the propagation of 2-dimensional waves in a thermo-elastic micropolar solid layer which can stretch and contract. Thermo-elastic Rayleigh wave velocity equation in the micropolar medium with stretch has been deduced from the above theory. The wave velocity equation obtained is in agreement with the classical result of Rayleigh when the layer is unstretched and thermal and micropolar effects are negligibly small.     

Two-dimensional wave propagation in a micropolar thermo-elastic layer

The object of the present paper is to investigate the 2-dimensional thermo-elastic wave propagation in a micropolar solid layer. The wave velocity equation for the thermo-elastic Rayleigh wave in the micropolar medium has been deduced from the above theory and in the limiting case the wave velocity equation so obtained is in agreement with the corresponding classical problem when the thermal and micropolar effects are vanishingly small.     

Influence of principal material directions of thin orthotropic structures on Rayleigh-edge wave velocity

The paper is concerned with Rayleigh-edge wave propagation in thin panels made of two types of materials. The first one is a long-fiber-reinforced composite and second one is a cubic crystallic structure. The influence of principal material directions on Rayleigh-edge wave velocity is studied theoretically and experimentally. Theoretical solution is based on finite element approach. The propagation in the principal material directions is also investigated analytically. Experimental solution utilizes for non-contact measurements a laser vibrometer. The measurements are carried out on the composite panels. It has been found that Rayleigh wave velocity depends significantly on the directions of material axes. It has been also ascertain that the Rayleigh-edge wave propagation exhibits no geometric dispersion from point of view of the precision and frequency range of computational model.     

Surface waves in fibre-reinforced anisotropic elastic media

The aim of this paper is to investigate surface waves in anisotropic fibre-reinforced solid elastic media. First, the theory of general surface waves has been derived and applied to study the particular cases of surface waves — Rayleigh, Love and Stoneley types. The wave velocity equations are found to be in agreement with the corresponding classical result when the anisotropic elastic parameters tends to zero. It is important to note that the Rayleigh type of wave velocity in the fibre-reinforced elastic medium increases to a considerable amount in comparison with the Rayleigh wave velocity in isotropic materials.     

An energy-based discontinuous Galerkin method for coupled elasto-acoustic wave equations in second-order form

We consider wave propagation in a coupled fluid-solid region separated by a static but possibly curved interface. The wave propagation is modeled by the acoustic wave equation in terms of a velocity potential in the fluid, and the elastic wave equation for the displacement in the solid. At the fluid solid interface, we impose suitable interface conditions to couple the two equations. We use a recently developed energy-based discontinuous Galerkin method to discretize the governing equations in space. Both energy conserving and upwind numerical fluxes are derived to impose the interface conditions. The highlights of the developed scheme include provable energy stability and high order accuracy. We present numerical experiments to illustrate the accuracy property and robustness of the developed scheme.     

含泥沙的流固层状介质界面波传播特性研究

在弹性波传播理论的基础上,结合边界条件,导出了流固层状介质导波特征方程,计算特征方程的频散曲线;然后结合Urick、Urick-Ament和Harker-Temple这三种悬浊液模型,计算流体层中的泥沙含量和颗粒粒径与界面波波速的关系;分析比较不同模型下泥沙含量及颗粒粒径与波速的关系图,讨论不同参数对波速的影响,得出了三种模型下波速随泥沙含量和颗粒粒径的变化趋势,最后发现Urick-Ament模型同时适用于检测悬浊液的泥沙含量和泥沙颗粒粒径,且在三种模型中有相对较好的可靠性和实用性。     

Rayleigh surface wave propagation in an orthotropic rotating magneto-thermoelastic medium subjected to gravity and initial stress

Abstract

The prime objective of the present article is to analyze the effects of rotation and initial stress on the propagation of Rayleigh surface waves in a homogeneous, orthotropic magneto-thermoelastic half space subjected to gravity field. The frequency equations in closed form are derived and the amplitude ratios of surface displacements, temperature change during the Rayleigh wave propagation on the surface of half space have been computed analytically. The highlights of this study are the effects of different parameters (rotation, magnetic field, initial stress, and gravity) on the velocity of Rayleigh waves. Variation in phase velocity of Rayleigh waves against a wave number is shown graphically. Some particular cases have been deduced. Also, the classical Rayleigh wave equation is obtained as a special case of the present study. Numerical example has been carried out and represented by the means of graphs. Impacts of various involved parameters appearing in the solutions are carefully analyzed. In fact, in the absence of various parameters, these equations are in agreement with the results for isotropic medium.     

Acoustic microscopy measurement of elastic constants and massdensity

A method is presented to determine the elastic constants and the mass density of isotropic and anisotropic solids and anisotropic thin films. The velocity and attenuation of leaky surface acoustic waves (SAWs) have been obtained for specified propagation directions from V(z) curves measured by line-focus acoustic microscopy (LFAM). The experimentally obtained velocities have been compared to velocities obtained from a measurement model for the V(z) curve which simulates the experiment. Since the measured and simulated V(z) curves have the same systemic errors, the material constants are free of such errors. For an isotropic solid, Young's modulus E, the shear modulus G and the mass density ρ have been determined from the leaky Rayleigh wave velocity and attenuation, measured by LFAM, and a longitudinal wave velocity measured by a pulse-echo transit-time technique. For a cubic-crystalline solid, the ratios of the elastic constants to the mass density (c₁₁ /ρ, c₁₂/ρ, c₄₄/ρ) have been determined from the directional variation of measured SAW velocities, using a preliminary estimate of ρ. The mass density ρ has subsequently been determined by additionally using the attenuation of leaky SAWs in crystal symmetry directions. For a cubic-crystalline thin film deposited on a substrate, the elastic constants and the mass density (c₁₁, c₁₂, c₄₄, ρ) of the film have been determined from the directional variation of the measured SAW velocities, and a comparison of the corresponding attenuation coefficient with the measured attenuation coefficient has been used to verify the results     

Rayleigh Wave Propagation for the Detection of Near Surface Discontinuities: Finite Element Modeling

The paper presents a finite element study designed to gain physical insight into the effect of surface discontinuities on Rayleigh wave propagation in structural elements. In particular, a series of array measurements at various locations within a plate are simulated and compared with experimental measurements. Conversion of array measurements into the frequency-wavenumber domain reveals propagating Lamb modes, which are used to define Rayleigh wave motion. Numerical results show that Rayleigh waves measured after passing a fracture are composed of long wavelength Rayleigh wave energy propagating past the slot and short wavelength Rayleigh wave energy formed behind the slot.     

A finite element‐based level set method for fluid–elastic solid interaction with surface tension

A numerical method for simulating fluid–elastic solid interaction with surface tension is presented. A level set method is used to capture the interface between the solid bodies and the incompressible surrounding fluid, within an Eulerian approach. The mixed velocity–pressure variational formulation is established for the global coupled mechanical problem and discretized using a continuous linear approximation in both velocity and pressure. Three ways are investigated to reduce the spurious oscillations of the pressure that appear at the fluid–solid interface. First, two stabilized finite element methods are used: the MINI‐element and the algebraic subgrid method. Second, the surface integral corresponding to the surface tension term is treated either by the continuum surface force technique or by a surface local reconstruction algorithm. Finally, besides the direct evaluation method proposed by Bruchon et al., an alternative method is proposed to avoid the explicit computation of the surface curvature, which may be a source of difficulty. These different issues are addressed through various numerical examples, such as the two incompressible fluid flow, the elastic inclusion embedded into a Newtonian fluid, or the study of a granular packing. Copyright © 2012 John Wiley & Sons, Ltd.     

On interface crack propagation with variable velocity for longitudinal shear problems

The antiplane strain problem of straight interface crack propagation between two elastic half-spaces under arbitrary variable loading is considered. The crack edge is specified as an arbitrary smooth function of time. It is assumed that the crack speed is less than the smaller of the shear wave velocities of two media. An integral transform method and factorization technique are used to solve the problem. The solutions are worked out for semi-infinite crack and finite crack problems. The dynamic stress intensity factors at the crack tip of the moving interface crack are given and it is found that the stress intensity factor of the interface crack is slightly higher than that in the homogeneous medium with slower shear wave velocity.     

流-固多层结构中软层介质参数反演研究

建立了固体层内含软层介质的多层流-固界面模型。使用传递矩阵法,导出固体层内含软层介质的流-固界面波的频散方程。根据频散方程计算频散曲线,改变软层介质的深度、厚度及横波波速,观察频散曲线的变化。使用有限元软件建立仿真模型,引入遗传反向传播(Back Propagation, BP)神经网络,对模型参数进行了反演。反演结果表明,使用遗传BP神经网络,能有效地反演出软层介质的深度、厚度与横波波速参数。     

Statistical error analysis of time and polarization resolved ultrasonic measurements

The time and polarization resolved ultrasonic technique which we previously developed has been demonstrated to simultaneously provide measurements of the wave velocity in the coupling liquid, and the leaky surface wave and leaky longitudinal wave velocities in solid samples. To document the measurement precision associated with this technique, a statistical method is employed for the data fit and error analysis. With the help of statistical analysis, the simple ray model used to determine wave velocities in this technique is first confirmed by theoretical data which are predicted by the Green's function. Error analysis is then applied to the experimental data. The results show that this technique has a relative expanded uncertainty (equal to twice the standard deviation) of 0.03% for the wave velocity in water, and an uncertainty less than 0.2% and 2%, respectively, for the leaky surface and leaky longitudinal wave velocities in a crown glass sample. The uncertainty in the repeatability for leaky surface wave measurements is observed to be much less than the expanded uncertainty of a single measurement set. This methodology also has been applied to a set of steel samples. The results allow that the expanded uncertainty for leaky surface wave velocities is less than 0.07%, enabling a correlation of the measured velocities with specific sample heat treatments.     

Rayleigh waves in a thermoelastic solid half space using dual-phase-lag model

The present paper deals with the study of Rayleigh waves in a thermoelastic homogeneous isotropic solid half space in the context of dual-phase-lag model. The medium is subjected to stress free, thermally insulated, boundary conditions. The equation for the phase velocity of Rayleigh waves and the analytical expressions for the amplitudes of the displacements, temperature and thermal stresses have been derived. The expressions are obtained for a wave traveling along the free surface. The results discussed numerically and illustrated graphically to show effect of the coupling parameter and phase-lags.