Elastic wave propagation and scattering in solids with uniaxially aligned cracks

In this article, elastic wave propagation and scattering in a solid medium permeated by uniaxially aligned penny-shaped microcracks are studied. The crack alignment refers to the case in which the unit normals of all cracks are randomly oriented within a plane of isotropy. The analysis is restricted to the limit of the noninteraction approximation among individual cracks. Explicit expressions for attenuations and wave speeds of the shear horizontal, quasilongitudinal, and quasishear vertical waves are obtained using stochastic wave theory in a generalized dyadic approach. The ensemble average elastic wave response is governed by the Dyson equation, which is solved in terms of the anisotropic elastic Green's dyadic. The analysis of expressions is limited to frequencies below the geometric optics limit. The resulting attenuations are investigated in terms of the directional, frequency, and damage dependence. In particular, the attenuations are simplified considerably within the low frequency Rayleigh regime. Finally, numerical results are presented and discussed in terms of the relevant dependent parameters.     

利用超声相干技术在室温和高压下研究几种不同性能的玻璃

 综合使用超声相干技术几种不同的测量方法，分别研究两类三种不同性能的玻璃材料，测量它们的声速和衰减在室温及高压条件下的变化规律。结果表明：两类玻璃的声速和衰减以及由此而得到的弹性常数存在较大差异。两种硅玻璃在高压下，声速随压力变化的规律相似，压力升高时，纵波速度随之单调增加，横波速度线性减少，纵波衰减也随压力升高呈增加趋势。不同的是：两种玻璃横波衰减随压力的变化规律完全相反，水白玻璃的衰减增加，窗口玻璃的减小。上述几种方法的测量结果基本一致，且在相应的压力范围内与布里渊散射的实验结果基本吻合。     

Ultrasonic wave propagation in heterogeneous solid media: theoretical analysis and experimental validation

This research deals with the ultrasonic characterization of thermal damage in concrete. This damage leads to the appearance of microcracks which then evolve in terms of volume rate and size in the material. The scattering of ultrasonic waves from the inclusions is present in this type of medium. The propagation of the longitudinal wave in the heterogeneous media is studied via a homogenization model that integrates the multiple scattering of waves. The model allows us to determine the phase velocity and the attenuation according to the elements which make the medium. Simulations adapted to the concrete are developed in order to test the responses of the model. These behaviors are validated by an experimental study: the measurements of phase velocity and attenuation are performed in immersion, with a comparison method, on a frequency domain which ranges from 160 kHz to 1.3 MHz. The analysis of different theoretical and experimental results obtained on cement-based media leads to the model validation, on the phase velocity behavior, in the case of a damage simulated by expanded polystyrene spheres in granular media. The application to the case of a thermally damaged concrete shows a good qualitative agreement for the changes in velocity and attenuation.     

Effect of porous surface layer on wave propagation in elastic cylinder immersed in fluid

To study the damage to an elastic cylinder immersed in fluid, a model of an elastic cylinder wrapped with a porous medium immersed in fluid is designed. This structure can both identify the properties of guided waves in a more practical model and address the relationship between the cylinder damage degree and the surface and surrounding medium. The principal motivation is to perform a detailed quantitative analysis of the longitudinal mode and flexural mode in an elastic cylinder wrapped with a porous medium immersed in fluid. The frequency equations for the propagation of waves are derived each for a pervious surface and an impervious surface by employing Biot theory. The influences of the various parameters of the porous medium wrapping layer on the phase velocity and attenuation are discussed. The results show that the influences of porosity on the dispersion curves of guided waves are much more significant than those of thickness, whereas the phase velocity is independent of the static permeability. There is an apparent "mode switching" between the two low-order modes. The characteristics of attenuation are in good agreement with the results from the dispersion curves. This work can support future studies for optimizing the theory on detecting the damage to cylinder or pipeline.     

Theoretical investigations on structural, elastic and electronic properties of thallium halides

Theoretical investigations on structural, elastic and electronic properties, viz. ground state lattice parameter, elastic moduli and density of states, of thallium halides (viz. TlCl and TlBr) have been made using the full potential linearized augmented plane wave method within the generalized gradient approximation (GGA). The ground state lattice parameter and bulk modulus and its pressure derivative have been obtained using optimization method. Young's modulus, shear modulus, Poisson ratio, sound velocities for longitudinal and shear waves, Debye average velocity, Debye temperature and Grüneisen parameter have also been calculated for these compounds. Calculated structural, elastic and other parameters are in good agreement with the available data.     

The anisotropy of elastic waves in a tellurium crystal

For acoustic waves propagating in an acoustooptic tellurium crystal, the dependence of their polarization on the propagation direction with respect to the crystal axes is discussed. The characteristic features of waves propagating in the crystal are considered; these features manifest themselves in an excess of the phase velocity of shear acoustic modes over the velocity of longitudinal modes. The change in the wave type from quasi-longitudinal to quasi-transverse as a result of the variation in the propagation direction of ultrasound is investigated. It is shown that such a behavior of bulk acoustic waves is caused by the specific relation between the elastic moduli, which differs from the corresponding relations observed in other acoustooptic materials.     

Nonlinear elasticity in structurally inhomogeneous materials: An experimental study

Experimental results on the propagation of longitudinal and torsional elastic waves in polycrystalline copper under elastoplastic strain are reported. The strain in the interval of 0–0.06 was created by applying heavy tensile loads to the samples. The Young and shear moduli, Poisson ratio, and nonlinear acoustic parameters of longitudinal and torsional elastic waves were measured as functions of the static strain. The nonlinear acoustic parameters were found to behave anomalously in loading-unloading cycles in the plastic strain region. The experimental results are discussed. The nonlinear properties of structurally inhomogeneous materials are explained in terms of the clapping nonlinearity and hysteretic nonlinearity mechanisms.     

Coherent waves in a multiply scattering poro-elastic medium obeying Biot's theory

Twersky's theory is generalized to multiple scattering by a uniform random distribution of cylinders in a poro-elastic medium. The high-frequency regime only, where no dispersion effects occur in the absence of scatterers, is investigated in the frame of Biot's theory. The scatterers lie within a slab of the host medium, and an incident wave gives rise to a fast longitudinal coherent wave, a slow longitudinal one, as well as a shear one in the slab. The dispersion equations of those three coherent waves are derived. The shear coherent wave propagates independently of the other two, while the longitudinal coherent waves obey a coupled dispersion equation involving conversion terms. Numerically speaking, coupling effects are significant only when forward scattering by a single cylinder of the fast wave into the slow one (or the slow wave into the fast) is larger than forward scattering with no conversion.     

Coherent waves in a multiply scattering poro-elastic medium obeying Biot's theory

Twersky's theory is generalized to multiple scattering by a uniform random distribution of cylinders in a poro-elastic medium. The high-frequency regime only, where no dispersion effects occur in the absence of scatterers, is investigated in the frame of Biot's theory. The scatterers lie within a slab of the host medium, and an incident wave gives rise to a fast longitudinal coherent wave, a slow longitudinal one, as well as a shear one in the slab. The dispersion equations of those three coherent waves are derived. The shear coherent wave propagates independently of the other two, while the longitudinal coherent waves obey a coupled dispersion equation involving conversion terms. Numerically speaking, coupling effects are significant only when forward scattering by a single cylinder of the fast wave into the slow one (or the slow wave into the fast) is larger than forward scattering with no conversion.     

Observation of the "Luxemburg-Gorky effect" for elastic waves

An experimental observation of a new nonlinear-modulation effect for longitudinal elastic waves is reported. The phenomenon is a direct elastic wave analogy with the so-called Luxemburg-Gorky (L-G) effect known over 60 years for radio waves propagating in the ionosphere. The effect consists of the appearance of modulation of a weaker initially non-modulated wave propagating in a nonlinear medium in the presence of an amplitude-modulated stronger wave that produces perturbations in the medium properties on the scale of its modulation frequency. The reported transfer of modulation from one elastic wave to another was observed in a resonator cut of a glass rod containing a few small cracks. Presence of such a small damage drastically enhances the material nonlinearity compared to elastic atomic nonlinearity of homogeneous solids, so that the pronounced L-G type cross-modulation could be observed at strain magnitude in the stronger wave down to 10(-7) and smaller. Main features of the effect are pointed out and physical mechanism of the observed phenomena is discussed.     

DISCRETE HUYGENS' MODELLING APPROACH TO WAVE PROPAGATIONS IN A HOMOGENEOUS ELASTIC FIELD

The application of the discrete Huygens' modelling has been discussed for acoustic wave propagation problems, in which the scalar wave field problems have been focused. The present paper extends the application of the modelling to the elastic wave propagation in a homogeneous elastic medium in which two types of waves, the longitudinal wave and the shear wave, are independent except at the boundary. Each wave can be treated like a scalar wave until the two waves reach the boundary where they couple so as to satisfy the displacement or stress boundary condition. We propose the approach confining ourselves to the two-dimensional field. Some examples are demonstrated, whose solutions are compared with the vectorial wave modelling and finite difference modelling solutions whenever they are available.     

Longitudinal and lateral low frequency head wave analysis in soft media

This article studies the influence of the head wave in the lateral and longitudinal components of the displacements generated by the radiation of low-frequency elastic waves in an isotropic and homogeneous soft solid. Low-frequency shear waves are used to characterize elastic properties of soft tissues. In this context, it is useful to have a detailed study of the low-frequency wave field in this kind of material. A soft medium is characterized by the fact that the head wave is found in the source's axis. Even though its amplitude is small compared with the shear wave, it is possible to be observed experimentally by recording consecutive ultrasonic A-lines while the low-frequency wave propagates inside the medium. A standard one-dimensional speckle tracking technique is employed to measure the displacements. Experimental results were interpreted through the exact Green's function solution to the half-space problem. According to the theoretical and experimental analysis, the head wave and surface related terms in general contribute to the displacements in the low-frequency range. This article thoroughly analyzes and experimentally shows the contribution of the head wave for the lateral component, which is not fully addressed by the literature.     

Comparison between the dispersion curves calculated in complex frequency and the minima of the reflection coefficients for an embedded layer

Analytical solutions of Lamb functions for symmetric and antisymmetric elastodynamic modes propagating within a solid layer embedded in an infinite medium are presented. Alternative theoretical analyses of such modes are performed, first in terms of the usual approach of harmonic heterogeneous plane waves (real frequency and complex slowness) and then in terms of transient homogeneous plane waves (complex frequency and real slowness). An example structure of a 0.1-mm-thick "alpha case" (an oxygen-rich phase of titanium that is relatively stiff) plate embedded in titanium is used for the study. A large difference between the usual dispersion curves calculated in real frequency and complex slowness and those calculated in complex frequency and real slowness is shown. Thus the choice between a spatial and a temporal parameter to describe the imaginary part of the guided waves is shown to be significant. The minima and the zeros of the longitudinal and shear plane-wave reflection coefficients are calculated and are compared with the dispersion curves. It is found that they do not match with the dispersion curves for complex slowness, but they do agree quite well with the dispersion curves for complex frequency. This implies that the complex frequency approach is better suited for the comparison of the modal properties with near-field reflection measurements.     

Polarization of elastic waves in tellurium single crystal

We study special cases of elastic bulk wave propagation in a crystal of tellurium, in which the phase velocity of shear waves can exceed those of longitudinal waves. The impact of the piezoelectric effect on the phase velocity and polarization of waves is discussed.     

First-Principles Calculations for Elastic Properties of ZnS under Pressure

The pressure dependence of elastic properties of ZnS in zinc-blende （ZB） and wurtzite （WZ） structures are investigated by the generalized gradient approximation （GGA） within the plane-wave pseudopotential density functional theory （DFT）. Our results are in good agreement with the available experimental data and other theoretical results. From the high-pressure elastic constants obtained, we find that the ZB and WZ structures of ZnS are unstable when the applied pressures are larger than 15.8 GPa and 21.3 GPa, respectively. The sound velocities along different directions for the two structures are also obtained. It is shown that as pressure increases, the sound velocities of the shear wave decrease, and those of all the longitudinal waves increase. An analysis has been made to reveal the anisotropy and highly noneentral forces in ZnS.     

A Helmholtz resonator buried in the ground as a source of seismic waves and low-frequency sound in the atmosphere

The procedure is given for calculating the total power of low-frequency sound and seismic waves produced by a Helmholtz resonator in the form of an air-filled spherical cavity buried in the ground and supplied with a hole through which it is connected with the atmosphere. The sound is generated by air oscillations in the resonator’s neck section that is open to the atmosphere, while the compression and shear elastic waves are generated in the bulk of the ground by cyclic pressure fluctuations that act on the spherical walls of the cavity. Calculations show that the coincidence of the resonance frequencies (within approximately ten to hundred hertz), at which both the sound radiation to the atmosphere and the elastic seismic radiation in the form of longitudinal and transverse bulk waves are maximum, can occur only when the resonator is placed in a loose ground characterized by reduced elastic characteristics. In these conditions, the power of transverse waves exceeds the sound power by a factor of two and the power of longitudinal waves is smaller than the sound power by a factor of several tens.     

Specificity of the phenomenon of acoustoelasticity in a two-dimensional internally structured medium

A two-dimensional model of a microstructured medium is considered in the form of a square lattice consisting of elastically interacting circular particles with translational and rotational degrees of freedom. The interactions between the particles are modeled by a set of elastic springs. Differential equations are derived to describe the propagation and interaction of acoustic waves in such a medium. The relation between the velocities of wave propagation and the small strain arising in the structure under external action is determined. Analytical expressions that determine the difference between the squares of the velocities of both longitudinal and shear waves propagating in two mutually perpendicular directions in a medium with an externally induced anisotropy are derived and analyzed.     

Nonlinear Longitudinal Strain Waves in a Solid Exposed to Pulsed Laser Radiation

The propagation of longitudinal strain waves in a solid with quadratic nonlinearity of elastic continuum was studied in the context of a model that takes into account the joint dynamics of elastic displacements in the medium and the concentration of the laser-induced point defects. The input equations of the problem are reformulated in terms of only the total displacements of the medium points. In this case, the presence of structural defects manifests itself in the emergence of a delayed response of the system to the propagation of the strain-related perturbations, which is characteristic of media with relaxation or memory. The model equations describing the nonlinear displacement wave were derived with allowance made for the values of the relaxation parameter. The influence of the generation, relaxation, and the strain-induced drift of defects and the flexoelectricity on the propagation of this wave was analyzed. It is shown that, for short relaxation times of defects, the strain can propagate in the form of both shock fronts and solitary waves (solitons). Exact solutions depending on the type of relation between the coefficients in the equation and describing both the shock-wave structures and the evolution of solitary waves are presented. In the case of longer relaxation times, shock waves do not form and the strain wave propagates only in the form of solitary waves or a train of solitons. The contributions of the finiteness of the defect-recombination rate and the flexoelectricity to linear elastic moduli and spatial dispersion are determined.     

Temporal analysis of tissue displacement induced by a transient ultrasound radiation force

One of the stress sources that can be used in dynamic elastography imaging methods is the acoustic radiation force. However, displacements of the medium induced by this stress field are generally not fully understood in terms of spatial distribution and temporal evolution. A model has been developed based on the elastodynamic Green's function describing the different acoustic waves generated by focused ultrasound. The function is composed of three terms: two far-field terms, which correspond to a purely longitudinal compression wave and a purely transverse shear wave, and a coupling near-field term which has a longitudinal component and a transverse component. For propagation distances in the shear wavelength range, the predominant term is the near field term. The displacement duration corresponds to the propagation duration of the shear wave between the farthest source point and the observation point. This time therefore depends on the source size and the local shear modulus of the tissue. Evolution of the displacement/time curve profile, which is directly linked to spatial and temporal source profiles, is computed at different radial distances, for different durations of force applications and different shear elastic coefficients. Experimental results performed with an optical interferometric method in a homogeneous tissue-mimicking phantom agreed with the theoretical profiles.     

Localization of a transverse elastic wave in a semibounded acoustic superlattice of ferrimagnetic and superconducting layers: 3. Leaky surface modes and associated resonances

In terms of the effective medium method, conditions for the existence of leaky shear surface acoustic waves in a semibounded fine-layered magnetic superlattice consisting of ferrimagnetic and superconducting layers are determined. On this basis, the possibility of a resonance interaction between a surface elastic SH wave propagating in the magnetic superlattice and a shear bulk wave propagating in the adjacent nonmagnetic medium is investigated.