Forward ultrasonic scattering from multidimensional solid or fluid inclusions buried in multilayered elastic structures

The scattering of elastic waves by multidimensional objects buried in a multilayered elastic background medium insonified by ultrasonic forces is studied. The framework developed is based on an integral equation formalism for elastic scattering, where a Born approximation for an inhomogeneous background medium is applied to obtain a closed-form expression for the scattered field. Both compressional and shear waves are allowed to propagate inside the layers, and take into account cross-polarization at the boundaries and multiple reflections within the layers to compute the scattered field. The procedure has been tested in cases where the Born approximation is severely put to test (100% contrast in shear modulus).     

Propagation of inhomogeneous plane waves in anisotropic viscoelastic media

A new technique is explained to study the propagation of inhomogeneous waves in a general anisotropic medium. The harmonic plane waves are considered in a viscoelastic anisotropic medium. The complex slowness vector is decomposed into propagation vector and attenuation vector for the given directions of propagation and attenuation of waves in an unbounded medium. The attenuation is further separated into the contributions from homogeneous and inhomogeneous waves. A non-dimensional inhomogeneity parameter is defined to represent the deviation of an inhomogeneous wave from its homogeneous version. Such a partition of slowness vector of a plane wave is obtained with the help of an algebraic method for solving a cubic equation and a numerical method for solving a real transcendental equation. Derived specifications enable to study the 3D propagation of inhomogeneous plane waves in a viscoelastic medium of arbitrary anisotropy. The whole procedure is wave-specific and obtains the propagation characteristics for each of the three inhomogeneous waves in the anisotropic medium. Numerical examples analyze the variations in propagation characteristics of each of the three waves with propagation direction and inhomogeneity strength.     

具有非均匀损伤带状区域中波的传播

对弹性波在二次曲线变化的非均匀损伤介质中的传播理论进行了研究。通过非均匀损伤区两端界面处力的平衡条件和位移连续性条件对方程式进行求解，利用勒让德多项式，求出了二次曲线变化的非均匀损伤介质中波动方程的解析形式解。对带状渐增和渐减的非均匀损伤介质中波的传播进行了实例计算分析，讨论了弹性波在二次曲线变化的非均匀损伤介质中传播的一般性质。     

材料性质对纤维增强复合材料动力学特性的影响

基于弹性动力学理论,对纤维增强复合材料结构中弹性波散射及动应力集中问题进行了分析研究。将非均匀界层区处理为具有相同厚度的多层弹性介质。给出了结构各区域弹性波分析解的表达式。根据位移与应力在界面处的连续条件,确定了弹性波模式系数。给出了界面处动应力集中系数的表达式。作为算例,计算了两种纤维增强复合材料结构中各界面动应力集中系数的数值结果,并分析了界层材料性质以及结构尺寸对各界面动应力集中系数的影响。     

Dynamics of the Moving Ring Load Acting in the System “Hollow Cylinder + Surrounding Medium” with Inhomogeneous Initial Stresses

This paper studies the influence of the inhomogeneous initial stress state in the system consisting of a hollow cylinder and surrounding elastic medium on the dynamics of the moving ring load acting in the interior of the cylinder. It is assumed that in the initial state the system is compressed by uniformly distributed normal forces acting at infinity in the radial inward direction and as a result of this compression the inhomogeneous initial stresses appear in the system. After appearance of the initial stresses, the interior of the hollow cylinder is loaded by the moving ring load and so it is required to study the influence of the indicated inhomogeneous initial stresses on the dynamics of this moving load. This influence is studied with utilizing the so-called three-dimensional linearized theory of elastic waves in elastic bodies with initial stresses. For solution of the corresponding mathematical problems, the discrete-analytical solution method is employed and the approximate analytical solution of these equations is achieved. Numerical results obtained within this method and related to the influence of the inhomogeneous initial stresses on the critical velocity of the moving load and on the response of the interface stresses to this load are presented and discussed. In particular, it is established that the initial inhomogeneous initial stresses appearing as a result of the action of the aforementioned compressional forces cause to increase the values of the critical velocity of the moving load.     

The effect of inhomogeneity and anisotropy on Stoneley waves

Summary In this paper we study the dispersion equation of Stoneley waves that are travelling in an inhomogeneous elastic half-space over an anisotropic homogeneous elastic half-space.The phase velocity is calculated as a function of the wave number. The results indicate that the effect of anisotropy on such waves is small and can be neglected, while the effect of inhomogeneity is very pronounced. The results show that Stoneley waves do not exist after some cut-off value of the wave number.     

Effects of inhomogeneity on surface waves in anisotropic media

This paper investigates the effects of anisotropy and inhomogeneity on surface waves in elastic media. Exponential variation in properties are assumed for the elastic parameters and material density. The classical equations of motion for propagation of waves in an inhomogeneous transversely isotropic elastic solid are deduced. The equations of motion for surface waves are derived and general surface waves are investigated. This general theory is then utilized to investigate Rayleigh, Love and Stoneley waves. Results obtained in the above cases reduce to the corresponding well-known classical results when inhomogeneity and anisotropy are not present. It is seen that inhomogeneity has significant effects on dispersion characteristics. Numerical calculations are included for Love waves and some conclusions have been drawn from the above calculations.     

Acoustic reflection from the boundary of anisotropic thermoviscoelastic solid with fluid

Vertical slownesses of waves at a boundary of an anisotropic thermoviscoelastic medium are calculated as roots of a polynomial equation of degree eight. Out of the corresponding eight waves, the four, which travel towards the boundary are identified as upgoing waves. Remaining four waves travel away from the boundary and are termed as downgoing waves. Reflection and refraction of plane harmonic acoustic waves are studied at a plane boundary between anisotropic thermoviscoelastic solid and a non-viscous fluid. At this fluid-solid interface, an incident acoustic wave through the fluid reflects back as an attenuated acoustic wave and refracts as four attenuating waves into the anisotropic base. Slowness vectors of all the waves in two media differ only in vertical components. Complex values of vertical slowness define inhomogeneous refracted waves with a fixed direction of attenuation, i.e. perpendicular to the interface. Energy partition is calculated at the interface to find energy shares of reflected and refracted waves. A part of incident energy dissipates due to interaction among the attenuated refracted waves. Numerical examples are considered to study the variations in energy shares with the direction of incident wave. For each incidence, the conservation of incident energy is verified in the presence of interaction energy. Energy partition at the interface seems to be changing very slightly with the azimuthal variations of the incident direction. Effects of anisotropy, elastic relaxation and thermal parameters on the variations in energy partition are discussed. The acoustic wave reflected from isothermal interface is much significant for incidence around some critical directions, which are analogous to the critical angles in a non-dissipative medium. The changes in thermal relaxation times and uniform temperature of the thermoviscoelastic medium do not show any significant effect on the reflected energy.     

Energy flux characteristics of inhomogeneous waves in anisotropic thermoviscoelastic media

This study aims to calculate the wave-field characteristics of four attenuating waves in anisotropic thermoviscoelastic medium. An energy balance equation relates the complex-valued energy flux vector to the time-averaged densities of kinetic energy, strain energy and dissipated energy of plane harmonic waves in the medium. A complex slowness vector defines the inhomogeneous propagation of an attenuating wave in the medium. This slowness vector is specified with the phase velocity and the two non-dimensional attenuation parameters of the wave. One of the attenuation parameter defines the inhomogeneity strength of the wave as a measure of its deviation from homogeneous propagation. The phase velocity, attenuation parameters, polarizations of particles, propagation direction are combined to define the group velocity, ray direction and quality factor of attenuation of an inhomogeneous wave in the medium. Numerical examples are considered to study the variations of these characteristics of energy flux with propagation direction and inhomogeneity strength for each of the four attenuating waves in the medium. The effects of anisotropic symmetries are analyzed on the velocities of waves. The decay-rate of energy densities is exhibited with offset in the propagation-attenuation plane.     

Reflection and refraction of plane waves at interface between two piezoelectric media

This paper analyses reflection and refraction of plane waves at a perfect interface between two anisotropic piezoelectric media. The equations of elastic waves, quasi-static electric field, and constitutive relationships for the piezoelectric media are derived. A solution based on the inhomogeneous wave theory is developed to address the inconsistency between the numbers of independent wave modes in the media and the numbers of interfacial boundary conditions to obtain accurate reflection and refraction coefficients in case of strong piezoelectric media, where all the elastic and electric continuity conditions across the interface are satisfied simultaneously. The study shows that there exist independent and zero energy wave modes satisfying the general Snell’s law and propagating along the interface for any incident wave angle. These waves can be treated as pseudo surface waves. It is further found that all the reflection/refraction waves including the pseudo surface waves obey the energy conservation law at the interface boundary. In addition, the analysis also reveals that the reflection and refraction elastic waves can turn into pseudo surface waves at some critical incident angles.     

弹性参数任意变化的非均匀土层的二维受力分析

该文利用线性分层模型模拟弹性参数按任意函数形式变化的非均匀土层,首先求解了覆有非均匀土层的半平面表面受集中线荷载的二维问题,然后以此为基本解,利用奇异积分方程技术求解了表面受刚性体作用的接触问题,计算了给定荷载下的接触表面力和沉降,讨论了弹性模量和泊松比的变化梯度对结果的影响。     

Propagation of inhomogeneous waves in anisotropic piezo-thermoelastic media

A mathematical model for the propagation of harmonic plane waves in an anisotropic piezo-thermoelastic medium is explained through three relations. Two of them relate the stress-induced harmonic variations in temperature and electric potential to mechanical displacement of material particles. The third is a system that defines modified Christoffel equations for wave propagation in the medium. The solution of this system is ensured by a quartic equation whose complex roots explain the existence and propagation of four attenuating waves in the medium. The effects of piezoelectricity and thermoelasticity on the wave propagation are analyzed in the discussion of special cases. An angle between propagation direction and direction of maximum attenuation defines the attenuated wave as inhomogeneous wave. The complex slowness vector for each of the four attenuated waves in the medium is resolved to calculate the phase velocity and the attenuation factor for its propagation as an inhomogeneous wave along a general direction in three-dimensional space. The variations in phase velocities and attenuation factors with propagation direction are computed, for a realistic numerical model.     

Linear <Emphasis Type="Italic">s</Emphasis>-polarized surface waves in a medium inhomogeneous in one dimension

Linear s-polarized surface waves can exist at the boundary between an isotropic homogeneous medium and a medium inhomogeneous in one dimension (1D-inhomogeneous medium). This is related to deformation of the spatial envelope of the electric and magnetic components of the surface wave propagating in the 1D-inhomogeneous medium (in particular, in a plane-stratified medium). Such linear s-polarized surface waves can appear only provided that the refractive index of the inhomogeneous medium increases with the distance from the interface.     

脉冲源反演介质参数的近似波前法

在时域内对弹性波动方程退化的非均匀介质声波方程，引入背景场参数与扰动参数，并化为积分方程形式；针对脉冲源情况，根据射线理论中的传递方程和程函方程，对非均匀介质中的波场形式引入一种波前近似形式，得到波散射点满足散射关系曲线及散射波幅值与介质参数扰动比的代数关系方程式；为求解非均匀介质中散射波场及反演介质参数提供了一种方法，通过对一个完整算例全部过程的模拟，验证了此方法的正确性。     

Disturbance of SH-type waves due to moving stress discontinuity in an anisotropic soil layer overlying an inhomogeneous elastic half-space

The disturbance and propagation of SH-type waves in an anisotropic soil layer overlying an inhomogeneous elastic half-space by a moving stress discontinuity is considered. Stress discontinuity moves with non-uniform velocity and is impulsive in nature. The displacements are obtained in exact form by the method due to Cagniard modified by de Hoop. The numerical result is calculated for special cases and the natures are depicted graphically.     

The Korteweg-de Vries-Burgers hierarchy in fluid-filled elastic tubes

In this work, contribution of higher order terms in modified reductive perturbation method is studied for the propagation of weakly nonlinear waves in fluid-filled elastic tubes. The basic set of equation of fluid and equation of tube is reduced to the Korteweg-de Vries-Burgers equation for the first order displacement component in the radial direction and a linear Korteweg-de Vries-Burgers inhomogeneous equation for the second order displacement component in the radial direction. Dynamical processes of the solitary waves have been numerically analyzed by solving the Korteweg-de Vries-Burgers equation for the first order and the linearized KdV-Burgers equation with an inhomogeneous equation for the second order using pseudo-spectral method.     

On the propagation of waves from spherical and cylindrical cavities in anisotropic materials

The propagation of waves from a spherical or cylindrical cavity in an inhomogeneous anisotropic elastic solid is considered. In the first instance, integral transforms are used to provide solutions to specific boundary value problems involving elastic media exhibiting certain inhomogeneities. It is then noted that the Bergman integral operator method provides a more general analysis. Finally, an asymptotic approach having a wide range of application is discussed and employed to construct wavefront and high-frequency expansions for the solution field in general media.     

非均匀复合材料板中剪切波传播的研究

基于弹性界层中弹性波干涉理论,采用有效介质法,研究了剪切波在非均匀、纤维随机分布复合材料板中的传播,得到了非均匀弹性介质内的有效波数。通过满足弹性有界层的上、下边界条件,得到了非均匀界层中的频散方程。作为特例,绘出了不同参数下板中的前四阶频散曲线。可以看出,非均匀弹性有界层中的频散曲线和均匀界层中的有很大不同。最后分析了纤维和基体特性比、纤维的体积份数以及板厚与纤维半径比对频散曲线的影响。     

Acoustic channels and lenses in a medium with inhomogeneous velocity field

A homogeneous moving medium can feature waveguide propagation of acoustic oscillations, provided that the velocity of medium is inhomogeneous. A waveguide of a finite length is equivalent to a lens. The waveguides and lenses are nonreciprocal, whereby their characteristics are significantly different for the acoustic waves propagating in opposite directions. Estimates are obtained and the possible applications are discussed.