三斜晶体介质中三维平面波的反射

讨论三斜晶体介质半空间应力自由边界处三维平面波的传播.给出了1个寻找三维准P(qP)、准SV(qSV)和准SH(qSH)波的所有3个相速度解析表达式的方法.得出了三斜介质中qP、qSV、qSH波反射系数振幅比的三维闭式解,将其用于研究不同入射角时,对应的反射系数的数值变化,给出了不同极角和方位角时的图示.最后通过数值实例表明,与二维的情况相比较,三维各向异性对反射系数的影响更明显.     

弹性固体和充满两种互不相溶粘性流体的多孔固体之间界面的反射和折射及其衰减波

在充满两种互不相溶粘性流体的多孔固体中,研究弹性波的传播.用3个数性的势函数描述3个纵波的传播,用1个矢性的势函数单独描述横波的传播.根据这些势函数,在不同的组合相中,定义出质点的位移.可以看出,可能存在3个纵波和1个横波.在一个弹性固体半空间与一个充满两种互不相溶粘性流体的多孔固体半空间之间,研究其界面上入射纵波和横波所引起的反射和折射现象.由于孔隙流体中有粘性,折射到多孔介质中的波,朝垂直界面方向偏离.将入射波引起的反射波和折射波的波幅比,作为非奇异的线性代数方程组计算.进一步通过这些波幅比,计算出各个被离散波在入射波能量中所占的份额.通过一个特殊的数值模型,计算出波幅比和能量比系数随入射角的变化.超过SV波的临界入射角,反射波P将不再出现.越过界面的能量守恒原理得到了验证.绘出了图形并对不同孔隙饱和度以及频率的变化,讨论它们对能量分配的影响.     

Transient response of SH waves in a layered half-space with sub-surface and interface cracks

The transient scattering of SH waves by sub-surface and interface cracks parallel to the free surface in a layered elastic solid is investigated. The problem in frequency domain is solved by using a hybrid method which combines the finite element method of the near field with the boundary integral representation of the far field. The transient responses are then obtained by inverting the spectra via fast Fourier transform with the incident pulse Ricker of wavelet. Numerical results are presented for the surface displacements, dynamic stress intensity factors and wave motion in the layered half-space. Furthermore, the propagations of reflected, diffracted, and direct impact waves at any instant are clearly identified by the present method. To understand the mechanism of elastic wave interaction is very important in the field of ultrasonic non-destructive evaluation (NDE) and fracture mechanics studies.     

Reconstruction of a Source from Observational Data

A procedure is described for determining the strength, position, and startup time of a surface force source acting on an elastic half-space from recorded data on the vertical displacements (seismograms) of a linear oscillator (seismograph). The algorithm is based on a previously published analytical solution of the Lamb problem. Special attention is given to the role of the Rayleigh wavefront as a generator of displacements much larger than in the approach of P waves and SV waves to the seismograph, revealing the Rayleigh wave as the primary indicator of a source's space–time position.     

On Love-type waves in a finitely deformed magnetoelastic layered half-space

In this paper, the propagation of Love-type waves in a homogeneously and finitely deformed layered half-space of an incompressible non-conducting magnetoelastic material in the presence of an initial uniform magnetic field is analyzed. The equations and boundary conditions governing linearized incremental motions superimposed on an underlying deformation and magnetic field for a magnetoelastic material are summarized and then specialized to a form appropriate for the study of Love-type waves in a layered half-space. The wave propagation problem is then analyzed for different directions of the initial magnetic field for two different magnetoelastic energy functions, which are generalizations of the standard neo-Hookean and Mooney?CRivlin elasticity models. The resulting wave speed characteristics in general depend significantly on the initial magnetic field as well as on the initial finite deformation, and the results are illustrated graphically for different combinations of these parameters. In the absence of a layer, shear horizontal surface waves do not exist in a purely elastic material, but the presence of a magnetic field normal to the sagittal plane makes such waves possible, these being analogous to Bleustein?CGulyaev waves in piezoelectric materials. Such waves are discussed briefly at the end of the paper.     

An asymmetric wave field in a transversely isotropic elastic medium

A transversely isotropic homogeneous elastic medium excited by a point force perpendicular to the anisotropic axis is considered. The wave field in this medium is constructed and investigated. The front sets of the SV and SH waves are in contact with one another at a point. The front sets in the vicinity of this point are investigated additionally. If we consider the SH wave (or the SV wave) separately, then a false plane front set arises in this region. In considering the SH and SV waves in combination, this false front set disappears. Bibliography: 7 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 332, 2006, pp. 163–174.     

Vibrations of the surface of an elastic double-layered half-space with a periodic system of cracks

The two-dimensional problem of the normal incidence of a plane transverse wave from the far field on to the free surface of an elastic double-layered half-space, comprising a homogeneous layer attached to a semi-infinite base of a different elastic material, is considered. At the boundary between the two media there is a system of plane cracks, arranged periodically along the separation line, which models the fracture zone at the interface between dense solid rock and soft sedimentary rock. The effect of the fractures on the transmission of a transverse seismic wave generated by a deep-focus earthquake, and of the type of vibrations of the free surface of the ground that result, is studied. It is difficult to predict whether the seismic wave is strengthened or weakened by the fracture zone. The effect of the system of cracks on vibrations of the free surface largely depends on the physical and geometrical parameters and, primarily, on the vibration frequencies.     

Surface waves in micropolar thermoelasticity

Free surface waves of arbitrary form in a homogeneous and isotropic linear micropolar thermoelastic half-space with stress-free plane boundary are investigated. It is found that all physical quantities associated with the waves are derivable from two scalar functions and that there exist two families of waves in general. One of these is the classical thermoelastic wave modified under the influence of the microelastic field and the other is a new surface wave not encountered in classical elasticity. The waves are not necessarily plane waves and even when these are assumed to propagate in a fixed direction parallel to the boundary, unlike in classical elasticity, the problem is not one of plane strain. Explicit expressions for the displacement vector, microrotation vector and the temperature are obtained and the nature of deformation has been analysed. Several earlier results are deduced as particular cases of the more general results obtained here.     

Scattering of Plane Elastic Waves on a Small Obstacle Inside a Layer

The problem on the diffraction of a plane elastic wave with horizontal polarization (SH wave) on a small obstacle placed in a layer is investigated. The layer is situated on a half-space with stress-free boundary. The obstacle is assumed to be a circular cylinder with radius small in comparison with the length of the incident wave. The polarization of the incident wave is parallel to the axis of the cylinder. It is proved that the small inhomogeneity radiates as a linear source such that the intensity of the radiation is proportional to the area of the cross-section of the obstacle and the jump of the squared transverse velocities in the layer and in the obstacle. Bibliography: 5 titles.     

Rayleigh type wave dispersion in an incompressible functionally graded orthotropic half-space loaded by a thin fluid-saturated aeolotropic porous layer

This paper is concerned with the Rayleigh wave dispersion in an incompressible functionally graded orthotropic half-space loaded by a thin fluid-saturated aeolotropic porous layer under initial stress. Both the layer and half-space have subjected to the incompressible in nature. The particle motion of the Rayleigh type wave is elliptically polarized in the plane, which described by the normal to the surface and the focal point along with wave generation. The dispersion of waves refers typically to frequency dispersion, which means different wavelengths travel at a different velocity of phase. To deal with the analytical solution of displacement components of Rayleigh type waves in a layer over a half-space, we have taken the assistance of different methods like exponential, characteristic polynomial and undetermined coefficients. The dispersion relation has been derived based upon suitable boundary conditions. The finite difference scheme has been introduced to calculate the phase velocity and group velocity of the Rayleigh type waves. We also have derived the stability condition of the finite difference scheme (FDS) for the phase and group velocities. If a wave equation has to travel in the time domain, it is necessary to achieve both accuracy and stability requirements. In such cases, FDS is preferred because of its power, accuracy, reliability, rapidity, and flexibility. The effect of various parameters involved in the model like non-homogeneity, porosity, and internal pre-stress on the propagation of Rayleigh type waves have been studied in detail. Graphical representations for the effects of various parameters on the dispersion equation have been represented. Numerical results demonstrated the accuracy and versatility of the group and phase velocity depending on the stability ratio of the FDS.     

Scattering theory for the elastic wave equation in perturbed half-spaces

In this paper we consider the linear elastic wave equation with the free boundary condition (the Neumann condition), and formulate a scattering theory of the Lax and Phillips type and a representation of the scattering kernel. We are interested in surface waves (the Rayleigh wave, etc.) connected closely with situations of boundaries, and make the formulations intending to extract this connection.

The half-space is selected as the free space, and making dents on the boundary is considered as a perturbation from the flat one. Since the lacuna property for the solutions in the outgoing and incoming spaces does not hold because of the existence of the surface waves, instead of it, certain decay estimates for the free space solutions and a weak version of the Morawetz arguments are used to formulate the scattering theory.

We construct the representation of the scattering kernel with outgoing scattered plane waves. In this step, again because of the existence of the surface waves, we need to introduce new outgoing and incoming conditions for the time dependent solutions to ensure uniqueness of the solutions. This introduction is essential to show the representation by reasoning similar to the case of the reduced wave equation.

     

Propagation of longitudinal viscoelastic waves in a three-layer medium

The nonstationary problem of propagation of a longitudinal plane one-dimensional stress wave through a plane-parallel viscoelastic layer of finite thickness separating two linear elastic half-spaces with different properties is solved in the linear formulation. A plane wave traveling in one of the half-spaces is normally incident on the boundary of the layer (one-dimensional problem). The field in the other elastic half-space, excited as a result of the multiple reflection of the fronts from the boundaries of the layer, is investigated. Graphs of the small displacements at a given point of the elastic half-space are presented. The solution of the problem is based on the dynamic correspondence principle formulated by Bland [3].Central Scientific-Research Institute of Machine Building, Moscow. Translated from Mekhanika Polimerov, No. 1, pp. 151–156, January–February, 1971.     

An energy approach to the proof of the existence of Rayleigh waves in an anisotropic elastic half-space

An approach based on investigating the energy functional is applied for the first time to the classical problem of Rayleigh waves in an anisotropic half-space with a free boundary. The main object of the investigation is an ordinary differential operator in a variable characterizing the depth. An investigation of the spectrum by variational methods enables a new proof to be given of the existence of a Rayleigh wave in a linear elastic half-space with arbitrary anisotropy, which does not rest on the Stroh formalism.     

磁场对液体-微伸缩固体介面波传播的影响

在一个传播理想的非粘性液体半空间,和一个传播理想的微伸缩弹性固体半空间之间,研究介面处纵波的反射和透射.在两个半空间中,满足介面处必需的边界条件下,得到控制方程的适当解,是一组以不同反射和透射波振幅比表示的5个非齐次方程.以水和铝-环氧树脂合成材料介面为实际例子,用Gauss消除法的Fortran程序求解方程组.考虑存在和不存在外加横向磁场两种情况,在某些入射角范围内,计算振幅比的数值解.最后用图形给出横向磁场对不同反射和透射波振幅比的影响.     

Boundary layer method in the problem of far propagation of surface SV-waves

The SV polarized wave field is investigated in an elastic gradient layer of constant width. A point source is situated on the boundary of the layer. Rigid contact conditions are assumed to be valid on the boundary between the layer and an elastic half-space. It is shown that the interference field in the principal approximation far from the source does not depend on the relation between the phase velocity and the transversal and longitudinal velocities in the half-space. Bibliography: 11 titles.     

Higher-Order Asymptotic Approximations for Surface Love Waves of SH Type in Tranversely Isotropic Elastic Media

A uniform asymptotics of the surface Love modes for a special case of anisotropy (tranverse isotropy) of an elastic media is obtained. In constructing the asymptotics of surface waves, the space-time (ST) ray method is employed. The wave field of each Love mode is represented as the sum of the ST caustic expansion involving the Airy functions with a real eikonal and two correction terms that are ST ray solutions, which in fact are inhomogeneous waves with complex eikonals. The eikonals and coefficients of the caustic and ray series are sought in the form of expansions in powers of two variables. The first variable is the distance from the surface, whereas the other characterizes the proximity of the caustic of a ray field to the boundary surface. Thanks to the specific structure of the elasticity tensor for a transversely isotropic medium, the boundary surface is necessarily a plane. A recursion process of computation of higher terms of the asymptotic expansion allows one to trace the conversion of the formulas obtained to the known ray solutions for isotropic elastic media. Relations between the elasticity parameters of a medium are obtained that ensure the existence of SH Love waves in a transversely isotropic medium and that are consistent with the conditions of the positiveness of the elastic energy of deformation. Bibliography: 6 titles.     

Rayleigh wave motions in an orthotropic half-space under time-harmonic loadings: A theoretical study

Rayleigh surface wave motion in a homogeneous orthotropic elastic solid half-space under time-harmonic sources is theoretically investigated. In this article, closed-form expressions of the Rayleigh wave field as a result of a time-harmonic concentrated line load are simply determined by using reciprocity theorems. For the verification purpose, analytical predictions are also obtained through Fourier transform technique with the aid of the residue theorem. The solutions found by the two approaches are shown to be mathematically the same. As an example of calculation, surface waves due to a set of buried loadings in the orthotropic half-plane are then examined in detail. A discussion of these results is presented to explore the influence of the loading types on the displacement amplitudes of the generated wave fields.     

High-frequency asymptotics of acoustic pressure for bounded wave beam scattering by an elastic sphere

Asymptotic high-freqeuncy estimates are obtained for the amplitudes of specular and non-specular reflections with extraction of the contribution of sound reradiation into the surrounding medium by Rayleigh type surface elastic waves. The conditions are found that govern the magnification of scattering in the opposite direction. The theoretical explanation of the book reflection effect /1/ for bounded sound beam incidence on the plane interface of a fluid-elastic solid is given by many authors in different situations (/12/, say). As for non-specular reflection of a plane sound wave by bounded elastic bodies (plates, cylinders, rods, and shells enclosed in a screen), studied most thoroughly in /3–9/, this effect is a consequence of satisfying the space-time resonance conditions between the incident acoustic wave and the normal surface waves excited in an elastic solid under total internal reflection.     

On the Rayleigh wave on a curvilinear boundary between elastic and fluid media

Along the boundary between elastic and fluid media, the surface Rayleigh wave propagates. The velocity of this wave v _R0 in the case of a plane boundary is less than the velocity of the Rayleigh wave v _R on a free plane boundary of an elastic medium and less than the velocity v _P0 in a fluid medium. To investigate the velocity v _R0 in the case of curvilinear boundaries, the propagation of Rayleigh waves under consideration along cylindrical and spherical surfaces is studied. The velocity of the Rayleigh wave depends on the curvature of the wave trajectory and the curvature in the direction perpendicular to the trajectory. Furthermore this velocity depends on the presence or absence of a fluid medium. Bibliography: 5 titles.     

A complementary theory of light scattering by homogeneous spheres

A theory of the scattering of electromagnetic waves by homogeneous spheres, the so-called Mie theory, is presented in a unique and coherent manner in this paper. We begin with Maxwell's equations, from which the vector wave equations are derived and solved by means of the two orthogonal solutions to the scalar wave equation. The transverse incident electric field is mapped in spherical coordinates and expanded in known mathematical functions satisfying the scalar wave equation. Determination of the unknown coefficients in the scattered and internal fields is achieved by matching the electromagnetic boundary conditions on the surface of a sphere. Far-field solutions for the electric field are then given in terms of the scattering functions. Transformation of the electric field to the reference plane containing incident and scattered waves is carried out. Extinction parameters and the phase matrix are derived from the electric field perpendicular and parallel to the reference plane. On the basis of the independent-scattering assumption, the theory is extended to cases involving a sample of homogeneous spheres.