Diffraction of Plane Electromagnetic Waves on a Small Obstacle Inside a Layer

The problem on the diffraction of the electromagnetic plane wave on a small obstacle in a layer is investigated. The obstacle is assumed to be a circular cylinder and its radius is small in comparison with the length of the incident wave. It is proved that the small obstacle radiates as a linear source. Its intensity is proportional to the area of a cross-section and the jumps of the dielectric and magnetic constants on the interfaces. Bibliography: 4 titles.     

Diffraction of Plane Elastic Waves with Vertical Polarization on a Small Obstacle in a Layer

The problem on the diffraction of elastic plane waves with vertical polarization on a small obstacle (elastic inhomogeneous inclusion) inside a layer is investigated. The layer is situated on an elastic half-space. A three-layer model of isotropic elastic media is considered. The obstacle is assumed to be a circular cylinder with radius that is small in comparison with the length of the incident wave. The polarization of the incident wave is assumed to be orthogonal to the axis of the cylinder. The diffractional addition on the small obstacle to the reflected wave in an elastic layer is proved to have a larger order than the order of the first term with respect to the parameter , where is the wave number, r is the distance between the obstacle and the observation point. The small obstacle generates a cylindrical wave the intensity of which is proportional to the area of the cross-section of the obstacle and to the jumps of the square velocities in the layer and in the obstacle. Bibliography: 6 titles.     

Scattering of Plane Electromagnetic Waves on a Small Inhomogeneity in a Slightly Curved Layer

The diffraction problem for the electromagnetic plane wave scattered on a small inhomogeneity in a slightly curved layer is investigated. The inhomogeneity is assumed to be a cylinder. The area of the cross-section and the the diameter of the cylinder are small in comparison with the length of the incident wave. It is proved that the small inhomogeneity radiates as a point source the power of which is proportional to the area of the cross-section and to the jumps of the dielectric and magnetic constants on the interfaces. The bend of the layer manifests itself in the exponential factors of reflected and refracted waves and in the radiation pattern of scattered waves. Bibliography: 10 titles.__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 297, 2003, pp. 93–115.     

Scattering of Plane Electromagnetic Waves from a Small Inhomogeneity in a Slightly Curved Layer

The problem on the diffraction of the elastic plane wave of horizontal polarization (SH wave) from a small inhomogeneity lying in a slightly bent layer is investigated. The layer is situated on the boundary of a half-space. The inhomogeneity is assumed to be a cylinder the cross-section diameter of which is small in comparison with the length of the incident wave. The wave is polarized parallel to the axis of the cylinder. It is proved that the small inhomogeneity radiates as a point source the intensity of which is proportional to the area of the cross-section of the inhomogeneity and to the jumps of the squared velocities in the layer and in the inhomogeneity. Bibliography: 10 titles.__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 297, 2003, pp. 106–115.     

Scattering on a Small Inhomogeneity in an Elastic Medium

Problems on the diffraction of elastic plane waves (transverse and longitudinal) scattered on a cylinder are investigated. The radius a of the cylinder is small enough ( , where is the wave number). The waves of horizontal polarization (SH waves) are scattered similarly to the electromagnetic wave of the respective polarization. It is proved that a small inhomogeneity radiates as a point source, with its amplitude proportional to the difference of the Lamé parameters and and to the area of a cross section of the inhomogeneity. The scattering of a plane wave of vertical polarization is subject to a more complicated law of radiation, because of the vector nature of the problem, and the respective components of the displacement vector are represented in terms of the scalar and vector potentials. However, the scattering of the wave field on the small inhomogeneity has qualitatively the same asymptotic behavior as in the case of the SH wave. Bibliography: 4 titles.     

Scattering of Plane Harmonic Waves in an Infinite Elastic Solid by an Arbitrary Configuration of Two-dimensional Obstacles

The problem of the multiple scattering of plane harmonic wavesin an infinite elastic solid by arbitrary configurations oftwo-dimensional obstacles is considered. Sets of integral equationsrelating the multiple scattering functions to the single scatteringfunctions are derived. The integral equations are replaced bya set of algebraic equations which are then solved by an iterativeprocedure. Some results are given for the scattering of a planeharmonic P or SV wave by an identical pair of parallel circularcylindrical cavities.     

Scattering Frequencies and a Class of Perturbed Systems of Elastic Waves

We consider the system of elastic waves in three dimensions under the presence of an impurity of the medium which we represent by a real-valued function q(x) (or q(x,t)). The medium is assumed to be isotropic and occupies the whole space Ω = ℝ³. We study the location of the scattering frequencies associated with such phenomenon. We conclude that there is a large region on the complex plane which is free of scattering frequencies. In the remaining region they are discrete provided that q satisfies suitable assumptions concerning its behaviour at infinity.     

On the Reciprocity Principle in the Scattering of Plane Electromagnetic Waves by a Conic Scatterer

Let a plane electromagnetic wave be scattered by a perfectly conducting cone. The diffraction process creates a spherical wave scattered by the vertex of the cone. The diffraction coefficients of this wave, whose analytic expressions are derived in the present paper, possess some symmetry properties. Bibliography: 2 titles.     

多孔弹性层的刚性边界对扭转表面波传播的影响

根据介质的力学性能,正如Cowin及Nunziato一样,导出多孔弹性层覆盖在多孔弹性半空间上时,研究其刚性边界对扭转表面波传播的影响.导出了速度方程并对其结果进行了讨论.发现介质中可能存在两类扭转表面波阵面,而Dey等(Tamkang Journal of Science and Engineering,2003,6(4):241-249.)给出的没有刚性边界面时,存在3类扭转表面波阵面.研究还揭示,多孔弹性层中Love波也可能随同扭转表面波一起存在.值得注意的是,刚性边界面多孔弹性层中Love波的相速度,不同于自由边界面多孔弹性层中的相速度.实际观察到扭转波的色散性,以及速度随着振荡频率的增大而减小.     

Interaction of Elastic Waves

We derive and analyze asymptotic equations for the interaction of weakly nonlinear elastic waves. We show that there are resonant triads involving two transverse and one longitudinal wave provided the wave speeds satisfy a certain irrationality condition. We study initial value and signaling problems, and the interaction of sawtooth wave packets.     

Numerical Study of Properties of Quasilocal Plane Waves of the Modal Type in the Case of a Thin Low-Velocity Layer that is in Contact with an Elastic Half-Space

Numerical study of properties of quasilocal plane waves of the modal type propagating deep into a medium is carried out with the example of the model of a low-velocity elastic layer in the case of rigid contact with the underlying half-space. It is established that the genesis of these waves is closely related to singular complex roots of the dispersion equation of the problem. Eighteen variants of the model differing by relative parameters of the problem, which have a physical meaning, are considered. For every variant, seismograms of modal and body waves are computed and a comparison of them in intensity is carried out. Bibliography: 4 titles. Dedicated to P. V. Krauklis on the occasion of his seventieth birthday __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 308, 2004, pp. 182–196.     

弹性和电-微拉伸广义热弹性固体中的平面波在不完全边界上的传播

讨论了平面波入射在弹性固体(介质(M))和电-微拉伸广义热弹性固体(介质M)的界面上时,波的反射和透射问题.介质M中存在5种反射波(纵向位移(LD)波、热(T)波、纵向微拉伸(LM)波和2种横向耦合位移和微转动波(CD(Ⅰ)和CD(Ⅱ)波));介质(M)中存在2种透射波(纵(P)波和横(SV)波).得到不完全边界上不同反射波和透射波的振幅比,并导出法向力刚度、切向力刚度和完全粘接时的振幅比.对LD波和CD(Ⅰ)波,图示出振幅比随不同入射角的变化.显示出反射波和透射波的振幅比受到介质的刚度、电场、拉伸和热特性的影响.推演出一些有价值的特例.     

Scattering of Inertial Waves in a Rotating Fluid

The scattering of plane inertial waves by both a flat strip and a circular cylinder whose generators are perpendicular to the rotation vector is examined. The properties of the reflected and diffracted fields, viz. spatial decay, propagation, structure, etc....are contrasted with those of the classical scattering fields in the limit where the wave length is small compared to the size of the scatterer.     

Torsion Waves on the Cylindrical Surface of a Semiinfinite Elastic Medium

Torsion waves on a cylindrical cavity in a semiinfinite elastic medium are investigated. The waves are generated by steady-state torsional vibrations of a flat, circular punch coupled with the half-space. A technique of contour transformation of the integrals involved in problems of this kind is described. An algorithm and numerical results are given for calculating the modulus of the complex amplitude of the displacement vector on the cylindrical surface as a function of the vertical coordinate in both the near and far fields.     

双I—型裂纹断裂动力学问题的非局部理论解

研究了非局部理论双中I－型裂纹弹性波散射的力学问题,并利用富里叶变换使本问题的求解转换为三重积分方程的求解,进而采用新方法和利用一维非局部积分核代替二维非局部积分核来确定裂纹尖端的应力状态,这种方法就是Schmidt方法,所得结是比艾林根研究断裂静力学问题的结果准确和更加合理,克服了艾林根研究断裂静力学问题时遇到的数学困难,与经典弹性解相比,裂纹尖端不再出现物理意义下不合理的应力奇异性,并能够解释宏观裂纹与微观裂纹的力学问题。     

Conformal Geometry of Gravitational Plane Waves

By Brinkmann’s theorem the only Ricci flat and nonflat 4-manifolds admitting non-homothetic conformal vector fields are certain pp-waves. It seems that the converse direction was never completely clarified Which metrics really do occur? It is well known that the conformal group of a nonconformally-flat spacetime is atmost seven-dimensional and that seven is attained for certain pp-waves. Here we explicitly determine all solutions with a seven-dimensional conformal group. In other words We determine all Ricci flat Lorentzian manifolds admitting a seven-dimensional conformal group. They come in three particular families of gravitational plane waves. All of them are exact analytic solutions in terms of elementary functions. Furthermore, it turns out that Ricci flat Lorentzian manifolds with a six-dimensional conformal group are not necessarily real analytic.