SH Waves in a Homogeneous Transversely Isotropic Medium Generated by a Concentrated Force

SH waves in homogeneous, transversely isotropic media generated by a concentrated force are investigated. To this end, we construct the part of the Green tensor responsible for SH waves and derive its asymptotics at large distances from the source point. Bibliography: 7 titles.     

The Effect of Inhomogeneity of Elastic Properties on the Stress State in Composite Cylindrical Panels

The effect of inhomogeneity of elastic properties in the circumferential direction on the distribution of stress and displacement fields in orthotropic cylindrical panels is studied. The mechanical properties of the panels and the load acting on them are constant in the axial direction, which makes it possible to neglect the influence of the curvilinear ends. From the initial relations of a three-dimensional problem of the elasticity theory of inhomogeneous anisotropic bodies, a resolving system of partial differential equations is obtained, whose solution is presented in the form of truncated Fourier series, so that the conditions of free support of the rectilinear ends are satisfied. This allows us to separate the variables and to get a system of ordinary high-order differential equations, which is integrated by a stable numerical method. The problem on the stress-strain state of an orthotropic composite panel with a varying relative volume content of reinforcing elements in the circumferential direction is solved. The effect of the change in the reinforcement density on the stresses and displacements of the panel is studied.     

横观各向同性压电材料中正三角形孔口快速传播裂纹的解析解

利用复变函数方法,通过引入合适的数值保角映射研究了横观各向同性压电材料中正三角形孔口快速传播裂纹的反平面剪切问题,并在电非渗透型与电渗透型两种边界条件下,结合柯西积分,导出了力-电耦合作用下以速度v传播时的Ⅲ型裂纹的动态应力强度因子和电位移强度因子的解析解.最后,考虑面内电载荷和面外机械载荷共同作用,分析了三角形孔尺寸、裂纹尺寸、外载变化对裂尖场强度因子的影响.     

Scattering by a Cylindrical Trap in the Critical Case

We study a two-dimensional analog of the Helmholtz resonator with walls of finite thickness in the critical case, for which there exists a frequency which is simultaneously the limit of poles generated both by the bounded component of the resonator and by a narrow communication channel. Under the assumption that the limit frequency is a simple frequency for the bounded component, by using the method of matched asymptotic expansions, we construct asymptotics for the two sequences of poles converging to this frequency. We obtain explicit formulas for the leading terms of the asymptotics of poles and for the solution of the scattering problem.     

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.     

Electromagnetic Scattering in a Two-layered Medium

The object of this paper is to investigate the three-dimensional electro- magnetic scattering problems in a two-layered background medium. These problems have an important application in today＇s technology, such as to detect objects that are buried in soil. Here, we model both the exterior impedance problem and the inhomogeneous medium problem in R3. We establish uniqueness and existence for the solution of the two scattering problems, respectively.     

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.     

微极各向同性弹性板中的Rayleigh-Lamb波

研究了无应力作用条件下，均匀、各向同性、圆柱形微极结构弹性板中波的传播．导出了对称和斜对称模式下波传播的特征方程．对短波这一极端情况，无应力圆板中对称和斜对称模态波的特征方程退化为Pmyle曲表面波频率方程．并得到薄板的计算结果．给出了位移和微转动分量，并绘制了相应图形．给出了若干特殊情况的研究结果及对称和斜对称模态特征方程的图示．     

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.     

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.     

An Analysis of the Decay of Saint-Venant End Effects in a Transversely Isotropic Matrix with an Isotropic Covering

A calculation model is proposed for a numerical analysis of the decay of Saint-Venant end effects in a laminate material of irregular structure to which corresponds a transversely isotropic matrix with an isotropic covering. The elastic properties of the matrix correspond to those of a unidirectional glass-fiber-reinforced plastic. The problem is investigated within the framework of the concept of a representative element of the material. The decay of the end effect in the direction perpendicular to the isotropy plane of a transversely isotropic matrix for the case of symmetric deformation of the material is considered. The source of the end effect is simulated by a piecewise-constant periodic surface load. This load is local for the calculated region and changes within a part of the boundary comparable with the typical size of the structural heterogeneity of the material. The equations of the linear elasticity theory of orthotropic bodies, a model of piecewise-homogeneous media, and quantitative criteria of decay of the end effect are used. Starting from the base system of equations, a discrete problem is constructed and solved. The results of a computing experiment for the choice of a representative element and the results of determining the maximum extent of the end-effect zone for this element are presented.     

任意形状凸起地形对平面SH波的散射

将具有任意形状的凸起地形对称态SH波散射问题转换为契合问题加以研究,利用求解弹性波动问题的复变函数与保角映射方法,在包括任意形状凸起边界在内的一个区域中,构造一个在凸起边界上应力自由,其他部分位移和应力均为任意的驻波解,然后再将这个驻波解与其余下的区域中的散射波解在两个区域结合面上完成契合过程,由此决定出这两个区域中的驻波和散射波解答,最后对圆弧形和半椭圆形凸起进行了数值计算,并将计算结果与有限元法的数值解进行了比较。     

Asymptotics of the Wave Field in the Vicinity of the Symmetry Axis of a Transversely Isotropic Homogeneous Medium

Asymptotic formulas for the wave field, which describe the kiss singularity in a homogeneous transversely isotropic medium, are obtained. A physical interpretation of the results is presented. Bibliography: 10 titles.     

A Crack with Interfacial Bonds in an Isotropic Medium Strengthened with a Regular System of Stringers

An isotropic medium containing a system of foreign transverse rectilinear inclusions is considered. Such a medium can be interpreted as an infinite plate strengthened with a regular system of ribs (stringers) whose cross section is a very narrow rectangle. The medium is weakened by a rectilinear crack. The action of the stringers is replaced with unknown equivalent concentrated forces at the points of their connection with the medium. A model of a crack with areas where its faces interact with each other is investigated. This interaction is modeled by introducing bonds (adhesion forces) between faces in the crack tip zone. The boundary-value problem on equilibrium of the crack under the action of external tensile forces is reduced to a nonlinear singular integral equation, from the solution of which the tractions in the bonds are found. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 6, pp. 773–782, November–December, 2005.     

无限横观各向同性弹性圆柱中刚性圆盘的扭转振动

分析了无限横观各向同性弹性圆柱中，刚性圆盘的扭转振动问题．绘制的图形显示了材料的各向异性性质对应力强度因子的影响．     

竖直薄板浸没在表面覆盖冰层海水中时的水波散射

研究在一片均匀薄冰所覆盖的深水中,浸没其间的竖直平板引起的水波散射,冰层看作弹性薄板.通过对障碍物前方的势函数微分,问题被归结为一个超奇异的积分方程,应用适当的Green积分定理,应用一个包含Chebyshev多项式的有限级数配置法,求解该积分方程.得到反射系数和透射系数的数值结果,并在不同的波数和覆盖冰层参数下,用图形表示出来.     

Scattering by a perfect conductor in a waveguide: energy-preserving schemes for integral equations

^** Email: darkovolkov{at}yahoo.ca, darko{at}wpi.edu The scattering matrix for a perfectly conducting electricalcylinder (or a sound hard obstacle) in a waveguide is unitary.This is a well-known result which is a consequence of the conservationof power. When a numerical method is employed to approximatethe reflection and transmission coefficients of the cylinder,an approximate scattering matrix can be constructed. An integralequation of the second kind for an unknown density can be solved,and the density can then be used for computing the entries ofthe approximate scattering matrix. We show that this approximatematrix is unitary for cylinders of symmetric cross-section,regardless of the order of the approximation. In the nonsymmetriccase, the approximate scattering matrix still satisfies a conservationof energy condition, albeit in an unfamiliar form. As the orderof the approximation is increased, conservation of energy isalso satisfied in the more familiar form to machine accuracy.     

Stress Concentration near an Opening in a Composite Shell with Account of Material Inhomogeneity

Based on the theory of Timoshenko-type shells, the influence of material inhomogeneity on the stress concentration in a shell with an opening is investigated. Mechanical characteristics of the shell material in the opening zone vary according to a given linear law. The problem is solved by a variational-difference method. Results for a spherical orthotropic shell with a polar circular opening are presented.     

双空间指示函数方法在三维柱面对称波导中电磁波的反散射问题的推广

给出了双空间指示函数方法在三维柱面对称波导中电磁波的反散射问题的推广.基于这个观察:当Green函数的点源在障碍物内部时,那么远域数据的赋权积分可以很好地近似估计Green函数,但是当Green函数的点源在障碍物外部时,那么远域数据的赋权积分就不能很好地近似估计Green函数.建立一个积分方程:它的右边是点源在所重构区域的Green函数,那么我们可以知道这个积分方程的解的范数在未知障碍物的内部有极大值,而这些取得极大值的点所围成的区域恰好就是所重构的障碍物区域.方法最显著的优势在于它不依赖于未知障碍物的边界条件.     

Interaction of Moving Localized Oscillations with a Local Inhomogeneity in Nonlinear Hamiltonian Klein–Gordon Lattices

We study the interaction of moving localized oscillations with a local inhomogeneity in a discrete nonlinear Hamiltonian system. We conjecture that resonance with a static nonlinear localized oscillation centered at the local inhomogeneity is a necessary condition for observing the trapping phenomenon. Analytic calculations and numerical simulations agree well with our hypothesis.