Reflection and refraction of acoustic waves at the boundary between a magnetoacoustic material and a dielectric

Reflection and refraction of longitudinal and transverse acoustic waves at a plane boundary between an antiferromagnet and a dielectric are studied. The antiferromagnet is assumed to have an easy-plane anisotropy and to be in the state near the orientational phase transition in the magnetic field. A possibility of controlling the angles of the wave-type transformation upon reflection and the refraction angles, as well as all four coefficients of the wave transformation upon reflection and refraction, by the magnetic field is demonstrated. Conditions for the formation of the critical angles of internal reflection and the effect of the magnetic field on their values are specified. A possibility of the radiation of a grazing wave into the material bulk in the vicinity of the phase transition is analyzed.     

Diffraction of guided waves by the end face of a dielectric slab waveguide terminated with a finite conductive strip

The diffraction of guided waves by the end face of a dielectric slab waveguide short circuited with a finite conductive strip is analyzed. An integral equation technique is employed to formulate the corresponding boundary problem. The unknown term in this integral equations is the electric field E(x) on the terminal plane of the waveguide. The homogeneous term is determined from the incident guided wave. A method of moments technique is employed to compute approximately the electric field E(x) by using Laguerre functions as describing and testing functions. The reflection coefficients of the guided waves are computed by using the approximate expression of the E(x) field. Numerical results are given for several guide and conductor plate dimensions.     

Scattering of a plane wave from a periodic random surface: a probabilistic approach

This paper deals with a probabilistic formulation of the wave scattering from a periodic random surface. When a plane wave is incident on a random surface described by a periodic stationary stochastic process, it is shown by a group-theoretic consideration that the scattered wave may have a stochastic Floquet form, i.e. a product of a periodic stationary random function and an exponential phase factor. Such a periodic stationary random function is then written by a harmonic series representation similar to a Fourier series, where Fourier coefficients are mutually correlated stationary processes instead of constants. The mutually correlated stationary processes are represented by Wiener - Hermite functional series with unknown coefficient functions called Wiener kernels. In case of a slightly rough surface and TE wave incidence, low-order Wiener kernels are determined from the boundary condition. Several statistical properties of the scattering are calculated and illustrated in figures.     

Transverse magnetic scattering of two incident plane waves by a dielectric coated cylindrical reflector

Scattering characteristics of two plane waves are investigated for a circular cylinder covered by a dielectric substance. Fields are assumed to be transverse magnetic (TM) and represented in an exponential series form. The diffracted radiations are found by applying the boundary conditions to the wave functions. The wave transformation method and the orthogonality of the exponential functions are respectively employed to obtain an infinite series in the solution. Numerical results are evaluated by reducing the infinite series to a finite number of terms and comparing estimates with the single plane wave scattering situation.     

Approximate method of solving the problem of diffraction of a plane electromagnetic wave by a thin chiral layer covering a perfectly conducting plane

One-sided approximate impedance-type boundary conditions for a thin chiral layer placed on a perfectly conducting plane are derived. With these conditions, the problem of incidence of a plane electromagnetic wave on a chiral structure is solved. Approximate formulas for the coefficients of reflection of the fundamental and depolarized components are derived for the case of the perpendicular polarization of the electromagnetic wave (the electric field strength is normal to the plane of incidence). A comparison with an exact solution to the problem of diffraction by this chiral structure is made.     

电磁偏置各向异性石墨烯界面的传播矩阵

基于电磁场边界条件和相位匹配,推导出电、磁偏置下呈各向异性的石墨烯导电界面的传播矩阵,并进一步给出各向异性石墨烯界面的反透射系数解析解;该传播矩阵耦合了基本的横电波和横磁波极化,并包括偏置电、磁场的影响.将跨石墨烯界面传播矩阵嵌入各向同性分层介质传播矩阵,获得的新传播矩阵可用于解析分析平面电磁波以任意角度入射含各向异性石墨烯界面层状介质时的传播和反透射特性,并且为分层介质与各向异性导电界面复合结构的相关分析和设计提供了一种非常简单的工具.     

声悬浮液滴的表面毛细波及八阶扇谐振荡

采用声悬浮方法研究了自由液滴表面的毛细波形成机理,并利用主动调制声场技术激发了液滴的八阶扇谐振荡.实验结果表明,当声场调制频率接近液滴本征频率的两倍时,液滴将由轴对称受迫振荡向非轴对称扇谐振荡模态转变.实验与理论分析证实,参数共振是毛细波与扇谐振荡的形成原因.扇谐振荡的本征频率随液滴赤道半径的增大而减小,可通过修正的Rayleigh方程来描述. 关键词： 声悬浮 液滴 毛细波 扇谐振荡     

Scattering of a Gaussian beam by an anisotropically coated circular cylinder

A solution to the problem of Gaussian beam scattering by an anisotropically coated circular cylinder is presented. The incident Gaussian beam source is expanded as an approximate expression in the simple form with a Tayor’s series. The transmitted field in the anisotropically coated region is expressed as a infinite summation of eigen plane waves with different polar angles. The unknown coefficients of the scattered fields are obtained with the aid of the boundary conditions. The infinite series can be truncated under the prerequisite of achieving the solution convergence. Only the case of transverse-electric polarization is discussed. The similar formulation of transverse-magnetic polarization can be obtained by adopting the similar method. Some numerical results are presented and discussed. The result is in agreement with that available as expected when the Gaussian beam degenerates to a plane wave incidence case.     

平面波与线性粘弹海底的反射和折射

采用基于广义标准线性体Boltzmann叠加原理的固体流变模型来描述粘弹性海底底质结构,分析了沉积层和基岩的纵、横波速度频散和衰减的特点,计算了海水沉积层界面和沉积层基岩界面位移势反射和折射系数和能量反射和折射系数。结果表明,采取本模型的粘弹性海底的速度频散、衰减和已有文献的实验数据符合较好,能准确的描述海底底质的主要性质,反射和折射系数和声波的频率有关。      

Bulk and Surface Plane Waves Propagated in Chiroferrite in the Transverse Direction

The propagation of volume plane waves in a gyromagnetic chiral medium (chiroferrite) in the plane transverse to the magnetization direction and the propagation of surface waves in the half-space are investigated when an external magnetic field is applied perpendicularly to the direction of wave propagation along the boundary of the medium.     

Free vibration of two elastically coupled rectangular plates with uniform elastic boundary restraints

An analytical method is derived for determining the vibrations of two plates which are generally supported along the boundary edges, and elastically coupled together at an arbitrary angle. The interactions of all four wave groups (bending waves, out-of-plane shearing waves, in-plane longitudinal waves, and in-plane shearing waves) have been taken into account at the junction via four types of coupling springs of arbitrary stiffnesses. Each of the transverse and in-plane displacement functions is expressed as the superposition of a two-dimensional (2-D) Fourier cosine series and several supplementary functions which are introduced to ensure and improve the convergence of the series representation by removing the discontinuities that the original displacement and its derivatives will potentially exhibit at the edges when they are periodically expanded onto the entire x-y plane as mathematically implied by a 2-D Fourier series. The unknown expansions coefficients are calculated using the Rayleigh-Ritz procedure which is actually equivalent to solving the governing equation and the boundary and coupling conditions directly when the assumed solutions are sufficiently smooth over the solution domains. Numerical examples are presented for several different coupling configurations. A good comparison is observed between the current results and the FEA models. Although this study is specifically focused on the coupling of two plates, the proposed method can be directly extended to structures consisting of any number of plates.     

Scattering and active acoustic control from a submerged piezoelectric-coupled orthotropic hollow cylinder

A general exact analysis for three-dimensional scattering of a time-harmonic plane-progressive sound wave obliquely incident upon an arbitrarily thick bilaminated circular hollow cylinder of infinite extent, which is composed of a cylindrically orthotropic axially polarized piezoelectric inner layer perfectly bonded to an orthotropic outer layer, is presented. An approximate laminate model in the context of the so-called state space formulation along with the classical T-matrix solution technique involving a system global transfer matrix is employed to solve for the unknown modal scattering and transmission coefficients. Numerical example is given for an air-filled and water-submerged two-layered elasto-piezoelectric hybrid (steel/PZT4) hollow cylinder insonified by an obliquely incident unit-amplitude plane sound wave. Following the acoustic resonance scattering theory (RST), the total form function amplitude together with the associated global scattering, the far-field inherent background, and the resonance scattering coefficients of the nth normal mode are computed as a function of dimensionless frequency for selected angles of incidence, piezoelectric layer thickness parameters, and electrical boundary conditions (i.e., open/closed circuit or active). Also, the electrical voltage coefficients required for partial or complete cancellation of the reflected sound field are calculated. Limiting cases are considered and good agreements with the solutions available in the literature are obtained.     

平面横电磁波模的初值问题

经典理论所描述的电场和磁场处处同相的平面电磁波模并不存在.Maxwell方程组的解依赖于 电磁场的初始值或边界条件,根据不同的初始条件解得的平面电磁波模是不同的.结果表明 ,平面电磁波是横波,在不同的位置,由变化的电场激发的磁场或由变化的磁场激发的电场 振幅不同,电场与磁场的相位差也不同. 关键词： Maxwell方程组 最优微分方程 初始条件 平面电磁波     

Experimental validation of the scenario of the object microstructure determination using a two-position lidar system: a screen with random transmittance modulation

The two-position system is assembled on the basis of the bistatic sensing scheme. For the screen with random holes, three calibration stages were implemented: the preliminary, local, and microphysical calibrations. The coefficients relating the parameter of angular distortion of the beam passed through the screen to the transverse hole size were determined. For a halfplane-shaped light source, this coefficient is C ₃ = 0.7(21 %), for a point source, C ₃ = 0.8(14 %). These coefficients are close to that relating the diffraction angle of the plane wave at a hole to transverse size C = 0.6.     

Transverse rarefaction of a layer behind the front of a longitudinal wave of nonlinear thermal conductivity and features of plasma formation inside the target cavity

A solution of the two-dimensional problem is presented for a transverse rarefaction wave of a plane layer behind a wavefront of nonlinear thermal conductivity produced by an instantaneous cylindrical energy source with its axis normal to the layer surface. The matter can rarefy through the free surfaces of the layer or through holes in the boundary walls, which are coaxial with the energy source axis. Analytic solutions are obtained describing the formation of the rear boundary in the heated zone due to transverse matter rarefaction. The energy fraction transferred to the energy of hydrodynamic motion is also determined. Models of plasma formation inside the inner target cavity under the action of pulsed energy sources are considered as applications of the approach suggested. Requirements on the source and target parameters are formulated for efficient matter heating with minimum energy losses caused by hydrodynamic rarefaction of the matter. Translated from Preprint No. 14 of the P. N. Lebedev Physical Institute, Moscow (1998).     

Scattering by a homogeneous anisotropic-coated conducting elliptic cylinder

A solution to the two-dimensional scattering properties of a conducting elliptic cylinder coated with a homogeneous anisotropic elliptical shell is obtained. The conducting elliptic cylinder and the shell have the same eccentricity. The transmitted and scattered fields of the anisotropic shell are expressed as Mathieu functions in elliptic coordinates. The unknown coefficients of the scattered and transmitted fields are solved with the aid of the boundary conditions and the Galerkin's method. Only the transverse magnetic (TM) polarization is presented and the transverse electric (TE) polarization can be obtained in the same way. Some numerical results are presented and discussed. As expected the result is in agreement with that available when the coated elliptic cylinder degenerates to a coated circular one.     

Coupling of finite element and boundary integral methods for electromagnetic scattering in a two-layered medium

Consider a time-harmonic electromagnetic plane wave incident on an inhomogeneity embedded in a two-layered medium. In this paper, a method of coupling of finite element and boundary integral equation methods is presented for the solutions of electromagnetic scattering in both transverse electric and magnetic polarization cases. The well-posedness of the continuous and discrete problems, as well as optimal error estimates for the coupled variational approximations, are obtained. Numerical results are included to illustrate the accuracy with the optimal convergence property of the proposed method and to show the wave features in a two-layered medium.     

金属和Kerr非线性介质界面上表面等离子体激元的色散关系

从麦克斯韦方程组出发,结合边界条件,分别得到TM波和TE波在金属和Kerr非线性介质界面上表面等离子体激元的色散关系.由于非线性的存在,TM波的色散关系变得复杂,与光强、非线性系数有关.和线性情况一样,此界面不存在TE波.     

Diffraction of sound by an elastic cylinder near the surface of an elastic halfspace

Diffraction of an acoustic wave by an elastic cylinder near the surface of an elastic halfspace is considered. The solution relies on a Helmholtz-type integral equation and uses the Green function of an elastic halfspace. The latter function is represented in the form of an integral over the Sommerfeld contour on the plane of a complex variable that has the meaning of the angle of the wave incidence on the halfspace boundary. An integral equation for the sound pressure distribution over the cylinder surface is derived. This equation is reduced to an infinite system of equations for the Fourier-series expansion coefficients of this distribution. The results obtained are valid for the diffraction of a cylindrical wave and a plane wave. They also describe the diffraction of a spherical wave when the transmitter and receiver are far from the cylinder and lie in one plane that is orthogonal to the cylinder axis.