多排任意排列的弹性桩屏障对平面P波或SV波多重散射

提出可计算任意排列、任意圆截面多排弹性桩屏障对平面P波或SV波的多重散射理论方法,可弥补单重散射假定只在散射体截面尺寸相对入射波长可忽略情况下成立的不足,并考虑桩与桩间互相干涉现象。散射过程定义任意一弹性桩对入射P波或SV波的散射为第一重,第二重散射可将第一重散射波作为次生波源,继而对所有散射体皆遵循此过程;每一重散射均在桩土边界满足应力及位移连续条件,从而获得前一重与后一重散射的波函数迭代关系;总散射波场可由所有散射体各重散射叠加获得。数值计算考查相同截面多排桩屏障的散射重数、桩距、排距、桩土模量比等参数对屏障隔离效果影响。该方法可作为实际工程隔振设计理论参考依据。     

Coupled electromagnetic and elastic waves in random media

In this paper we have considered the wave propagation in a random medium embedded in a constant primary magnetic field after Karal[l]. The deviation of the magnetic permeability from homogeneity affects the frequency of the wave. A particular case taken the correlation, $\text{R}{}_{\mathrm{\mu 2\mu 2h}}\text{= <μ3}{}^2$$\text{e}{}^{\mathrm{?r/a}}$ where $\text{a}$ is the correlation length of inhomogeneity, has been considered.     

Some results on finite amplitude elastic waves propagating in rotating media

Summary. Two questions related to elastic motions are raised and addressed. First: in which theoretical framework can the equations of motion be written for an elastic half-space put into uniform rotation? It is seen that nonlinear finite elasticity provides such a framework for incompressible solids. Second: how can finite amplitude exact solutions be generated? It is seen that for some finite amplitude transverse waves in rotating incompressible elastic solids with general shear response the solutions are obtained by reduction of the equations of motion to a system of ordinary differential equations equivalent to the system governing the central motion problem of classical mechanics. In the special case of circularly-polarized harmonic progressive waves, the dispersion equation is solved in closed form for a variety of shear responses, including nonlinear models for rubberlike and soft biological tissues. A fruitful analogy with the motion of a nonlinear string is pointed out.     

流体饱和半空间中埋置球面P1、P2和SV波源动力格林函数

基于Biot流体饱和孔隙介质理论,采用Hankel积分变换方法,在频域内求解了流体饱和半空间中埋置球面P1、P2和SV波源的动力格林函数。首先由Hankel积分变换将空间域内球面波展开为波数域内柱面波的叠加;然后在半空间表面对称位置虚拟放置一同样大小的球面波源,这样对于球面膨胀波源(P1和P2波源),地表剪应力为零,但存在非零正应力和孔隙水压,对于球面剪切波源(SV波源),地表正应力和孔隙水压为零,但存在非零剪应力;最后叠加球面波源、虚拟波源和残余半空间表面应力产生的动力响应,即可求得流体饱和半空间中埋置球面波源波数域内的动力响应,空间域内埋置球面波源的动力格林影响函数则由Hankel逆变换求得。该文给出的球面波源动力格林函数,为建立以球面P1、P2和SV波动力格林函数为基本解的间接边界元方法,求解饱和多孔介质中三维轴对称弹性波散射问题奠定了基础。     

Exact solution for nonlocal vibration of double-orthotropic nanoplates embedded in elastic medium

An analytical approach for free vibration analysis of all edges simply-supported double-orthotropic nanoplates is presented. The two nanoplates are assumed to be bonded by an internal elastic medium and surrounded by external elastic foundation. The governing equations are derived based on the nonlocal theory and the expressions of the natural frequencies are proposed in an explicit form. The suggested model is justified by a good agreement between the results given by present model and available data in literature. The model is used to study the vibration of double-orthotropic nanoplates for three typical deformation modes. The influences of small scale coefficient, stiffness of the external and internal mediums and aspect ratio on the frequencies of the double-orthotropic nanoplates are also elucidated.     

Closed-form approximations for the angle-of-arrival variance of plane and spherical waves propagating through homogeneous and isotropic turbulence

The calculation of the aperture-averaged angle-of-arrival variance, observed with a telescope with a circular aperture, of a plane or spherical wave propagating through homogeneous and isotropic turbulence is one of the classical problems in the theory of wave propagation through random media. We present and discuss approximate closed-form solutions on the basis of the Rytov approximation. For both plane and spherical waves, the accuracy of the approximations is better than 0.25% for all ratios of aperture diameter and Fresnel length.     

Scattering of torsional waves by a spherical cavity in a long circular elastic cylinder

Summary. The axisymmetric wave equation is solved for the problem of torsional elastic waves scattered by a spherical cavity located symmetrically in an infinitely long circular cylinder. Using Fourier transforms, the problem is reduced to the solution of an infinite system of simultaneous equations, which is suitable for the numerical solution. The numerical results on the transmission and reflection coefficients are shown for various values of sphere radius and frequency. Equation of energy conservation is utilized to check the numerical procedure.     

Scattering of elastic waves by spherical inclusions with applications to low frequency wave propagation in composites

Scattering of plane elastic waves by a spherical inclusion is considered. A unified method of solution is presented which treats compressional and shear incidence on a similar basis. Explicit results are given for Rayleigh scattering. We apply the results of the single scattering problem to the propagation of low frequency waves in a composite containing a dilute concentration of spherical inclusions. Explicit formulae are given for the effective wave speeds and attenuations when the inclusions are voids. Both the compressional and shear wave speeds decrease initially as a function of frequency.     

Roles of propagating and evanescent waves in solid immersion lens systems

The electromagnetic field incident on the thin-film layers in a solid immersion lens (SIL) system is decomposed into contributions from homogeneous and inhomogeneous waves, which are commonly referred to as propagating and evanescent waves, respectively. The homogeneous and the inhomogeneous parts have different properties with respect to the field distribution in the gap and inside the recording layers. The homogeneous part is shown to diffract like a focused wave with a numerical aperture of 1, and the inhomogeneous part decays exponentially away from the bottom of the SIL. Two examples are discussed in detail, and the concept of a vector illumination system transfer function, which includes effects of the recording layers, is introduced.     

Interactions between spin waves and elastic waves in one-domain ferromagnetic insulators

The interaction between spin waves and the elastic waves is theoretically investigated in the ferromagnetic insulators which are made to behave like one-domain bodies by means of an applied magnetic field. The free energy of the material, that is, the potential of stresses, is derived by continuum approximations of a microscopic model, and the physical meaning of various contributions in the free energy is discussed. The dipole-dipole interaction which may be considered to be a long-range interaction is approximated by a nearest neighbor interaction. As an application of the theory, interactions of spin waves and elastic waves are studied. A correspondence between the microscopic and the continuum theories of ferromagnetic resonance is presented.     

Longitudinal and transverse waves in anisotropic elastic materials

Summary It is shown that a necessary and sufficient condition for a longitudinal wave to propagate in the direction n in an anisotropic elastic material is that the elastic stiffness C ₁₁ (n) is a stationary value (maximum, minimum or saddle point) at n. Explicit expressions of all n and the corresponding elastic stiffness C ₁₁ (n) for which a longitudinal wave can propagate are presented for orthotropic, tetragonal, trigonal, hexagonal and cubic materials. As to longitudinal waves in triclinic and monoclinic materials, only few explicit expressions are possible. We also present necessary and sufficient conditions for a transverse wave to propagate in the direction n. As an illustration, explicit expressions of all n, the polarization vector a and the wave speed c for which a transverse wave can propagate in cubic and hexagonal materials are given. The search for n in hexagonal materials confirms the known fact that a transverse wave can propagate in any direction. A longitudinal wave is necessarily accompanied by two transverse waves. However, a transverse wave can propagate without being accompanied by a longitudinal wave.     

Unsteady pressure waves and shock waves in elastic tubes containing bubbly air-water mixtures

Summary The flow of a two-phase fluid through elastic tubes is more complex than that of a single phase fluid. The mathematical model is based on an one-dimensional approach to the flow of a liquid-gas mixture. The one-dimensional equations for transient two-phase flow through elastic tubes are a system of nonlinear hyperbolic partial differential equations if the bubbles and the liquid particles move with the same velocity. Included in the model are the effects of wall elasticity, compressibility of the gas and the liquid, the surface tension and the variable area change. The propagation of finite pressure waves and shock waves in a liquid containing gas bubbles has been investigated. The results show a differently strong influence of the parameters on the wave propagation speed and on the shock wave relations.

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Zur Ausbreitung von Druck- und Stoßwellen in instationären Blasen-Flüssigkeitsströmungen durch elastische Leitungen

Zusammenfassung Es ist bekannt, daß bei der mathematischen Beschreibung einer Zweiphasenströmung insofern Schwierigkeiten auftreten können, als unter bestimmten Voraussetzungen sowohl reelle als auch komplexe charakteristische Richtungen auftreten können. Für den Fall gleicher Geschwindigkeiten von Blasen und Flüssigkeit erhält man aus den instationären Gleichungen ein nichtlineares hyperbolisches Differentialgleichungssystem. Berücksichtigt werden die Elastizität der Wandungen, die Kompressibilität des Gases und der Flüssigkeit sowie die Oberflächenspannung. Wellenausbreitungsgeschwindigkeiten und Stoßrelationen werden angegeben. Die Resultate zeigen einen unterschiedlich starken Einfluß der verschiedenen Parameter auf die Wellenaus-breitungsgeschwindigkeit und die Stoßrelationen.

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With 13 Figures     

Pure modes for elastic waves in crystals: mathematical modeling and search

A universal search method of pure longitudinal and pure transverse modes for elastic wave propagation in crystals, in general piezoelectrics, is presented. A mathematical model of pure modes for elastic waves based on adiabatic state equations for an arbitrary anisotropic piezoelectric medium and its equation of motion under elastic deformations in the rotated Cartesian coordinates is constructed. The condition for longitudinal normals is that all non-diagonal matrix elements of the effective elastic stiffness coefficients in the corresponding wave equation are equal to zero. Equating to zero non-diagonal elements only in one row of this matrix, one can obtain the condition for transverse normals. A computer program is prepared which allows to find the pure modes for elastic waves in crystals and to calculate their characteristics when symmetry class, elastic, piezoelectric, dielectric constants, and crystal density are known.     

The energy density and power flow of acoustic waves propagating in piezoelectric materials

It is shown that, for a plane bulk acoustic wave propagating in arbitrary piezoelectric media, the densities of mechanoelectrical and electromechanical energies are always equal in absolute value and have opposite signs. However, in general, the mechanoelectrical and electromechanical power flows of such a wave calculated by the traditional expression for the Poynting vector do not compensate each other, although the total density of these energies is always equal to zero. A discovered discrepancy based on the dissymmetry of piezoelectric constants with respect to the electrical and mechanical indexes may cause difficulties for calculation of important parameters for practical applications such as energy transport velocity of acoustic waves in piezoelectric materials.     

Momentum equation and simple waves in an elastic pipeline

A comparative analysis of momentum equations for an ideal-liquid flow in rigid and elastic pipelines has been performed. A fundamental difference of these equations has been shown using individual examples. The influence of the character of the boundary has been analyzed. A general solution analogous to the Riemann solution for propagation of a simple nonlinear wave in an elastic pipeline has been obtained. It has been shown that the wave shape changes for any velocity of the liquid in the pipeline and a shock wave occurs. The formation length of the shock wave has been evaluated. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 79, No. 5, pp. 147–151, September–October, 2006.     

Nonlinear response of a shear deformable S-FGM shallow spherical shell with ceramic-metal-ceramic layers resting on an elastic foundation in a thermal environment

This article presents an analytical approach to investigate the nonlinear stability of thick, functionally graded material (FGM) shallow spherical shells resting on elastic foundations, subjected to uniform external pressure and exposed to thermal environments. Material properties are assumed to be temperature dependent and graded in the thickness direction according to a Sigmoid power law distribution (S-FGM) in terms of the volume fractions of constituents. Using the first-order shear deformation theory and the Galerkin method, the effects of materials, geometry, elastic foundation parameters, and temperature on the nonlinear response of the thick S-FGM shells are analyzed and discussed in detail.     

Transfer matrix method for the solution of multiple elliptic layers with different elastic properties. Part I: infinite matrix case

This paper provides the transfer matrix method for the solution of multiple elliptic layers with different elastic properties. In the study, the medium is composed of an elliptic inclusion and many confocal elliptic layers. The conformal mapping and the continuation of analytic functions are used. In the mapping plane, the complex potentials in the inclusion and the individual layer are expressed in the form of Laurent series. The correct form of the complex potentials in the inclusion is addressed. From the continuation condition for traction and displacement along the interface, the relation between the coefficients in the Laurent series of complex potentials for two adjacent layers can be evaluated. This relation is expressed in a matrix form, and it is called the transfer matrix. Using the transfer matrixes successively and the traction condition at remote place, the problem is finally solved. Numerical examples for two cases, the two-phase case and the three-phase case, are presented.     

球面波传播特性和围岩动态裂纹产生的数值试验研究

利用非线性动力有限元分析程序,对于半无限岩土介质中的洞室,研究了球面波在围岩中的传播特性和动态裂纹的产生过程,比较了球面波在毛洞和锚杆加固洞室围岩中的衰减规律和动态裂纹形态的差别。结果表明:围岩动态裂纹是自由面产生的反射拉伸波及其相互叠加以及加固区与未加固区相互错动剪切的综合作用造成的;球面波强度在毛洞围岩中的衰减速度比在加固洞室中的快;锚杆加固洞室的破坏程度比毛洞轻一些;将模拟所得加固洞室围岩破坏形态与相应模型试验的结果进行了比较,发现洞室破坏形态及规律较为一致,说明了数值分析结果是可信的。研究结果对球面波的认识和防护工程的加固设计具有较好的参考价值。