GENERALIZED RAY APPROXIMATE METHOD TO INVERSE MEDIUM PARAMETERS

In this paper,the inverse problem of the medium parameters in an inhomogeneousmedium is studied and a generalized ray approximate form of the total wave field is described.First,the acoustic wave equation derived from the elastic wave equation is studied,the referential variablesand perturbational variables are introduced,and the integral equation of the medium perturbational pa-rameters is obtained.Then from the point of view of the local principles of the wave function in an in-homogeneous medium,a generalized ray approximate form of the total wave field in an inhomoge-neous medium is described,and attention is focused on the Fredholm integral equation of the firstkind.Finally,the medium parameters in half-plane are inversed.Numerical examples show when theperturbations of the medium parameters are about 0.5,this method can effectively inverse its varia-tion.Apparently,this method is better than the conventional Born weak scattering approximation.     

二维介质参数的大扰动反演方法

对非均匀介质参数反演问题进行了研究，并提出了用于反演二维介质参数的广义射线近似方法．利用参考场量和扰动变量对声波方程中的介质参数进行处理，并利用Ｇｒｅｅｎ函数理论得到扰动参数比的积分方程．基于非均匀介质中波函数的局部理论和射线理论，引入了全波场的广义射线近似形式，通过定义介质参数函数，把反演目标归结为其第一类Ｆｒｅｄｈｏｌｍ积分方程．利用积分变换方法得到二维介质的介质参数函数，从而得到介质参数，在Ｂｏｒｎ近似方法中，反演的介质参数扰动不能超过２０％，但是在本文中介绍的方法能够有效地反演其扰动比不超过５０％的变化情况     

非均匀介质散射问题的体积分方程数值解法

将非均匀介质视为某一均匀背景介质中的扰动，可建立用均匀背景介质格林函数作基本解的体积分方程．给出了配置法求解体积分方程的数值方法，首先解得扰动域内各点以速度扰动为权的波场函数，然后回代计算得到观测面上各接收点的散射波场．与边界元法和Ｂｏｒｎ近似法计算结果比较表明该方法具有很高的精度，可得到穿过非     

介质参数反演的广义射线近似方法

在对无粘性介质参数反演问题进行的研究中，引入一种全波场广义射线近似形式，提出一种新的反演参数的方法，文中，首先对由弹性波动方程演变成的声波方程进行分析，引入背景场量和扰动量，并结合Ｇｒｅｅｎ函数理论，得到了介质参数的积分方程；然后结合前人对非均匀介质中波函数局部理论的定性分析，引入一种全波场广度射线近似形式，把问题归结为一个第一类Ｆｒｅｄｈｏｌｍ积分方程；最后对半空间问题层状介质模型进行了反演，算     

径向非均匀介质中圆形夹杂的动应力分析

基于复变函数理论,研究了径向非均匀弹性介质中均匀圆夹杂对弹性波的散射问题. 介质的非均匀性体现在介质密度沿着径向按幂函数形式变化且剪切模量是常数. 利用坐标变换法将变系数的非均匀波动方程转为标准亥姆霍兹(Helmholtz) 方程. 在复坐标系下求得非均匀基体和均匀夹杂同时存在的位移和应力表达式. 通过具体算例分析了圆夹杂周边的动应力集中系数(DSCF). 结果表明:基体与夹杂的波数比和剪切模量比,基体的参考波数和非均匀参数对动应力集中有较大的影响.      

A boundary element solution to scattering of elastic SH wave by arbitrarily shaped inclusions embedded in an infinite anisotropic medium

Scattering problems for inhomogeneous bodies are investigated by the integral equation method. The boundary integral equation (BIE) for the scattered displacement field associated with finite inhomogeneities in an anisotropic medium are derived with the help of the generalized Green's identity. The discretization of BIE is based upon the constant element, linear element and quadratic element. Several numerical examples for calculating the scattering displacement, stress and scattering cross section from a cylinder, an interface crack, and two elliptic cylinders are given. Results show that the present method can be advantageously applied to a wide range of scattering problems of elastic waves.     

Stress Analysis for an Elastic Semispace with Surface and Graded Layer Coatings under Induced Torsion

In this paper, the axisymmetric torsional problem of a coating structure consisting of a surface coating, a functionally graded layer and a substrate under a rigid cylindrical punch is investigated. The coating and substrate are homogeneous materials with distinct physical properties while the intermediate layer is inhomogeneous with its shear modulus changing exponentially along the thickness direction. The Hankel integral transform technique is employed to reduce the torsional problem to a singular integral equation with a Cauchy kernel. The circumferential shear stress and displacement fields in the coating structure are calculated by solving the integral equation numerically. The results show that the stiffness ratio has significant effect on the distribution of the circumferential stress and displacement at the interface.     

A THEORETICAL SOLUTION OF CYLINDRICAL SHELLS FOR AXISYMMETRIC PLAIN STRAIN ELASTODYNAMIC PROBLEMS

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅａｎａｌｙｓｉｓｆｏｒｄｙｎａｍｉｃｐｒｏｂｌｅｍｏｆｅｌａｓｔｉｃｂｏｄｉｅｓｈａｓｂｅｅｎｓｔｕｄｉｅｄｆｏｒｍａｎｙｙｅａｒｓ.Ｂａｓｅｄｏｎｔｈｅｍｏｍｅｎｔｌｅｓｓｔｈｉｎｓｈｅｌｌｔｈｅｏｒｙ ,ＨｕｔｈａｎｄＣｏｌｅ[1]ｓｔｕｄｉｅｄｔｈｅｓｔｒｅｓｓｗａｖｅｉｎａｓｐｈｅｒｉｃａｌｓｈｅｌｌｐｒｏｄｕｃｅｄｂｙｐｒｅｓｓｕｒｅｌｏａｄｓｉｎ 1 955.Ｍｃｉｖｏｒ[2 ]ｄｉｓｃｕｓｓｅｄｔｈｅｆｌｅｘｕｒａｌｓｔｒｅｓｓａｎｄｍｅｍｂｒａｎｅｓｔｒｅｓｓｉｎａ…     

各向异性介质的弹性波散射问题的边界元方法

本文引用加权残数法建立了各向异性介质内含任意形式异质夹杂时的散射问题的边界积分方程式,导出了相应的辐射条件,计算了内含圆柱体,椭圆柱体、界面裂纹情形下对SH 波的散射位移场、应力场以及散射横截面.数值结果表明本方法用于解答各向异性介质的弹性波散射问题具有良好的精度和应用前景.     

THE PERIODIC CRACK PROBLEM IN BONDED PIEZOELECTRIC MATERIALS

The problem of a periodic array of parallel cracks in a homogeneous piezoelectric strip bonded to a functionally graded piezoelectric material is investigated for inhomogeneous continuum.It is assumed that the material inhomogeneity is represented as the spatial varia- tion of the shear modulus in the form of an exponential function along the direction of cracks. The mixed boundary value problem is reduced to a singular integral equation by applying the Fourier transform,and the singular integral equation is solved numerically by using the Gauss- Chebyshev integration technique.Numerical results are obtained to illustrate the variations of the stress intensity factors as a function of the crack periodicity for different values of the material inhomogeneity.     

A theoretical solution of cylindrical shells for axisymmetric plain strain elastodynamic problems

A method is developed for the transient responses of axisymmetric plain strain problems of cylindrical shells subjected to dynamic loads. Firstly, a special function was introduced to transform the inhomogeneous boundary conditions into the homogeneous ones. Secondly, using the method of separation of variables, the quantity that the displacement subtracts the special function was expanded as the multiplication series of Bassel functions and time functions. Then by virtue of the orthogonal properties of Bessel functions, the equation with respect to the time variable was derived, of which the solution is easily obtained. The displacement solution was finally obtained by adding the two parts mentioned above. The present method can avoid the integral transform and is fit for arbitrary loads. Numerical results are presented for internally shocked isotropic and cylindrically isotropic cylindrical shells and externally shocked cylinders, as well as for an externally shocked, cylindrically isotropic cylindrical shell that is fixed at the internal surface. Contributed by Ding Hao-jiang Foundation item: the National Natural Science Foundation of China (10172075) Biography: Ding Hao-jiang (1934-)     

双相介质半空间中圆孔对透射SH波的稳态分析

研究了平面SH波在半空间双相弹性介质中的传播。通过Green函数和积分方程方法,按照复变函数描述,对透射波被圆孔散射的情况进行稳态分析。将双相介质半空间沿界面剖分为1/4空间介质Ⅰ和含圆孔的1/4空间介质Ⅱ,分别构造了介质Ⅰ和介质Ⅱ中反平面点源荷载的Green函数,按双相介质中平面SH波的处理方法,给出介质Ⅰ和介质Ⅱ中的平面位移波,两种介质之间的相互作用力与对应Green函数的乘积沿界面的积分与平面位移波叠加得到介质Ⅰ和介质Ⅱ中的全部位移场。按照界面的位移连续条件,定解积分方程组,得到问题的稳态解,并给出圆孔位置和介质参数对散射的影响。     

同震断层三维裂纹扩展波动时域超奇异积分法

应用波动时域超奇异积分法将P波、S波和磁电热弹多场耦合作用下同震断层任意形状三维裂纹扩展问题转化为求解以广义位移间断率为未知函数的超奇异积分方程组问题;定义了广义应力强度因子,得到裂纹前沿广义奇异应力增量解析表达式;应用波动时域有限部积分概念及体积力法,为超奇异积分方程组建立了数值求解方法,编制了FORTRAN程序,以三维矩形裂纹扩展问题为例,通过典型算例,研究了广义应力强度因子随裂纹位置变化规律;分析了同震断层裂纹扩展中力、磁、电场辐射规律.      

基于积分方程方法的弹性波多重散射计算

运用积分方程方法计算了含多个随机分布椭圆柱型孔洞的随机非均匀介质中相干波的速度和衰减系数,分析了这种介质的频散特性。首先,建立了散射位移场满足的积分方程,推导了单个椭圆柱孔洞的散射截面计算公式。接着分析了在含多个随机分布椭圆柱型孔洞的随机非均匀介质中弹性波的多重散射,给出在统计平均意义下的相干波的波速和衰减系数计算公式。然后用Matlab进行了编程,给出了一个数值算例,并将计算结果与波函数展开法进行了比较,分析了随机空隙介质的频散特征及其孔洞椭圆偏心率和材料空隙率的影响。     

双材料中平片裂纹问题的超奇异积分方程解法

利用三维断裂力学的超奇异积分方程方法,对双材料空间中重直于界面的平片裂纹Ⅰ型问题进行了研究。首先根据双材料空间的弹性力学基本解,使用边界积分方程方法,在有限部积分的意义下导出了以裂纹面位罗间断为未知函数的超奇异积分方程,并为其建立了数值法。在此基础上,讨论了用裂纹面位移问题计算应力强度因子的方法。最后用此计算了几个典型的Ⅰ型下片裂纹问题的应力强度因子,其数值结果令人满意。     

Lamb's integral formulas of two-phase saturated medium for soil dynamic with drainage

When dynamic force is applied to a saturated porous soil,drainage is common.In this paper,the saturated porous soil with a two-phase saturated medium is simulated,and Lamb's integral formulas with drainage and stress formulas for a two-phase saturated medium are given based on Biot's equation and Betti's theorem(the reciprocal theorem).According to the basic solution to Biot's equation,Green's function Gij and three terms of Green's function G4i,Gi4,and G44 of a two-phase saturated medium subject to a concentrated force on a spherical coordinate are presented.The displacement field with drainage,the magnitude of drainage,and the pore pressure of the center explosion source are obtained in computation.The results of the classical Sharpe's solutions and the solutions of the two-phase saturated medium that decays to a single-phase medium are compared.Good agreement is observed.     

Superposition of finite-amplitude waves propagating in a principal plane of a deformed Mooney–Rivlin material

Here we consider finite-amplitude wave motions in Mooney–Rivlin elastic materials which are first subjected to a static homogeneous deformation (prestrain). We assume that the time-dependent displacement superimposed on the prestrain is along a principal axis of the prestrain and depends on two spatial variables in the principal plane orthogonal to this axis. Thus all waves considered here are linearly polarized along this axis. After retrieving known results for a single homogeneous plane wave propagating in a principal plane, a superposition of an arbitrary number of sinusoidal homogeneous plane waves is shown to be a solution of the equations of motion. Also, inhomogeneous plane wave solutions with complex wave vector in a principal plane and complex frequency are obtained. Moreover, appropriate superpositions of such inhomogeneous waves are also shown to be solutions. In each case, expressions are obtained for the energy density and energy flux associated with the wave motion.     

The scattering of general SH plane wave by interface crack between two dissimilar viscoelastic bodies

The scattering of general SH plane wave by an interface crack between two dissimilar viscoelastic bodies is studied and the dynamic stress intensity factor at the crack-tip is computed. The scattering problem can be decomposed into two problems: one is the reflection and refraction problem of general SH plane waves at perfect interface (with no crack); another is the scattering problem due to the existence of crack. For the first problem, the viscoelastic wave equation, displacement and stress continuity conditions across the interface are used to obtain the shear stress distribution at the interface. For the second problem, the integral transformation method is used to reduce the scattering problem into dual integral equations. Then, the dual integral equations are transformed into the Cauchy singular integral equation of first kind by introduction of the crack dislocation density function. Finally, the singular integral equation is solved by Kurtz's piecewise continuous function method. As a consequence, the crack opening displacement and dynamic stress intensity factor are obtained. At the end of the paper, a numerical example is given. The effects of incident angle, incident frequency and viscoelastic material parameters are analyzed. It is found that there is a frequency region for viscoelastic material within which the viscoelastic effects cannot be ignored. This work was supported by the National Natural Science Foundation of China (No.19772064) and by the project of CAS KJ 951-1-20     

Love waves in functionally graded piezoelectric materials

To investigate the features of Love waves in a layered functionally graded piezoelectric structure, the mathematical model is established on the basis of the elastic wave theory, and the WKB method is applied to solve the coupled electromechanical field differential equation. The solutions of the mechanical displacement and electrical potential function are obtained for the piezoelectric layer and elastic substrate. The dispersion relations of Love waves are deduced for electric open and short cases on the free surface respectively. The actual piezoelectric layer–elastic substrate systems are taken into account, and some corresponding numerical examples are proposed comparatively. Thus, the effects of the gradient variation about material constants on the phase velocity, the group velocity, the coupled electromechanical factor and the cutoff frequency are discussed in detail. So the propagation behaviors of Love waves in inhomogeneous medium is revealed, and the dispersion and the anti-dispersion are analyzed. The conclusions are significant both theoretically and practically for the surface acoustic wave devices.     

圆夹杂内裂纹对SH波的动力响应

利用特殊函数的Graf加法公式和波函数展开方法得出了圆夹杂内作用集中力的格林函数．根据Bessel函数的渐近性质，对所得格林函数的奇异部分和有界部分进行了分离．利用所得的格林函数和互易定理得出了圆夹杂内裂纹在SH波作用下的散射场．根据裂纹的散射场建立了圆夹杂内裂纹的超奇异积分方程．对超奇异积分方程的数值求解，可得裂纹端点的动应力强度因子。