剪切波作用下埋藏刚性椭圆与周围介质部分脱胶时的动力分析

本文利用波函数展开法和奇异积分方程技术研究了ＳＨ型反平面剪切波作用下埋藏刚性椭圆柱与周围介质部分脱胶时的动力特性，将脱胶区看作表面不相接触的椭圆弧形界面裂纹，利用波函数展开法，并引入裂纹位错密度函数为未知量，将问题归结为奇异积分方程。通过数值注解积分方程获得了远场和近场物理参量，度讨论了共振特性和各参数对共振的影响。     

SH波对有部分脱胶衬砌的圆形孔洞的散射

本文研究了圆形孔洞内衬砌与孔洞部分脱胶时对ＳＨ波的散射．将脱胶区看作表面不相接触的弧形界面裂纹，利用波函数展开法，并引入裂纹面的位错密度函数，将问题归结为一组奇异积分方程．通过数值计算获得了动应力强度因子（ＤＳＩＦ）和远场位移及散射截面（ＳＣＳ）．结果显示：由于脱胶，ＤＳＩＦ和ＳＣＳ在较低的频率上发生共振．     

P波对界面部分脱胶的刚性圆柱夹杂物的散射

本文求解了弹性Ｐ波对界面部分脱胶的可动刚性圆柱夹杂物的散射问题。将脱胶区看作表面不相接触的弧形界面裂纹，借助波函数展开法并利用边界条件将问题转化为一组对偶级数方程。然后通过引入裂纹面的位错密度函数，将其化为一组具有Ｈｉｌｂｅｒｔ核的第二类奇异积分方程，并进一步化为Ｃａｕｃｈｙ型奇异积分方程组，数值求解方程组可获得动应力强度因子，夹杂物刚体振动位移和散射截面等重要参量。结果显示该类结构在较低的频率上发生共振，此低频共振特性与脱胶区大小，入射波方向、材料组合等多种参数有关。与已有方法相比，本文的方法更具一般性，适用于任意材料组合。     

平面波对有部分脱胶衬砌的圆形孔洞的散射

将波函数展开法与奇异积分方程技术相结合研究了平面波对有部分脱胶衬砌的圆形孔洞的散射。将脱离区看作弧形裂纹并忽略裂纹表面的相互作用。将衬砌和基体中的波场展开成Fou-rier-Bessel级数,利用混合边界条件得到一组对偶级数方程组并进一步转化成Hilbert奇异积分方程。数值求解给出了脱离区大小和衬砌厚度对动应力强度因子(DSIF)和散射截面(SCS)的影响。结果显示由于脱胶,动应力强度因子和散射截面呈现明显的低频共振特性。     

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。     

奇异积分方程在裂纹体弹性波散射问题中的应用

结合２０多年来国内外的研究成果，评述奇异积分方程在裂纹体弹性波散射问题中的应用，特别是在界面裂纹散射问题中的应用．讨论如何将裂纹散射问题归结为奇异积分方程、如何用数值法求解这些方程等问题，并指出奇异积分方程法与其他积分方程法的关系．最后展望了奇异积分方程在裂纹体散射问题中可能的应用前景     

纤维增强复合材料圆柱型界面裂纹分析

以裂纹面上的位错函数为未知量将圆柱型界面裂纹问题化成一组奇异积分方程的求解问题．应用Ｍｕｓｋｈｅｌｉｓｈｖｉｌｉ的奇异积分方程理论，分析了圆柱型界面裂纹尖端应力场．针对裂纹尖端分别存在和不存在接触区两种情况，确定了裂纹尖端应力场的奇异性．利用数值方法计算了圆柱型界面裂纹尖端接触区尺寸对剪应力强度因子的影响．     

与两相材料界面接触的裂纹对SH波的散射

利用积分变换方法得出了两相材料中作用简谐集中力时的格林函数．根据所得的格林函数并利用Betti-Rayleigh互易定理得出了与界面接触裂纹的散射波场．裂纹的散射波场可分解为两部分，一部分为奇异的散射场，另一部分为有界的散射场．利用分解后的散射场，可得裂纹在SH波作用下的超奇异积分方程．根据裂纹散射场的奇异部分和Cauchy型奇异积分的性质得出了裂纹和界面接触点处的奇性应力指数和接触点角形域内的奇性应力．利用所得的奇性应力定义了裂纹和界面接触点处的动应力强度因子．对所得超奇异积分方程的数值求解可得裂纹端点和接解点处的应力强度因子。     

尖端具有吸附性接触的界面裂纹对瞬态弹性波作用下的动态响应

建立并研究一类接触型界面裂纹模型对瞬态弹性波作用下的动态响应问题。文中利用积分变换和积分方程法推导了确定这类问题的奇异积分方程组。采用围道积分技术和切比雪夫多项式展开技术，得到了待定系数的非线性代数方程组。最后给出了裂纹尖端接触区大小和接触应力随时间变化的数值结果，揭示了这种接触裂纹的动力学特性及物理上的合理性。     

半平面多边缘裂纹反平面问题的奇异积分方程

利用复变函数和奇异积分方程方法,求解弹性范围内半平面多边缘裂纹的反平面问题．提出了满足半平面边界自由的由分布位错密度表示的单边缘裂纹的基本解,此基本解由主要部分和辅助部分组成．将半平面多边缘裂纹问题看作是许多单边缘裂纹问题的叠加,建立了一组Cauchy型奇异积分方程．然后,利用半开型积分法则求解该奇异积分方程,得到了裂纹端处的应力强度因子．最后,给出了几个数值算例．     

DYNAMIC ANALYSIS OF A BURIED RIGID ELLIPTIC CYLINDER PARTIALLY DEBONDED FROM SURROUNDING MATRIX UNDER SHEAR WAVES

This paper investigates the dynamic behavior of a buried rigid ellipticcylinder partially debonded from surrounding matrix under the action of anti-planeshear waves (SH waves). The debonding region is modeled as an elliptic arc-shapedinterface crack with non-contacting faces. By using the wave function (Mathieufunction) expansion method and introducing the dislocation density function as anunknown variable, the problem is reduced to a singular integral equation which issolved numerically to calculate the near and far fields of the problem. The resonanceof the structure and the effects of various parameters on the resonance are discussed.     

Stress Concentration Near an Elliptic Crack in the Interface Between Elastic Bodies under Steady-State Vibrations

The paper addresses the three-dimensional problem on steady-state vibrations of an elastic body consisting of two perfectly joined dissimilar half-spaces with an elliptic mode I crack located in one of the half-spaces normally to the interface. The problem is reduced to a boundary integral equation for the crack opening function. The integration domain of the equation is bounded by the crack domain, and the interaction between the crack and the interface is described by a regular kernel. The equation is solved using the mapping method. Numerical results are obtained for the case where the surfaces of the elliptic crack are subjected to harmonic loading with constant amplitude. The dependences of the stress intensity factors on the wave number are presented for various relationships among the mechanical constants that ensure the absence of near-surface waves     

多个纵向环形界面裂纹对P波散射的动应力强度因子

研究多个纵向环形界面裂纹的Ｐ波散射问题。以裂纹面的位错密度函数为未知量,利用Ｆｏｕｒｉｅｒ积分变换,将问题归结为第二类奇异积分方程,然后通过数值求解,获得裂纹尖端的动应力强度因子。最后给出了双裂纹动应力强度因子随入射波频率变化的关系曲线。     

非圆截面杆中非线性扭转波方程的解析求解

研究了非圆截面杆中非线性扭转波动方程的精确求解问题. 利用直接积分与微分变换相结合的方法,得到了该方程的隐式通解. 通过对积分常数和方程系数的不同情形的讨论, 给出了该方程的三角函数、双曲函数、椭圆函数、指数函数以及它们的组合形式的解,分别对应于的非线性扭转波的孤立波、周期波以及冲击波等多种传播形式.     

Dynamic stress concentration around elliptic cavities in saturated poroelastic soil under harmonic plane waves

Potential function and complex function in the elliptic coordinate system are employed to solve the problem of scattering harmonic plane waves by multiple elliptic cavities in water saturated soil medium. The steady state Biot’s dynamic equations of poroelasticity are uncoupled into Helmholtz equations via given potentials. The stresses and pore water pressures are obtained by using complex functions in elliptic coordinates with certain boundary conditions. Finally, the dynamic stresses for the case of two interacting elliptic cavities are obtained and discussed in details via a numerical example.     

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     

Unsteady motion of an elliptic cylinder under a free surface

A problem of generation of nonlinear unsteady waves on the surface of an ideal liquid in an infinitely deep fluid due to the motion of a submerged elliptic cylinder is considered. The initial formulation of the problem is reduced to an integrodifferential system of equations for the function defining the free surface shape and for the normal and tangential components of velocity on the free surface. The small-time asymptotics of the solution is constructed for the case of cylinder motion with a constant acceleration from the state at rest.     

深水波理论的新进展

大海是令人神往的。诗人们愿意用大海来抒发感情。更重要的是,在大海中蕴藏着丰富的能量、矿物和生物资源。即使在交通十分发达的今天,它仍不失为沟通世界各大洲的重要渠道之一。但是,大海并不总是那样平静那样驯服。咆哮起来,惊涛骇浪可以折断巨轮,倾覆平台;海啸和风暴潮可以冲决堤坝,破坏海工建筑,吞噬成千上万人的生命。要征服大海不是一件轻而易举的事。人们尊敬古代那些开拓海上通道的先驱者。在中国历史上就有这样      

尖端具有线性粘着力作用的加层空间的界面裂纹对稳态弹性波的散射

本文研究一类粘着型界面裂纹的弹性波散射问题．文中利用积分变换和积分方程方法推导了确定这类问题的奇异积分方程组．采用围道积分技术和切比雪夫多项式展开技术，得到了待定系数的非线性代数方程组．最后本文给出裂纹尖端粘着区的大小和界面应力的数值结果．