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 dual integral SOLUTION OF TIMOSHENKO BEAM BY DUAL INTEGRAL TRANSFORMATION METHOD Timoshenko梁的对偶积分变换解法 A Method of Solving a Kind on Dual Integral Equations Via Decoupling Into Canonical Cauchy Singular Integral Equations 一类对偶积分方程组正则化为Cauchy奇异积分方程组解法 Orthogonal Polynomial Solving Method of General Singular Dual Integral Equations 一般形式的奇异对偶积分方程组正交多项式求解法 A Class of Two-Dimensional Dual Integral Equations and Its Application 一类二维对偶积分方程的解及其应用 By Hankel integral transform, the problem is reduced to a set of dual integral equations which are transformed into a set of singular integral equations. 文中采用Hankel积分变换,将散射问题转化为求解对偶积分方程,进而变换为奇异积分方程组. In this paper,from the definition of Mellin transform we derive it's inversion theorem and solve a dual integral equation by using above result: 本文从梅林变换的定义出发导出其反演定理及基本性质,并用此变换求解对偶积分方程。 The exact analytic solution of a Mode Ⅲ Griffith crack in the material was obtained by using the Fourier transform and dual integral equations theory, and so the displacement and stress fields, the stress intensity factor and strain energy release rate were determined. 通过应用Fourier分析和对偶积分方程理论 ,得到了立方准晶材料Ⅲ型裂纹问题的精确解析解 ,并由此确定了位移与应力场 ,应力强度因子和应变能释放率 . In the present paper,the dual integral equations with complex exponential function are studied based on solving method of copson. 在断裂力学和热弹性动力学中,常常会出现含复指数函数对偶积分方程的求解,此类方程不能直接用Copson-S ih方法求解。 by using the Fourier integral transform and the boundary conditions, the problem is reduced to a dual integral equations. The dynamic stress intensity factors at the crack tip are obtained by the using Copson methods and the numerical integral technique. As an example, the eects of the parameter and the frequency of SH wave on norm dynamic stress intensity factors are discussed. 研究了正交各向异性功能梯度材料中直裂纹对SH波的散射问题,材料两个方向的剪切模量和密度假定为指数模型,通过积分变换-积分方程方法,建立数学模型,化为对偶积分方程,用Copson方法求解对偶积分方程,最后得到动应力强度因子,并且给出了数值算例,讨论了在SH波作用下,裂纹尖端的动应力强度因子与入射波的频率,入射角的关系． ON A FORMAL SOLUTION OF DUAL INTEGRAL EQUATION SYSTEM IN MEASUREMENT OF SEMICONDUCTORS 半导体电磁测量中一个对偶积分方程组的形式解 SIMPLE METHOD OF SOLVING DUAL INTEGRAL EQUATIONS FOR GRIFFITH-CRACK PROBLEMS Griffith裂纹积分变换解法中对偶积分方程的简单解法——形式函数待定法 The Solution of a Dual Integral Equation System with the Method of Gaussian Integration Gauss权重法求解半导体电磁测量中的一个对偶积分方程组 A Method of Solving Complex and More General Dual Integral Equations and the Application of the Solution to Solid Mechanics 更一般形式的复杂对偶积分方程组的解法及其解在固体力学中的应用 Theoretical Solutions of General Dual Integral Equations with Trigonometric Functions 含三角函数的一般形式对偶积分方程组的理论解 THEORETICAL SOLUTIONS OF COMPLEX DUAL INTEGRAL EQUATIONS ON THE MORE GENERAL FORM WITH TRIGONOMETRIC FUNCTION 含三角函数的一般形式复杂对偶积分方程组的理论解 For the flexible circular plate or the one with a rigid core, through modifying the right term of the dual integral equations according to mixed boundary value condition, the corresponding dual integral equations are derived. The influence of the elasticity of the elastic plate, or the size of the core and the compliance of the elastic part of the elastic plate with core is analyzed by some numerical examples. 而对于饱和地基上弹性圆板和含刚核弹性圆板的振动,将对偶积分方程的右端项按混合边值条件做适当的修改,得到相应的Fredholm积分方程,通过数值算例分析了弹性板的柔度、或含刚核圆板刚域尺寸与弹性部分柔度的大小对动力响应的影响。 Combining the mixed boundary conditions at the bottom surface of the foundation, the dual integral equations of the torsional vibrations of a rigid circular foundation resting on transversely isotropic saturated soil are established, which are further converted to a Fredholm integral equation of the second kind. By numerical method, the dynamic compliance coefficients of the foundation and the contact shear stress under the foundation are studied. 根据刚性基础底面处的混合边界条件,建立饱和地基上刚性圆形基础扭转振动的对偶积分方程,并将该对偶积分方程化为第二类Fredholm积分方程,通过数值计算得出不同条件时基础的动力柔度系数及基底接触剪应力分布规律; On the basis of the differential equations of an elastic foundation under the action of dynamic torque and the contact boundary conditions of the soil and foundation, the dual integral equations of an elastic cylindrical foundation subjected to harmonic torque are obtained under the help of Hankel transform. We can get the solutions of torsional dynamic interactions after solving the dual integral equations. Selected numerical examples are presented to investigate the influence of relevant parameters on the results. 对于弹性圆柱基础,由基础受动扭矩作用时的微分方程和基础与地基接触面处的应力和位移连续以及混合边界等条件,采用同样的积分变换方法得出了弹性基础上作用简谐扭转荷载时的对偶积分方程,解此积分方程求解了相应的动力响应问题,并通过算例分析了相关参数对弹性基础扭转振动的影响; At first, the governing differential equations are solved by Fourier transform, then, under consideration of the mixed boundary value condition, a pair of dual integral equations about the vertical vibration are listed which are converted to linear algebra equations by the Jacobi orthogonal polynomial and solved by numerical procedures. Consequently, the dynamic compliance coefficient Cv versus the dimensionless frequency is derived, and the program is compiled. 首先，采用Fourier积分变换解析求解了Biot方程，得到了该动力控制方程在Fourier变换域上的一组通解，然后由混合边值条件建立了地基上基础竖向振动的对偶积分方程，并应用Jacobi正交多项式将其转化为一组线性代数方程组，通过求解得到了不同无量纲频率下基础振动的动力柔度系数Cv，编制了相应的计算程序。 Fourier transform is employed to reduce to this mixed boundary value problem to three pairs of dual integral equations; also the new additional boundary conditions are discussed. 利用Fourier 变换技术将力电复合边值问题转化为三组对偶积分方程,并讨论了所需要新增的边界条件。

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