Numerical methods for solving singular integral equations obtained by fracture mechanical analysis of cracked wedge简

The numerical solutions to the singular integral equations obtained by the fracture mechanical analyses of a cracked wedge under three different conditions are considered. The three considered conditions are: (i) a radial crack on a wedge with a non-finite radius under the traction-traction boundary condition, (ii) a radial crack on a wedge with a finite radius under the traction-traction boundary condition, and (iii) a radial crack on a finite radius wedge under the traction-displacement boundary condition. According to the boundary conditions, the extracted singular integral equations have different forms. Numerical methods are used to solve the obtained coupled singular integral equations, where the Gauss-Legendre and the Gauss-Chebyshev polynomials are used to approximate the responses of the singular integral equations. The results are presented in figures and compared with those obtained by the analytical response. The results show that the obtained Gauss-Chebyshev polynomial response is closer to the analytical response.     

轴对称压电-压磁圆柱夹层结构的圣维南端部效应

研究了半无限长轴对称压电-压磁夹层结构的圆柱体圣维南端部效应的衰减问题。圆柱的端部承受自平衡磁电弹载荷;圆柱的内外表面为机械自由表面,但承受不同的电磁边界条件,即电学短路或电学开路及磁学短路或磁学开路边界条件。基于横贯各向同性压电或压磁材料在轴对称圆柱坐标系下的本构方程,推导了关于衰减率的特征方程并求得问题的数值解。结果表明,边界条件、内外径之比、材料厚度比对结构的衰减率都有显著的影响。     

横观各向同性圆柱体端部问题的三维弹性理论解

从位移的通解出发，用分离变量法得到横观各向同性圆柱体的位移和应力的特征函数展开式，并把位移势函数的解用付里叶积分的形式表示。利用留数运算，该积分解可以转换成类似于特征函数的展开式。通过混合端部边界问题，得到与特征函数解成双正交关系的另一组函数。利用这种双正交关系，可以处理不同的端部边界问题。     

表面粗糙层对两圆柱体接触的影响

本文应用粗糙面接触理论分析两粗糙圆柱体的接触问题,得出表面粗糙层对两圆柱体间的接触面积、接触压力分布和接近量的影响．     

正方形排列四圆柱体绕流特性及互扰效应研究

基于计算流体动力学理论,运用大涡模拟方法对雷诺数Re=3900三维正方形排列四圆柱体结构群的绕流问题进行数值计算,主要分析来流攻角与间距比两个参数对四圆柱体结构群流体参数及流场模态的影响。结果表明:来流攻角与间距比均对四圆柱体结构群绕流特性有较强的影响;来流攻角θ=0°、22.5°、45°下,临界间距比分别为3.5、4.0、3.0;间距比的变化会导致下游圆柱表面压力系数分布发生改变;另一方面,间距比较小时,四圆柱体结构之间的互扰作用均以临近效应为主;随间距比增大,上游圆柱尾流对下游圆柱有显著影响,其互扰作用会转变尾激效应。     

功能梯度压电圆柱体的旋转分析及其应用——内压和热荷载作用下的力学传感器

对旋转的功能梯度压电(FGP)圆柱体,进行了精确的热弹性分析．圆柱体同时承受电、热和力学荷载的作用,这是一个旋转传感器或者调节器的简化模型．应用能量法得到系统的控制微分方程．为了正确地评估能量函数,引进了一个被称为“附加能量”的新项．在两种边界条件下:自由旋转的圆柱体和受内压作用的圆柱体,求解所得到的控制方程．研究角速度对各个物理量沿半径分布的影响．所研究的结构也可以认为是,在压力及热荷载作用下,测量圆柱体角速度的一个传感器．结果表明,电势与角速度成正比例关系．     

The characteristics of sound radiation from a cylindrical shell coated with multiple compliant layers

The effect of multiple compliant layers on sound radiation from a finite cylindrical shell immersed in an infinite acoustic medium is studied. The transfer matrix is derived according to the continuous boundary conditions at each adjacent interface of the multi-layer system. With the shell theory and the acoustic wave equation, the theoretical model is developed to estimate the characteristics of sound radiation. The numerical calculation results show that the amount of the acoustic radiation power reduction increases as the wave speed or the density of the compliant layer decreases, and using multi-layer system could be more effective on noise reduction than the corresponding uniform single layer.     

滚动摩擦

我们都知道摩擦分为静摩擦、滑动摩擦和滚动摩擦。在讲静摩擦和滑动摩擦时提到静摩擦力和滑动摩擦力。在滚动摩擦中是否有滚动摩擦力呢?教学中,不少人提到:"滚动摩擦力比滑动摩擦力小。"这种提法对不对呢?下面我们来分析有关滚动摩擦的问题。