【作者】 马瑞成；

【导师】 赵凤群；

【作者基本信息】 西安理工大学 ， 应用数学， 2005， 硕士

【摘要】 本文首先介绍了求解微分方程边值问题的一种数值方法—微分求积法,然后采用微分求积法分别对输流管道和非保守矩形薄板的稳定性问题进行了分析研究,具体有如下三方面的研究内容。 用微分求积法分析了具有弹性支承的弹性地基上输流管道的稳定性问题。对一端固定一端具有弹性支承的弹性地基上的输流管道,用D’Alembert原理建立了运动的微分方程,然后用微分求积法分析了管道颤振失稳和发散失稳情况,讨论了地基反力、地基剪切模量和端部支承的弹性常数对管道失稳形式的影响,并画出了稳定性区域图。 对变厚度矩形板在非保守力作用下的振动和稳定性问题,本文采用微分求积法进行研究。利用微分求积法处理边界条件的灵活性,对于三种不同边界条件(四边简支、四边固支以及一边固支三边简支)的非保守变厚度矩形薄板,分别计算了不同边长比下板的振动频率和临界载荷随板厚比的变化曲线,并讨论了不同边界约束下板的失稳形式。 对由金属和陶瓷两种材料制成的功能梯度材料(Functionally Graded Material,FGM)矩形板在非保守力作用下的稳定性问题用微分求积法进行研究。首先根据振动理论及FGM构成特性建立了FGM矩形板的振动微分方程,然后用微分求积法对其进行数值求解,分别讨论了FGM板和各单相材料板的振动频率和临界载荷之间的关系,并进一步讨论了材料组分对FGM板的振动频率和临界载荷的影响。更多还原

【Abstract】 Differential Quadrature Method (DQM), one of numerical methods of solving boundary problem of differential equation is introduced in this paper. By using DQM, the dynamic stability of pipes conveying fluid and rectangular plates under the action of non-conservative force is studied. The main research work is as follows.The stability of pipes conveying fluid on the elastic foundation with elastic support is analyzed by using DQM. The governing differential equation of pipe conveying fluid on the elastic foundation with one end is fixed and the other end is subjected to elastic support is derived based on D’Alembert’s principle. The divergence and flutter instability of the pipe is discussed, and the effect of foundation reaction, foundation shear modulus and elastic constant of the elastic support on shape of instability of elastic pipe conveying fluid are analyzed, and the stability regional graphs (divergence region and flutter region) are plotted.The stability of varying thickness rectangular plate under the action of non-conservative force is analyzed. Because DQM is easy to handle the boundary condition, For three different boundary conditions, variation curves between thickness ratio of plate and vibration frequencies and critical loads are plotted, and the instability shapes of non-conservative varying thickness rectangular plate under different boundary conditions are discussed by DQM.The stability of Functionally Graded Material (FGM) rectangular plate made of metal and ceramic under the action of non-conservative force is analyzed. Based on vibration theory and structure property of FGM, the governing differential equation isderived, and the numerical solution is obtained by DQM. The vibration frequencies and critical loads of FGM plate and the two single-phase material plates (metal plate and ceramic plate) are compared, and the effect of volume fraction on vibration frequencies and critical loads are discussed.更多还原