极限流速的Galerkin直接法和科氏惯性力的影响

Galerkin direct method for limit velocity and influence of coriolis inertial force

根据变分原理导出了悬臂输液曲管的变分 积分方程 ,这是弯曲 扭转 流体三相耦合的动力学问题 ,无法解耦而单独求出弯曲和扭转的解析解 ,只能作近似计算 .有关文献用有限元法和迁移矩阵法对规则输液曲管进行了数值计算 ,得到了输液曲管的极限流速 ,但都没有考虑科氏惯性力的影响 .采用直接法 ,首先选取满足自然边界条件的试函数 ,而后求出了系统固有频率的近似解析公式 ,同时也得到了极限流速的近似解析公式 .通过算例分析了科氏惯性力对系统固有频率和极限流速的影响 .结果表明 ,采用该方法不仅可以得到问题的近似解析解 ,而且还具有相当高的精度 ,这是其它数值算法难以做到的 .因此可以说 ,Galerkin直接法为解决这类流

Based on variation principle, a free vibration variation-integration equation of cantilever curved pipe for conveying fluid is derived. This is a bending-torsion—fluid tree phase coupled dynamics problem. It is difficult to uncouple and to obtain bending and torsion analytic solution separately. We can only look for approximate solution or numeral results. By means of finite element method and transfer matrix method, some references had studied the problem of uniform curved pipe for conveying liquid whose limit velocity was presented without thinking about the influence of Coriolis inertial force. In this paper, Galerkin method is employed. First, test functions to satisfy natural boundary conditions are selected. Then the approximate analytic formulations of the system frequency are derived. Meanwhile the approximate analytic formulation of the limit velocity is got. A example illustrates the influence of Coriolis inertial force on the system frequency and its limit velocity. The research results show that the approximate analytic solutions can be obtained by this method and its accuracy is very good. The other numeral methods mentioned above cannot achieve these effects. So it can be said that Galerkin direct method is a powerful one for complex problems like fluid-solid coupled problem.