用直接法求简支输送管道的极限流速

根据变分原理导出了输送管道自由振动的积分．变分方程，这是一个流一固耦合问题，不可能得到它的解析解，只能求近似解或数值解．目前广泛应用的数值算法是有限元法、传递矩阵法、摄动法．本文采用Galerkin直接解法，首先选取满足自然边界每件的试函数，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．算例结果表明，采用该方法不仅得到了问题的近似解析解，而且具有相当高的精度，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．固耦合复杂问题提供了一种强有力的分析手段．

Calculating limit velocity of pipe of conveying fluid by directr method

Based on variational principle, free vibration integration-variation equation of pipe conveying fluid is derived. This is a liquid-solid coupled problem. Its analytic solution is difficult to be obtained, we can only look for approximate solution or numeral results. So far methods applied widely are finite element method, transmittance matrix method and disturbance method. Galerkin direct method is employed. First, test functions satisfyed natural boundary conditions are selected. Then approximate analytic formulations of system frequency are derived. Meanwhile approximate analytic fornaulation of limit velocity is got. The example illustrates that approximate analytic solutions can be obtained and the accuracy are very good by this method. The other numeral methods mentioned above can not achieve these effects. So we can say that Galerkin direct method is a powerful method for comolex oroblems like liauid-solid couoled oroblem.