用直接法求解半圆形输液曲管的极限流速

根据D.Alembert原理导出了半圆形输液曲管弯曲-扭转-流体耦合问题的自由振动方程。对这类方程解耦而单独求出弯曲、扭转的解析解非常困难,于是介绍了一种近似计算方法--直接法。采用直接法,首先选取满足自然边界条件但不一定满足方程的试函数作为方程的近似解,并使误差在整个空间上加权累积为零,这可解释为广义力在虚位移上所做的虚功之和为零(平衡方程的弱积分)。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,分析了曲管中流体流速对系统固有频率的影响,得出了更为精确的结果。

DIRECT METHOD FOR LIMIT VELOCITY OF A SEMI-CIRCLE CURVED PIPE CONVEYING FLUID

Bending-torsion-liquid coupling free vibration equations of a semi-circule curved pipe conveying fluid is derived, based on D. Alembert principle. For this class formula, it is difficult to uncouple and to get bending and torsion analytic solutions separately. An approching method--direct method is presented. First, test functions selected to satisfy natural boundary conditions, but not to assure meeting equations, are regarded as the approximate solutions of equations and let weighted-integrating of errors in whole space domain equal to zero. It is explained that the sum of virtual work done by generalized forces equal to zero (the weak integration of equilibrium eqation). Then approximate analytic formula of system frequency are obtained. Meanwhile, approximate analytic formulation of limit velocity is obtained. An example shows the influence of flowing velocity on the natural frequency of the curved pipe conveying fluid. More precise effect is presented.