中文摘要：

将微分求积法应用到5个边界条件下一端固定具有中间简支支承输流管道的横向振动问题研究中。基于输流管道的运动微分方程及边界条件，采用微分求积法进行离散化，获得由输流管道动力方程组及边界条件合成的矩阵表达形式。求解管道在不同中间支承位置处失稳时的临界流速。分析管道的失稳形式并发现在管道上存在一个特殊的位置备，逐渐增大流体流速到失稳临界值，当中间支承位置ξb〈ξl时，管道先发生颤振失稳，而当中间支承位置ξb〉ξl时，管道先发生发散失稳。研究发现输流管道的这个特殊位置随着管道材料与流体质量比的变化而不同，质量比越大，特殊位置备越靠近固定端。最后，讨论输流管道的质量比及轴向预紧力对发散、颤振失稳临界流速的影响。

英文摘要：

Differential quadrature method （DQM） is applied to investigate the transversal vibration of the fluid-conveying pipe including five condition boundaries, which is clamped at one end and has a simple support at some intermediate location. The differential equation of motion and condition boundaries of the pipe are discretized by using DQM and matrix expression made up with dynamical equations and condition boundaries is formed. The critical flow velocities of pipe under different location of intermediate support are obtained. Instability mechanism of pipe is analyzed. It is shown that there is a special location ξl in the pipe, while the flow velocities increase to the critical value gradually, for location of intermediate support ξb〈ξl, the pipe becomes unstable by flutter, and for ξb〉ξl it loses stability by divergence. The result shows that this special location changes with the variation of ratio of the pipe mass to the fluid mass, and special location 4l is approaching clamped support as mass ratio is increasing. At last the effect of axial pre-tightening force and mass ratio of the system on the critical flow velocity and stability is discussed.