Stability and Critical Flow Velocity Analysis of a Clamped Pipe Conveying Fluid with Intermediate Support

Abstract

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 ξbξl, the pipe becomes unstable by flutter, and for ξbξl, 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 ξl 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.