Postbuckling and vibration of end-supported elastica pipes conveying fluid and columns under follower loads

Abstract

Fluid-conveying pipes with supported ends buckle when the fluid velocity reaches a critical value. For higher velocities, the postbuckled equilibrium shape can be directly related to that for a column under a follower end load. However, the corresponding vibration frequencies are different due to the Coriolis force associated with the fluid flow. Clamped–clamped, pinned–pinned, and clamped–pinned pipes are considered first. Axial sliding is permitted at the downstream end. The pipe is modeled as an inextensible elastica. The equilibrium shape may have large displacements, and small motions about that shape are analyzed. The behavior is conservative in the prebuckling range and nonconservative in the postbuckling range (during which the Coriolis force does work and the motions decay). Next, related columns are studied, first with a concentrated follower load at the axially sliding end, and then with a distributed follower load. In all cases, a shooting method is used to solve the nonlinear boundary-value problem for the equilibrium configuration, and to solve the linear boundary-value problem for the first four vibration frequencies. The results for the three different types of loading are compared.