A theoretical model is constructed for the large deflection deformation of a rigid-plastic cantilever with a tip mass loaded by a transverse follower-force pulse applied to its tip. The purpose of constructing and analysing such a model is to provide an analytical basis for studying unconstrained pipe whip. The equations for the initial travelling hinge phase and the root rotation phase are derived and solved numerically. Pipe kinematics and deformations are deduced and comparisons are made to several pipe whip tests. Finally the model is used to give indications of the variation in the zone of influence for different constant follower force magnitudes and different ratios of tip mass to pipe mass.
The modelling of the deformation of a straight pipe undergoing pipe-whip is a complex problem. The simplest approach is to formulate a small deflection rigid-plastic analysis in which the pipe is treated as a cantilever beam under end load. In this, the blowdown force pulse is represented by a constant force applied for a fixed time. The effects of geometry changes are neglected in the governing equations and axial forces are usually ignored. Briefly, the motion of the pipe occurs in three phases according to this model. A stationary plastic hinge is produced when the load is applied which remains fixed in position as long as the force is maintained. When the force ceases to act, the motion moves into the second· phase, the plastic hinge travels towards the root of the cantilever. In the third and fmal phase, the pipe (beam) rotates about the root until all the kinetic energy of the beam have been dissipated. The energy input to the pipe can be calculated and the proportions of the energy dissipated in the three phases can be calculated.