In-plane whipping of bent cantilever pipes

The dynamic elastic-plastic behaviour of a bent cantilever pipe subjected to an in-plane force pulse at its tip is described. A theoretical model based on a large deflection formulation of dynamic beam theory is described. This takes into account the plastic hardening-softening behaviour which is characteristic of a pipe when it is subjected to large changes in curvature. This beam model was first formulated and applied by Reid et al. (1995b, 1996), who demonstrated that it was able to describe quite accurately the characteristics of freely whipping, straight cantilever pipes. The present paper extends this model to enable it to be applied to bent cantilever pipes and covers cases in which the bend angle is opened. or closed. Previous attempts (Wang, 1991) to analyse these problems using a rigid, perfectly-plastic model were not completely successful due to the inability to identify admissible modes of deformation for all circumstances. A systematic programme of pipe whip tests has been carried out in UMIST on right-angled bent pipes. To illustrate the validity and use of the theoretical model, two typical cases are considered and the results compared with the experimental data extracted from high-speed films of the tests. Excellent agreement between the two is demonstrated.