Dynamic torsional buckling: Prebuckling waves and delayed instability

We study torsional buckling of a rod within the dynamics context, recognising that in a real experiment a twisting moment is not instantaneously applied and therefore an angular velocity (a spin) always accompanies a twist. We derive and solve the wave equation that governs prebuckling torsion dynamics and highlight the compatibility problem between initial and boundary conditions (corner singularity) plaguing numerical solution of the equation. We deal with this problem by introducing a smoothing function. Prebuckling torque oscillations are a major concern in various turbine applications. Torsional instability, upon further increase of the applied moment, is found to be delayed by the dynamic loading. We determine the dependence of the critical load on the rate of application of the moment by computing initial postbuckling solutions and extrapolating back to the critical point. For these computations we use the geometrically-exact Cosserat rod equations, which we discretise with the generalised-α method. We argue that in addition to inertia a gyroscopic effect may play a role in the delay. Our results may help explain delayed torsional buckling recently observed in simulation studies of flexible marine risers.