Dynamic torsional buckling: prebuckling waves and
delayed instability
X.W. Zhao & G.H.M. van der Heijden
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-$\alpha$ 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.
keywords: Cosserat rod, torsional wave, torsional buckling, delay of
buckling, corner singularity
Communications in Nonlinear Science and Numerical Simulation
69, 360-369 (2019)