Vibrations of beams and rods carrying a moving mass
X.W. Zhao, G.H.M. van der Heijden & Z.D. Hu
We study the vibration of slender one-dimensional elastic structures (beams,
cables, wires, rods) under the effect of a moving mass or load. We first
consider the classical small-deflection (Euler-Bernoulli) beam case, where
we look at tip vibrations of a cantilever as a model for a barreled launch
system. Then we develop a theory for large deformations based on Cosserat
rod theory. We illustrate the effect of moving loads on large-deformation
structures with a few cable and arch problems. Large deformations are found
to have a resonance detuning effect on the cable. For the arch we find
different failure modes depending on its depth: a shallow arch fails by
in-plane collapse, while a deep arch fails by sideways flopping. In both
cases the speed of the traversing load is found to have a stabilising effect
on the structure, with failure suppressed entirely at sufficiently high speed.
Journal of Physics: Conference Series 721, 012016 (2016)