Planar dynamics of large-deformation rods under moving loads
X.W. Zhao & G.H.M. van der Heijden
We formulate the problem of a slender structure (a rod) undergoing large
deformation under the action of a moving mass or load motivated by
inspection robots crawling along bridge cables or high-voltage power lines.
The rod is described by means of geometrically exact Cosserat theory which
allows for arbitrary planar flexural, extensional and shear deformations.
The equations of motion are discretised using the generalised- method. The
formulation is shown to handle the discontinuities of the problem well.
Application of the method to a cable and an arch problem reveals interesting
nonlinear phenomena. For the cable problem we find that large deformations
have a resonance detuning effect on cable dynamics. The problem also offers
a compelling illustration of the Timoshenko paradox. For the arch problem
we find a stabilising (delay) effect on the in-plane collapse of the arch,
with failure suppressed entirely at sufficiently high speed.
keywords: Cosserat rod, large deformation, shear deformation, moving load,
generalised- method, jump discontinuity, detuning effect, Timoshenko
paradox, delay effect, in-plane arch collapse
Journal of Sound and Vibration 412, 309-325 (2017)