Dynamics of large-deformation structures under moving loads

These include space tethers, satellite antennae, launch systems, robotic arms, pipelines, cranes, flexible manipulators, high-speed train railroads and highway bridges with moving vehicles.

The classic example of a moving-mass problem is the idealisation of a vehicle-bridge system in which the moving vehicle is treated as a moving load and the bridge is modelled as a small-deformation beam. However, with the current drive to use thinner and lighter materials in order to save material and reduce costs, large deformations of slender structures become increasingly important.

In recent work we have developed a formulation for the problem of a slender structure undergoing large deformations under the action of a moving mass or load, motivated by inspection robots crawling along bridge cables or high-voltage power lines. The structure is modelled as a geometrically-exact Cosserat Rod that allows for arbitrary planar flexural, extensional and shear deformations. The formulation handles the discontinuities of the problem well - for example, the shear force has a step discontinuity where the point load is applied.

Application of the method to a cable and an arch problem reveals interesting new non-linear phenomena. For the cable problem we find that large deformations have a resonance detuning effect on cable dynamics. For the arch problem the moving load has a stabilising effect: buckling or collapse of a statically unstable arch is delayed by a moving load and suppressed altogether at sufficiently high speed.