Dynamics and stability of slender structures carrying a moving load or mass

Abstract

We study the dynamics of one-dimensional slender structures such as cables, arches and flexible springs, that carry a moving load or mass. In the case of a moving mass we assume that inertial effects can be ignored. The geometrically-exact Cosserat rod theory is used to model the structure, which is allowed to undergo arbitrary three-dimensional flexural and twisting deformations. We use the generalised-α method for both the spatial and temporal discretisation of the equations of motion and Newton iterations to solve the resultant system of algebraic equations. This numerical scheme has good properties of second-order accuracy, unconditional stability and allows for tunable numerical dissipation. The theory is applied to a cable problem motivated by motorised transport systems such as inspection devices moving along bridge or powerline cables. Large deformations are found to have a resonance-detuning effect on the cable. We also consider the problem of an arch subject to a load that would lead to in-plane collapse if it was applied statically. Movement of the load is found to have a stabilising effect on the structure with collapse delayed at small velocities and suppressed altogether at sufficiently high velocity.