Abstract Summary
We study the dynamics of one-dimensional slender structures such as beams and arches carrying a moving load. Nonlinear, geometrically-exact rod theory is used to model the structure, which is allowed to undergo arbitrary three-dimensional flexural and twisting deformations. The equations of motion are solved by using the generalised-alpha method for both spatial and temporal discretisation. We find that large deformations (geometrical nonlinearities) have a detuning effect on the resonance and cancellation phenomena of the structure under moving loads. For these results we have obtained new exact expressions for the natural frequencies of circular beams and arches. We find that the collapse scenario (bifurcation) of a circular arch depends strongly on the opening angle of the arch. The speed of the moving load has a very strong effect on vibrations of the structures, including on the free vibrations after passage of the load. High speed tends to stabilise an arch or even to prevent in-plane collapse or out-of-plane instability where a static load of the same magnitude would induce it. We comment on the wider phenomenon of bifurcation delay due to finite rates of application of loads.
