Steady-state response of periodically supported structures to a moving load

Steady-state vibrations of periodically supported structures under a moving load are analytically investigated. The following three structures are considered: an overhead power line for a train, a long suspended bridge and a railway track. The study is based on the application of so-called `periodicity condition', which implies that the shape of a structure is repetitive in time with space translation equal to the distance between neighboring supports. Main attention in the paper is paid to the effect of the load velocity on dynamic response of the structures. It is shown that the higher the load velocity, the wider the deflection field. Deflection of structures grows as the load velocity increases. This grow, however, can be not monotonical due to appearance of critical velocities related to resonances on sub-harmonics of a periodic structure.