Historical Review on Resonance and Cancellation of Simply Supported Beams Subjected to Moving Train Loads: From Theory to Practice

The advent of railways and especially highspeed railways marks great strides in human transportation history. To guarantee exclusive right-of-way, highspeed railways are often built on equal simply supported beams resting on piers. In this paper, a historical review will be given of the resonance and cancellation phenomena observed for simply supported beams traveled by a set of moving loads, as they are typical of highspeed railways. The phenomenon of resonance was observed by early investigators including Timoshenko, Bolotin, Frýba, Matsuura, etc. However, the phenomenon of cancellation was noted lately in 1997 by Yang et al. By letting the conditions of resonance and cancellation coincident, they proposed the optimal span length for suppressing the resonance of simple beams, which is equal to 1.5 times the car length. This 1.5 times rule has been verified and adopted in the design of some highspeed railways. In this article, the theoretical solution for the problem will be revisited for unveiling the key parameters such as the resonance speed (in temporal domain) and resonance wavelength (in spatial domain). Then a rather in-depth review will be given of existing works on the resonance and cancellation of railway bridges from the waves perspective. Some new developments along these lines will also be identified.