Keywords: cancellation, resonance, moving loads, high-speed bridges, simply supported beams, simply supported plates.

This paper explores the cause of the phenomenon of cancellation in simply supported beams and plates subjected to travelling constant loads. In the literature devoted to moving load problems, cancellation has received special attention from a number of researchers [1]. The physical interpretation and the mathematical formulas derived in [1] were pioneering in the field and they are of undeniable value. However, the interpretation conceals the true nature of cancellation, and the formulas do not explain satisfactorily all possible cases.

The cause of cancellation lies in a quite curious fact: for certain speeds of a single moving load, the free vibrations which usually remain after the passage of the load simply disappear, leaving the structure completely at rest. This is true for simply supported undamped beams and plates under concentrated, constant forces travelling at a constant speed.

As it is known, when this kind of structure is subjected to trains of loads, resonance situations emerge very often due to the regularity of the distances between consecutive loads. For certain relations of the bridge length with respect to the characteristic load distance, the cancellation and resonance speeds coincide, and the latter is totally suppressed. This explains why some resonance peaks expected in the response of high-speed bridges do not appear in practice; or in other words, it explains why it is impossible to excite a resonant response in certain bridges by using certain types of train. In real bridges, which are damped structures, cancellation is not perfect and some free vibrations are present after the passage of the loads, but they are of very small amplitude and can not build up into significant resonances.

This paper provides simple but exact mathematical formulas which predict the cancellation speeds for any kind of train passing over simply supported beams or plates. Also, a formula has been given for predicting the length ratios which lead to the suppression of the resonance phenomenon. As mentioned before, this takes place when the characteristic load distance of the train is such that a resonance speed coincides with a cancellation speed.

1

Y.B. Yang, J.D. Yau, Y.S. Wu, "Vehicle-bridge interaction dynamics with applications to high-speed railways", World Scientific Publishing, 2004.

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