Critical speed and resonance criteria of railway bridge response to moving trains

The dynamic response of railway bridges to moving trains is complicated because of the involvement of the moving loads and the moving masses. Among various response characteristics, bridge resonance is of particular interest in terms of the structural effect and safety of the bridge. As far as the global bridge response is concerned, it is generally understood that when one of the apparent trainload excitation frequencies coincides with the fundamental natural frequency of the bridge, resonance could occur. However, such a general criterion is of little practical use because a typical trainload would involve numerous apparent frequencies (at equal intervals); consequently, for a given bridge (natural frequency), there could be many train speeds that satisfy the preceding resonance condition. Therefore, it is necessary to establish the relative severity of the resonance associated with each resonance scenario. This paper presents the development of a new resonance severity indicator, called Z factor, for the assessment of the resonance effect. It is found that the resonance severity is essentially governed by the ratio between the bridge and carriage lengths. When the carriage mass is significant, the same Z factor will apply; however, the underlying resonance speeds will change because of the altered natural frequency of the bridge-train system. Numerical results demonstrate that the proposed methods are effective for the determination of the resonance effects associated with the potential resonance speeds.