Dispersion Analysis in Periodically Coupled Train–Bridge Systems

This study employs the wave dispersion relation of periodic structures to demonstrate the dual resonance mechanism occurring as a train traverses a series of bridges. Dual resonance occurs when the resonant speeds of both the train and the bridge coincide, leading to resonance in the bridge and progressively amplifying the train’s responses from the front to the rear carriages. This phenomenon involves a complex interaction between the bridge’s temporal resonance and the train’s spatial periodicity. This interaction creates a unique spatiotemporal vibration pattern. To understand the wave dispersion in this periodically coupled system, we model it as two interconnected spring-mass systems connected by contact springs. The analytical approach allows us to identify the key parameters governing the wave dispersion relation and wave-transmitting phenomena between two periodic structures. The wave dispersion analysis reveals that continuous beams have broader passbands, allowing them to transmit more waves and vibrations from moving trains than simply supported beams. This reduces resonance and leads to smoother system performance for continuous beams. Consequently, when a train travels on an equal-span continuous bridge at its resonance speeds, its vibrations can be efficiently transmitted to the bridge through these passbands, thereby mitigating resonance.