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Based on the finite Fourier series and the energy variation principle, an analytical calculation method for the dynamic response of multi-span bridge-track structure systems under the action of moving load series is proposed. The applicability of this method is verified by the comparison of the results with the analytical and numerical approaches. Based on the proposed method, the dynamic response of double-layer and four-layer beam models, commonly used in railway bridge systems is solved, and the calculation formulas of resonance and vibration cancelation velocity of multi-layer beam systems are proposed. The influence of the span number of simply supported beams and the length of subgrade sections on the dynamic response of the four-layer beam system is investigated. The results show that the deflection of the dynamic response of double-layer and four-layer beam systems reaches the maximum value near the mid-span. These two systems have multiple critical speeds under moving loads. When the resonance and vibration cancelation of the multi-beam system occur simultaneously, the vibration cancelation plays a leading role. The span number of simply supported beams and length of subgrade sections influence the dynamic response of the four-layer beam system but have no significant effect on the critical velocity of resonance and vibration cancelation. At present, there is a lack of research on analytical or semi-analytical methods for the dynamic response of multi-span bridge-track structure systems. This research may provide a theoretical basis for the planning, design, operation, and maintenance of bridge-track structure systems to a certain extent.

Dynamic response analysis of multi-span bridge-track structure system under moving loads