Keywords: train-bridge time-varying system, dynamic equations, train model, bridge model, algorithm.

A review of the trends in the development of dynamic algorithms for train-bridge time-varying systems is summarised. The major achievements and recent progress on the coupling vibration for train-bridge time-varying systems are discussed according to research methods, train model, bridge model, wheel-rail contact relationship, excitation source of train -bridge interaction, and solution of the coupling equations: some existing problems are mentioned. The direction of further research on the train-bridge time-varying system in the future is also indicated. Because of the complexity of the bridge coupling vibration research, some issues have still to be further improved. It is predicted that research on bridge-vehicle system coupling vibration will develop further in the following areas:

a)

the establishment of a dynamic theory for a large system and its applications;

b)

issues of train safety on the bridge under special loads: including wind loads, seismic excitations, and pseudo-excitation etc.;

c)

the range of problems in the surrounding environment; and the impact of problems with the train-bridge system vibrations on the environment;

d)

the research on vibration control of high-speed railway bridges;

e)

the application of symplectic algorithms in train-bridge time-variation system calculations; and

f)

the skilled treatment of bridge models.

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