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A new simple explicit two-step method and a new family of predictor-corrector integration algorithms are developed for use in the solution of numerical responses of dynamic problems. The proposed integration methods avoid solving simultaneous linear algebraic equations in each time step, which is valid for arbitrary damping matrix and diagonal mass matrix frequently encountered in practical engineering dynamic systems. Accordingly, computational speeds of the new methods applied to large system analysis can be far higher than those of other popular methods. Accuracy. stability and numerical dissipation are investigated. Linear and nonlinear examples for verification and applications of the new methods to large-scale dynamic problems i n railway engineering are given. The proposed methods can be used as fast and economical calculat Ion tools for solving large-scale nonlinear dynamic problems in engineering.

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Train-track-bridge dynamic interaction is a fundamental concern in the field of railway engineering, which plays an extremely important role in the optimal design of railway bridges, especially in high-speed railways and heavy-haul railways. This paper systematically presents a state-of-the-art review of train-track-bridge dynamic interaction. The evolution process of train-bridge dynamic interaction model is described briefly, from the simplest moving constant force model to the sophisticated train-track-bridge dynamic interaction model (TTBDIM). The modelling methodology of the key elements in the TTBDIM is systematically reviewed, including the train, the track, the bridge, the wheel-rail contact, the track-bridge interaction, the system excitation and the solution algorithm. The significance of detailed track modelling in the whole system is highlighted. The experimental research and filed test focusing on modelling validation, safety assessment and long-term performance investigation of the train-track-bridge system are briefly presented. The practical applications of train-track-bridge dynamic interaction theory are comprehensively discussed in terms of the system dynamic performance evaluation, the system safety assessment and train-induced environmental vibration and noise prediction. The guidance is provided on further improvement of the train-track-bridge dynamic interaction model and the challenging research topics in the future. ARTICLE HISTORY