Abstract.A theory of one-dimensional physical and mathematical modelling of the composite (steel-concrete) bridge/track structure/highspeed train system is developed including viscoelastic suspensions of rail-vehicles with two two-axle bogies each, non-linear Hertz contact stiffness and one-sided contact between wheel sets and rails, the viscoelastic and inertia features of the bridge, the viscoelastic track structure on and beyond the bridge, approach slabs, and random vertical track irregularities. Compared to the state-of-the-art, the physical model developed in the study accurately reproduces dynamic processes in the considered system. Division of the system into the natural subsystems, a method of formulation of the equations of motion partly in implicit form and the finite element method are applied. Vibrations in the vertical plane of symmetry are described by more than nine matrix equations of motion with constant coefficients. Couplings and non-linearity are hidden in the generalized load vectors. The equations of motion are integrated using the implicit Newmark average acceleration method with linear extrapolation of the interactions between the subsystems.

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Abstract.A new series-of-types of single-span simply-supported railway composite (steel-concrete) bridges, with a symmetric platform, has been designed according to the Polish bridge standards. The designed bridges/viaducts are located on the main railways of the classification coefficient k = +2. A ballasted track structure adapted to high operating speeds has also been designed. The ultimate limit states and the limit states corresponding to the bridges undertaken are collected and discussed. The bridges have been designed in accordance with contemporary art engineering, with geometric and material optimization, avoiding overdesign. A new methodology of numerical modelling and simulation of dynamic processes in composite bridge/ballasted track structure/high speed train systems, developed in Part 2 and Part 3, has been applied and implemented in a problem-oriented computer programme. A new approach to predicting forced resonances in those systems is formulated and tested numerically. It has been proved that in the case of typical structural solutions of bridges and ballasted track structures, it is necessary to introduce certain limitations for operating speeds of trains.

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SUMMARYThe paper makes a contribution to the problem of a stream of loads crossing a single-span beam bridge. There are considered the basic load models, in the form of a stream of fixed amplitude forces, unsprung masses and viscoelastic oscillators. The matrix equations of motion of the system are formulated and discussed. The problem of dynamic stability and steady-state response of a bridge carrying a periodic stream of inertial loads is formulated and solved. The paper also includes a vibration study of a beam bridge subjected to a uniform stream of moving loads, of a limited or unlimited number of load cycles.