Vertical vibrations of composite bridge/track structure/high-speed train systems. Part 2: Physical and mathematical modelling

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

Vertical vibrations of composite bridge/track structure/high-speed train systems. Part 1: Series-of-types of steel-concrete bridges

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

Vertical vibrations of composite bridge/track structure/high-speed train systems. Part 2: Physical and mathematical modelling

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

Vertical vibrations of composite bridge/track structure/high-speed train systems. Part 3: Deterministic and random vibrations of exemplary system

Based on the one-dimensional quasi-exact physical and mathematical modelling of a composite (steel-concrete) bridge/track structure/high-speed train system (BTT), developed in Part 2, advanced computer algorithms for the BTT numerical modelling and simulation as well as a computer programme to simulate vertical vibrations of BTT systems are developed. The exemplary bridge under numerical quasi-static and dynamic analysis, designed according to Polish standards, has a 15.00 m span length and belongs to the SCB series-of-types developed in Part 1. The bridge is loaded by a German ICE-3 high-speed train moving at the resonant and maximum operating speeds. A continuously welded ballasted track structure adapted to high operating velocities is applied. The output quantities include: time-histories of the vertical deflection of the main beams at the midspan, time-histories of the longitudinal normal stress in the bottom fibres of the main beams at the midspan, time-histories of the vertical acceleration of the bridge deck at the midspan, time-histories of the vertical accelerations of the suspension pivots in car-bodies, time-histories of the dynamic pressures of the wheel sets of moving rail-vehicles. The design quantities, understood as the extreme values of the output quantities, are used to verify the design conditions. The basic random factor, i.e. vertical track irregularities of the track, is taken into consideration. Basic statistics of the design quantities treated as random variables are calculated and taken into account in the design conditions

Wpływ losowych nierówności toru na drgania wybranego układu most zespolony / nawierzchnia kolejowa / pociąg szybkobieżny

A theory of the quasi-exact physical and mathematical modelling of the composite (steel–concrete) bridge / ballasted track structure / high-speed train system (BTT) was developed, including viscoelastic suspensions of rail-vehicles on two-axle bogies, the non-linear Hertz contact stiffness and one-sided contact between the wheel sets and the rails, the viscoelastic and inertia features of the bridge, the viscoelastic track structure on and beyond the bridge, the approach slabs, and random track irregularities. Based on this theory, advanced computer algorithms for the BTT numerical modelling were written and a computer program to simulate the vertical vibrations of the BTT systems was developed. The bridge subject to the preliminary dynamic analysis and designed according to Polish standards has a 15.00 m span length. The bridge was loaded by the German ICE-3 high-speed train moving at the critical (180 and 270 km/h) and the maximum (300 km/h) operating speeds.Opracowano quasi-ścisłą teorię modelowania jednowymiarowego (1D), fizycznego i matematycznego, układu most zespolony / nawierzchnia kolejowa podsypko-wa / pociąg szybkobieżny (BTT), przy uwzględnieniu lepkosprężystych zawieszeń pojazdów szynowych na dwuosiowych wózkach jezdnych, nieliniowej sztywności kontaktowej Hertza i jednostronnego kontaktu między zestawami kołowymi a szynami, cech lepkosprężystych i bezwładnościowych mostu, lepko sprężystej nawierzchni kolejowej na moście i poza mostem, płyt przejściowych i losowych nierówności toru. Na podstawie tej teorii opracowano zaawansowane algorytmy komputerowe modelowania numerycznego układów BTT oraz program komputerowy do symulacji drgań pionowych tych układów. W ramach wstępnych badań dynamicznych rozważono most zaprojektowany zgodnie z polskimi normami, o rozpiętości teoretycznej przęsła 15,00 m, oznaczony kodem SCB-15. Most obciążono niemieckim pociągiem szybkobieżnym ICE-3, poruszającym się z prędkością krytyczną (270 km/h) i maksymalną (300 km/h)