Research On Adaptability Of Vehicle-Bridge Coupling Problem Calculation Method And Resonance Influence Degree Of Simply Supported Beam

With the progress of human society and the constant innovation of scientific and technological level,the scale and technology of China's transportation system have been continuously improved,and the construction of high-speed railway has entered a peak period of development.In view of the tremendous changes in bridge types,vehicle parameter design standards and Vehicle-Bridge material properties in the current era with rapid changes,in order to improve work efficiency and meet the requirements of traffic development in the new era,through comparison and analysis,this paper presents an accurate estimation of bridge vertical dynamic noise which is easy to be used by engineers in the range of common train speeds.The simplified calculation method should be adopted.In the process of vehicle-bridge coupling research,the complex calculation method is the space multi-degree-of-freedom complex vehicle-bridge coupling model.The simplified calculation method can be summarized as follows:simplifying the vehicle to the moving concentrated force,simplifying the vehicle to the moving mass and simplifying the vehicle to the moving spring mass acting on the bridge.Therefore,this paper studies the problem of accurately simulating the space multi-degree-of-freedom complex vehicle-bridge coupling model by moving load sequence model and moving wheel plus spring mass model.Based on this research,the formula of dynamic amplification coefficient is derived when bridge resonance occurs,and the dynamic amplification coefficient is proposed to indicate the influence degree of bridge resonance.The main research work and conclusions are as follows:(1)Based on Lagrange motion equation and vertical close assumption,the spatial motion equation of the spatial multi-degree-of-freedom complex vehicle-bridge coupling dynamic analysis model is given.The simplified calculation methods of single moving force model,moving mass model and moving wheel plus spring mass model are given to analyse the vertical displacement response of simply supported beam.The simplified conditions,solving process and application of the three models are compared and analyzed in detail.Based on the dynamic motion equation of a simply supported beam with and without damping under moving loads,two resonance critical velocity formulas of a simply supported beam without damping are deduced by using the triangular transformation formula.The resonance conditions of a simply supported beam without damping are analyzed.The first critical velocity is related to the length of the vehicle body,and the second critical velocity is related to the span of the bridge.(2)The program of the eight-section train moving load sequence model,moving wheel plus spring mass model and the spatial multi-degree-of-freedom complex vehicle-bridge coupling dynamic analysis model is compiled,and a finite element model of a 32 m double-track concrete simply supported box girder is established.By changing the speed,mass ratio and stiffness ratio of the moving load sequence model,moving wheel plus spring mass model and the space multi-degree-of-freedom complex vehicle-bridge coupling dynamic analysis model,the displacement deviation ratio is analyzed.The results show that the simplified calculation method has almost no effect on the approximate simulation of the space multi-degree-of-freedom complex model under different vehicle-bridge stiffness ratio conditions.The bigger the bridge mass ratio is,the bigger the deviation rate is;when the bridge resonates,the deviation rate is not only more than 5%,but also the mid-span displacement obtained by simplified calculation method is less than that obtained by complex calculation method.Taken into account the convenience of calculation and safety in practical engineering,the calculation method of space multi-degree-of-freedom complex model is proposed for high-speed train running speed in the range of 85%-115%of the resonance speed of simply supported beam.The simplified method of moving load train model is used to calculate the vehicle-bridge coupling problem when the running speed of high-speed train is outside the range of 85%-115%of the resonance speed of simply supported beam.Therefore,in practical engineering,according to the bridge resonance speed and train passing speed,the simplified calculation method or complex calculation method of vehicle-bridge coupling in speed interval is selected to analyze the problems between vehicles and bridges more simply.(3)Based on the accurate simulation of the simplified calculation method and the bridge resonance speed related to the length of the vehicle body,the formula of the first order dynamic amplification factor of a simply supported beam is deduced when resonance occurs..The degree of resonance of the simply supported beam is reflected by the dynamic amplification coefficient.Through the analysis,it is concluded that the dynamic amplification coefficient is related to the length of the vehicle body,the span of the bridge and the damping ratio,and the mass of the bridge.Within the range of parameters studied,bridge stiffness has little effect on the resonance influence degree of simple-supported beams;The resonance influence degree of simple-supported beams increases with the increase of vehicle body length;And the resonance influence degree of simple-supported beams decreases with the increase of damping ratio and bridge span.