Research On Free Vibration Characteristics And Dynamic Response Due To Moving Trains Of Long Span Suspension Bridge

Long span suspension bridge is an important bridge type crossing the strait and major rivers, and problems about stiffness and vibration usually control its application on the railway. The same time, the dynamic characteristics of suspension bridge is the basis of their dynamic analysis, and approximate calculation based on the principle of energy is an effective method to get the dynamic characteristics in the preliminary design stage. As dynamic characteristics has a number of factors, it is necessary to find a suitable approximate formula and analyze the impact of the design parameters.The linear differential equations of free vibration in suspension bridge was firstly reviewed, and their dimensionless forms were then got. It was found that the dynamic characteristics of single-span suspension bridge were determined by the cable sag and several dimensionless parameters, namely the elastic parameters of main cable, relative stiffness of stiffening girder to main cable, and the coefficient of spatial distribution of dead load. Then numerical solve of the dimensionless equations was got to analyse the effect of dimensionless parameters on dynamic characteristics.For single-span suspension bridge and three-span suspension bridge with continuous stiffening girder, the commonly used formula of dynamic characteristics was reviewed. Then the formulae for natural frequencies and modes of longitudinal-vertical coupling vibration and lateral flexural vibration were theoretically derived, in which the effect of the girder swing motion caused by tilt sling was taken into account. Through calculations on five single-span bridge examples and three three-span bridge examples, accuracy of these formulae was examined and sources of error were looking for. By the approximate formula and analysis of finite element model, the impact of design parameters on dynamic characteristics was studied, including the effect of sag-span ratio, stiffness of stiffening girder, dead load collection degree, ratio of side span and main span, and CFRP cable, cable tie, the continuous stiffening girder. In addition, the factor of the ratio of torsional and flexural vibration frequencies was studied.For a strait rail-cum-suspension bridge, the dynamic response of bridge structure due to moving train was studied by finite element analysis, including time-history curve, envelope diagram and dynamic magnification factor of dynamic response of stiffening girder, bridge towers, main cables and slings. The moving train modeled as moving loads and moving mass, the influence of train speed, the train inertia on the structural dynamic response was researched.The study in this paper indicated that:For engineering practice of large-span, single-span suspension bridge, the elastic parameters of main cable and vertical relative stiffness of girder had effects on vertical vibration fundamental frequency in small extent, while the elastic parameters of main cable had a much more effect on torsional vibration fundamental frequency than torsional relative stiffness of girder. Assuming that the torsional first-order symmetric mode as a half-wave sinusoidal curve would take little error. Span (main cable sag) was the most important factor of the dynamic characteristics. The ratio of torsional and flexural vibration fundamental frequencies was basically determined by the coefficient of spatial distribution of dead load and torsional relative stiffness of girder.The low order natural vibration of three-span continuous stiffening girder suspension bridge was characterized by the common vibration of cable and girder, while the side spans has a restraint effect related to the relative stiffness of stiffening girder and span ratio. Unless lateral flexural natural vibration, natural frequency would nearly not be effected by continuous stiffening girder. The dynamic response of the suspension bridge structure increased with the increase of the speed of trains, but with dynamic amplification factor no greater than1.10. The longitudinal displacement response of girder would be untrue, if the role of longitudinal damper at the end of girder was neglected. Dynamic response of suspension bridge was basically no difference under the action of moving load and moving mass.