A Study On Non-linear Dynamic Interaction Between Long-span Flexible Footbridge And Pedestrians

With the development of urbanization, When the footbridges are longer and more flexible, it is prone to induce excessive vibration problem when the natural frequencies of foot-bridge are close to the striding frequency of pedestrian. Up to now, a large number of long-span flexible footbridges have been built or under construction at home and abroad. However, there are a few of studies on the vibration problem about the footbridge.And the practical calculation formulas to estimate the effect of pedestrians passing-by, are still lagging behind the engineering practice of footbridges. In the dissertation, some problems about the dynamic interaction between pedestrians and footbridge such as the linear, nonlinear vibration response of footbridge and acting forces of pedestrians, are investigated theoretically and numerically.It is aimed at the characteristics and existing problems of pedestrian-induced bridge, basically the major researches which have been done are shown as follows:(1) In the dissertation, the analytical expression of vibration response by the individual pedestrian who was walking on the footbridge was deduced. The simplified expression of pedestrian-induced bridge vibration response is provided.The simplified maximum response values is convenient for the computation structure of maximum dynamic response. And it is compared with results of previous researchers. Most importantly, the correctness and accuracy of the method in the dissertation are proved.(2) The human body is regarded as the two degrees of freedom system. The crowd of pedestrian-bridge coupling system dynamic models are deduced when the crowd are walking on the footbridge. Some factors including the quality of the pedestrian and stride frequency of randomness are considered. Calculation procedure of interaction between pedestrians and bridge is made based on ANSYS platform. Moreover, the influence of crowd on the dynamic characteristics of the coupled system is analyzed. Crowd-bridge coupling system dynamic response and pedestrians induced vibration parameters sensitivity under different walking patterns are studied. Based on the response acceleration of pedestrians, the comfort level of pedestrians is evaluated.(3) The effect of pedestrians quality on the footbridge system frequency is taken into consideration. Based on the measured data of Millennium Bridge,the pedestrian-induced bridge nonlinear transverse vibration parameters model is set up on the basis of relationship between force and speed. Galerkin method is applied to disperse the vibration equation. The dissertation makes the theoretic and numerical analysis on the pedestrian footbridge vibration by applying the multi-scale method. The causes of wide-amplitude vibration on the Millennium Bridge and the parameter vibration in critical number, amplitude frequency and phase frequency characteristics are studied as well. Moreover, the number of pedestrians on the bridge per unit time, the mass per unit length of the girder, damping ratio, and the influence of initial conditions on the vibration amplitude are analyzed. The footbridge dynamic response of the entire process on the bridge is simulated. At last, the influence of time-lag on system parameters vibration is discussed.(4) With regard to the Flexible footbridge transverse parameters vibration problems, on the consideration of the time-lag effect by pedestrians on the bridge, lateral displacement of pedestrians on the Millennium Bridge, and speed are studied by applying multi-scale method. Some adjustments are made on two feedback adjusting models. The critical time-lag under the two situations are analyzed respectively. Time-lag, feedback adjustment coefficient of the Bridge on critical numbers and the influence of the response amplitude are studied as well. The results show that the influence of acting force time-lag and feedback adjustment on the Millennium Bridge vibration response cannot be ignored, considering the adjustment on the two adjusting models namely the horizontal displacement and transverse speed based on pedestrian footbridge.(5) The hybrid Van der Pol-Rayleigh oscillator is put forward and applied to simulate lateral force model of pedestrian. The experimental data by the predecessors fit with the relevant parameters of the model. The applied force on structure calculated by model meets with the sum of multiple harmonic loads which are put forward by scholars.(6) Based on the propositional pedestrian lateral force model, pedestrian-flexible footbridge transverse coupling system interaction dynamic model is set up to decouple the equation. Pedestrian-flexible footbridge amplitude-frequency equation and phase-frequency equation of the coupled system are deduced. By an example, The phase difference between the transverse relative displacement of pedestrian is studied. The phase difference between transverse absolute displacement of the pedestrians and lateral displacement of pedestrian bridge is studied as well. Meanwhile, the phase difference between lateral interaction and transverse incent-ive pace is researched. Finally, the relationship between transverse dynamic load coefficient of pedestrians and pedestrians lateral relative displacement is studied in the dissertation.