The Vibration Research And Parameter Analysis Of Suspension Footbridge Based On Crowd-Bridge Coupling Vibration Theory

With larger span, less mass and lower damping, the natural frequency of footbridge gradually reduces, which causes structures easier to vibrate under crowd excitation. Consequently, vibration comfort or even service safety may be affected. Therefore, it is necessary to analyze the vibration response of footbridges under walking crowd excitation at present. However, on one hand, load models are usually used to simulate crowd excitation which ignore the interaction between crowd and structures; on the other hand, although various human body models have been proposed, most of them are used to analyze the effect of static crowd on the structural dynamic characteristics, and rarely used to analyze the effect of walking crowd on the structural vibration response, let alone the parameter analysis based on crowed-bridge coupling vibration. To solve the above mentioned problems, following aspects have been researched in this thesis:(1) Combined with the researches on pedestrian load models and human body models, a human body dynamic model including time-invariant main body mass, stiffness, damping and time-variant coupling mass was proposed, and the lateral pedestrian load was expressed by a Fourier series model; the loads applied to pedestrian and bridge respectively were analyzed, then human body dynamic equilibrium equation was derived, and the solving method was determined by comparing linear acceleration method, Wilson-θ method and Newmark method.(2) The coordinated relationship of displacement and force between pedestrian and bridge was analyzed, and an analysis method of human-bridge coupling vibration was proposed, which was based on the coordinated relationship and realized by solving human body dynamic equilibrium equation in Newmark method and solving bridge dynamic equilibrium equation in full transient analysis method; the reliability of this method was proved using spring mass system moving over a beam and human body dynamic model moving over a beam, and the effects of time step, the number of substeps and loading type on calculation accuracy and solution efficiency were analyzed.(3) Taking a long-span suspension footbridge as an object, the natural frequency was obtained by modal analysis, and a reasonable damping ratio was determined by comparing norm provisions of various national standards; based on the analysis method proposed in this thesis and combined with spectrum analysis, effects of the parameters such as step frequency, crowd walking pattern, and population density on vibration response of the crowed-bridge coupling system were studied; a reasonable comfort evaluation method was determined by comparing the footbridge comfort evaluation index and limits of various national standards, then the allowed people number on the bridge was estimated.The results show that:　the analysis method proposed in this thesis is feasible, and calculation accuracy and solution efficiency of the method are both satisfactory when time step is 0.01s and the number of substeps is 1; the vibration response of middle span is synthetically influenced by two or three of the factors such as step frequency, crowd walking pattern, population density; the change regulations of vertical and lateral vibration responses are different; to evaluate the comfort of the footbridge, root mean square acceleration should be adopted as the comfort evaluation index, and the vibration total value should also be adopted to consider vertical and lateral coupling vibration of footbridge, which should be less than 0.5 m/s2.