Pedestrian excitation may consequently cause large-scale lateral vibration of the long-span softness of footbridges. Considering the influence of structural geometric nonlinearity, a nonlinear lateral parametric vibration model is established based on the relationship between force and speed. Taking the London Millennium Footbridge as an example, the Galerkin method is applied to formulate parametric vibration equations. In addition, the multi-scale method is used to analyze the parametric vibration of footbridge system theoretically and numerically. The paper aims to find out the reasons for the large-scale vibration of the Millennium Footbridge by calculating the critical number of pedestrians, amplitude-frequency, and phase-frequency characteristics of the Millennium Footbridge during parametric vibration. On the other hand, the paper also studies the influence parameters of the vibration amplitude as well as simulates the dynamic response of the bridge during the whole process of pedestrians on the footbridge. Finally, the paper investigates influences of the time-delay effect on the system parameter vibration. Research shows that: the model established in the paper is reliable; the closer the walking frequency is to two times of the natural frequency, the fewer number of pedestrians are required to excite large vibrations; when the number of pedestrians exceeds the critical number in consideration of nonlinear vibration, the vibration amplitude tends to be stable constant-amplitude vibration, and the amplitude of vibration response is unstable constant-amplitude vibration when only linear vibration is considered; the following factors have an impact on the response amplitude, including the number of pedestrians on footbridge per unit time, damping, initial conditions, and the number of pedestrians in synchronized adjustment. At last, when considering the lag of the pedestrian’s force on the footbridge, the time-lag effect has no effect on the amplitude but has an effect on the time needed to reach a stable amplitude.

In order to explore the changes of mechanical properties of cable-stayed arch composite bridge in different construction stages, this paper takes a 136m tensed-string arch bridge as the engineering background, briefly describes the construction steps of grid lifting, and adopts Madis/Civil finite element analysis software for modeling. The actual construction process of the arch bridge is simulated by classifying different construction stages. The static and dynamic mechanical properties and stability of arch Bridges are studied. Through research and analysis, the main conclusions are drawn that the cables of the tensioned arch bridge bear part of the load of the original arch rib and girder.

Accurate simulation of walking load is of great significance in conducting human-induced vibration analyses. However, accurate pedestrian walking load data obtained from long-span footbridges is scarce and data reliability depends on the sensor used for measurement. In the current work, Yanluo Footbridge with 102 m span was adopted as test site and Xnode high-precision acceleration wireless sensor was applied for measurements. An experimental investigation was performed on walking loads according to bipedal walking force model. In experimental studies, single-person and multi-person walking tests were performed at Yanluo Footbridge to measure corresponding stride frequency and dynamic load factor. The acceleration time-histories of walking pedestrians were accurately recorded using three-axis wireless acceleration sensor Xnode. Furthermore, the equation of dynamic load factor was derived by analyzing time-histories and power spectra and the design models of pedestrian walking load and crowd load were developed based on a great number of experimental data. Time histories of pedestrian walking loads showed regular periodic changes and dynamic load factor increased by increasing stride frequency. Using the walking load model developed in this work, the reliable structure response of human-induced vibration analysis can be obtained.