Abstract
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.
Highlights
As application of new materials and requirements for landscape design improves continuously, more and more largespan soft structures are applied in the design and construction of footbridges
The research on pedestrian-induced pedestrian bridge vibration mainly focuses on linear vibration, whereas few researches on nonlinear vibration have been found
This paper further studies the influence of time delay on parametric vibration
Summary
As application of new materials and requirements for landscape design improves continuously, more and more largespan soft structures are applied in the design and construction of footbridges. Some footbridges will generate excessive lateral vibration under the excitation of pedestrian movement [11,12,13,14,15] Due to their long span, soft footbridges are generally soft structures with low natural frequencies. Piccardo has studied the parametric vibration of footbridges and proposed a new mechanism that can trigger excessive lateral vibration when pedestrians cross the bridge [16]. Erefore, the research in this article will play a beneficial role in the improvement of existing standards, and provide guidance for the design and management of footbridges with a first-order transverse frequency less than 0.5 Hz. Aiming at the large-scale vibration of the low-frequency footbridge, the paper employs a nonlinear parametric vibration model of the footbridge under the loading of pedestrians, in order to reveal the causes for large-scale vibration of low-frequency footbridge. This paper further studies the influence of time delay on parametric vibration
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