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標題: | 行人側向擺動與橋的交互作用 Interaction between Bridge Vibration and Pedestrians’ Lateral Wobble |
作者: | Ping-Jung Lu 呂炳榮 |
指導教授: | 盧中仁(Chung-Jen Lu) |
關鍵字: | 千禧橋,同步,倒單擺,諧和平衡法,振動, Millennium Footbridge,inverted pendulum,synchronization,harmonic balance,vibration, |
出版年 : | 2019 |
學位: | 碩士 |
摘要: | 英國倫敦泰晤士河上的千禧橋開通不久便因大批遊客上橋引發嚴重的振動現象,而被迫關閉。P. Dallard等人對此作了相關研究,發現當時橋的振動主要來自橋的側向擺動,認為事件肇因於橋與人所產生的同步現象(synchronization)。此外,只有當橋上的人數達到一定數量時,橋才會發生嚴重的振動。之後,陸續有人朝同步或共振的方向去探討千禧橋的現象。Strogatz等人利用蔵本模型(Kuramoto model)模擬人的運動行為,數值積分的結果證實,行人的數目是導致橋振動的重要因子。然而,蔵本模型已隱含了同步會隨人數的增加而突現的因子,並不能完整說明千禧橋的振動。
本論文將人的側向擺動行為假設成Hof的倒單擺模型;橋的模型假設成彈簧–阻尼–質量系統(弱阻尼諧振系統),人–橋透過慣性力交互作用,在沒有預設是否同步的前提下討論同步現象。先由單人的系統開始,利用數值積分,找出不同型態的穩態解,再以諧和平衡法(harmonic balance),得到系統的週期解,並與數值積分的穩態解相比對。最後,將模型推廣至雙人,甚至多人並探討不同人數對系統同步的影響。 The London Millennium Footbridge on the River Thames was forced to close by a violent vibration due to a large number of pedestrians at its opening. P. Dallard et al. made a series of related research about the phenomenon. He found that the vibration of the bridge mainly came from the lateral oscillation and was caused by the synchronization between the bridge and the pedestrians. They also found that the bridge will vibrate only if the number of the pedestrians on the bridge reaches a critical value. The existence of the critical value for pedestrians has been explained successfully by Strogatz et al. by the Kuramoto model. However, the emergence of synchronization when a key parameter reaches a critical value is a property of the Kuramoto model. It remains an open question whether there exists a critical number of pedestrians beyond which synchronization emerges. In this thesis, we simulated the pedestrian behavior as Hof’s inverted pendulum model and the bridge as a spring-damping-mass system (weakly damped harmonic oscillator). The pedestrians and the bridge interact through the inertial force. We examined the steady-state response of the pedestrian-bridge system for the necessary conditions under which synchronization between the pedestrians and the bridge is possible. Started from a single-pedestrian system, we used numerical integration and the harmonic balance method to determine the steady-state solutions. We found that the pedestrian will syhchronize with the bridge eventually in most cases and there are two different types of synchronization motion. On the basis of these results, we examined the multiple-pedestrians and bridge system. Emphasis was put on the effect of the number of the pedestrians on the synchronization of the system. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/72601 |
DOI: | 10.6342/NTU201901391 |
全文授權: | 有償授權 |
顯示於系所單位: | 機械工程學系 |
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