Pedestrian Excitation on the London Millennium Footbridge

Dallard, Pat

doi:10.1061/40753(171)138

Cited by 144 publications

(282 citation statements)

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“…On the opening day the Millennium Bridge, a pedestrian footbridge crossing the Thames River in London, was observed to exhibit a pronounced lateral wobbling as more and more people streamed onto the bridge [36,37,81,42,92,101,1]. This phenomenon apparently occurred due to a resonance between a low order bridge oscillation mode and the natural average stepping frequency of human walkers: a small initial oscillation of the bridge induces some of the walkers to synchronize the timing of their steps to that of the bridge oscillations, thus exerting a positive feedback force on the bridge that derives the bridge oscillation to higher amplitude, eventually resulting in a large steady-state oscillation.…”

Section: Coupling In Huygens' Experimentsmentioning

confidence: 99%

“…This was one of the first observations of the phenomenon of the coupled harmonic oscillators, which have many applications in physics [89,16,[18][19][20]47,93,5,99], biology and chemistry [93,60,63,64,100,104]. In engineering very spectacular was synchronization of pedestrians on Millennium bridge [1,19,36,37,42,81,84,86]. Huygens originally believed the synchronization occurs due to air currents shared between two pendula, but later after performing several simple tests he dismissed this and attributed the sympathetic motion of pendula to imperceptible movement in the beam from which both pendula were suspended.…”

Section: Introductionmentioning

confidence: 99%

“…This phenomenon apparently occurred due to a resonance between a low order bridge oscillation mode and the natural average stepping frequency of human walkers: a small initial oscillation of the bridge induces some of the walkers to synchronize the timing of their steps to that of the bridge oscillations, thus exerting a positive feedback force on the bridge that derives the bridge oscillation to higher amplitude, eventually resulting in a large steady-state oscillation. Subsequent studies by the bridge builder showed that the oscillations did not develop unless the number of the pedestrians on the bridge was greater than a critical value [36,37]. Generally, the phenomenon on the Millennium Bridge can be considered as a particularly dramatic example of the emergence of global collective behavior in the systems of many coupled heterogeneous oscillators [100].…”

Section: Coupling In Huygens' Experimentsmentioning

confidence: 99%

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Synchronization of clocks

et al. 2012

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Abstract:In this report we recall the famous Huygens' experiment which gave the first evidence of the synchronization phenomenon. We consider the synchronization of two clocks which are accurate (show the same time) but have pendulawith different masses. It has been shown that such clocks hanging on the same beam can show the almost complete (in-phase) and almost antiphase synchronizations. By almost complete and almost antiphase synchronization we defined the periodic motion of the pendula in which the phase shift between the displacements of the pendula is respectively close (but not equal) to 0 or π.We give evidence that almost antiphase synchronization was the phenomenon observed by Huygens in XVII century. We support our numerical studies by considering the energy balance in the system and showing how the energy is transferred between the pendula via oscillating beam allowing the pendula's synchronization. Additionally we discuss the synchronization of a number of different pendulum clocks hanging from a horizontal beam which can roll on the parallel surface. It has been shown that after a transient, different types of synchronization between pendula can be observed;(i) the complete synchronization in which all pendula behave identically, (ii) pendula create three or five clusters of synchronized pendula. We derive the equations for the estimation of the phase differences between phase synchronized clusters. The evidence, why other configurations with a different number of clusters are not observed, is given.

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Section: Coupling In Huygens' Experimentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Coupling In Huygens' Experimentsmentioning

confidence: 99%

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Synchronization of clocks

et al. 2012

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“…Hence, TMDs are used effectively to vibration control where the structure remains linear, and a single mode dominates the structural response [2,8]. Under seismic events, on the other hand, buildings are designed to yield.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Behavior of Steel Frames With Tuned Mass Dampers

Hosseini¹,

Jouneghani²,

Rohanimanesh³

et al. 2017

Adv. Sci. Technol. Res. J.

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In this paper, the application of tuned mass damper in improving the response of structures is considered. At first, three frames of 3, 9 and 20 stories are evaluated in which time history analysis is done according to El -Straw earthquake. The maximum reduction of among the three mentioned frames belongs to a 20-stories structure in which the rate of story displacement reduction is between 25 to 45%, and this indicates that by increasing the height of the structure, the performance of tuned mass damper improved. In the second part, the effect of semi-active tuned mass damper is studied on a 10-stories frame. Studies showed that using a tuned mass damper system with viscous damper with controller force decreases the average of maximum displacement of roof story down to 39.9 % and this amount of reduction is 22.8% for semi-active tuned mass damper. Finally, the performance of tuned Single and multiple mass Damper is evaluated on a 20-stories frame, and the results show that single and multiple dampers decrease structures 'responses and the performance of tuned multiple dampers depends on the mass and frequency ratio and also concluded that the performance of tuned multiple mass dampers is reduced by transition to middle of the structure stories.

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“…Vibration beyond the normal range will influence pedestrian comfort while occupying the structure. As a classic example, the London Millennium Bridge in 2000 was temporarily closed following excessive pedestrianinduced vibrations during its inauguration [2].…”

Section: Introductionmentioning

confidence: 99%

Quantification of human-structure interaction

Caprani

Živanović

et al. 2015

MATEC Web of Conferences

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Abstract. In lightweight structural systems there is increasing evidence that the presence of humans influences the dynamics characteristics of the system. In the past, most effort on determining the footfall-induced vertical force to the walking surface has been conducted using rigid or non-flexible surfaces such as treadmills. However, should the walking surface be vibrating, the characteristics of human walking could change to maximize comfort. This interaction between the structure and human may account for the discrepancy between the levels of vibration predicted by theory and those observed in practice. Indeed, many design rules can be seen to be conservative, perhaps partly because knowledge of this human-structure interaction is limited. This work aims to address this problem by quantifying the magnitude of human-structure interaction through a comprehensive experimental programme. Novel experimental techniques are used to measure the human-imparted force on the walking surface. Both rigid and flexible (vibrating) surfaces are used, and we measure the imparted vibration response on a lively footbridge (the Warwick Bridge) which acts as the flexible surface. A range of test subjects is considered, walking at a range of pacing frequencies. Comparison is made between a notional vibration response from the footfall force imparted to the rigid surface and the actual vibration response caused by the footfall force imparted to the flexible surface. Key aspects of the experimental regime are also explained. Finally, some comparisons are made using footfall force models from the literature. It is concluded that human-structure interaction is a key phenomenon that should be taken into account in the design and assessment of vibration-sensitive structures.

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Pedestrian Excitation on the London Millennium Footbridge

Cited by 144 publications

References 0 publications

Synchronization of clocks

Synchronization of clocks

Dynamic Behavior of Steel Frames With Tuned Mass Dampers

Quantification of human-structure interaction

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