Long-term solutions of Macdonald's model for pedestrian-induced lateral forces

McRobie, FA

doi:10.1016/j.jsv.2012.12.027

Cited by 16 publications

(8 citation statements)

References 17 publications

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“…Further theoretical analyses of the model were conducted by Bocian et al [9], [10], McRobie [11] and McRobie et al [12]. A few experimental studies have also been conducted which give some support to the applicability of the IPM proposed by Macdonald [4].…”

Section: Introductionmentioning

confidence: 95%

Experimental identification of the behaviour of and lateral forces from freely-walking pedestrians on laterally oscillating structures in a virtual reality environment

Bocian

Macdonald

Burn

et al. 2015

Engineering Structures

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HighlightsA novel setup for investigating pedestrian–structure interaction is presented.Foot-placement is the main balance control mechanism on laterally vibrating ground.All components of pedestrian force are uncovered, including self-excited forces.Inverted pendulum pedestrian model qualitatively captures the nature of forces.The ground and visual conditions cause significant changes in pedestrian loading.

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Section: Introductionmentioning

confidence: 95%

Experimental identification of the behaviour of and lateral forces from freely-walking pedestrians on laterally oscillating structures in a virtual reality environment

Bocian

Macdonald

Burn

et al. 2015

Engineering Structures

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“…The work of Macdonald [10], itself a development of Barker's earlier work, [21], has motivated a number of researchers [14,15,22] to pursue a biomechanics-centric analysis of HSI. This approach typically utilises the inverted pendulum (IP) as a means of approximating human frontal plane CoM motion during locomotion, Fig.…”

Section: The Inverted Pendulum Model Of Frontal Plane Balancementioning

confidence: 99%

Experimental identification of the lateral human–structure interaction mechanism and assessment of the inverted-pendulum biomechanical model

Carroll

Owen

Hussein

2014

Journal of Sound and Vibration

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Experimental identification of the lateral humanstructure interaction mechanism and assessment of the inverted-pendulum biomechanical model. Journal of Sound and Vibration, 333 (22 A note on versions:The version presented here may differ from the published version or from the version of record. If you wish to cite this item you are advised to consult the publisher's version. Please see the repository url above for details on accessing the published version and note that access may require a subscription.For more information, please contact eprints@nottingham.ac.uk Experimental identification of the lateral human-structure interaction mechanism and assessment of the inverted-pendulum biomechanical model. AbstractWithin the context of crowd-induced lateral bridge vibration, human-structure interaction (HSI) is a widely studied phenomenon. Central to this study is the self-excited component of the ground reaction force (GRF). This force harmonic, induced by a walking pedestrian, resonates with lateral deck motion, irrespective of the pedestrian's pacing frequency. Its presence can lead to positive feedback between pedestrian GRFs and structural motion. Characterisation of the self-excited force as equivalent structural mass and damping has greatly improved the understanding HSI and its role in developing lateral dynamic instability. However, despite this evolving understanding, a key question has remained unanswered; what are the features of a pedestrian's balance response to base motion that give rise to the self-excited force? The majority of the literature has focused on the effects of HSI with the underlying mechanism receiving comparatively little attention. This paper presents data from experimental testing in which 10 subjects walked individually on a laterally oscillating treadmill. Lateral deck motion as well as the GRFs imposed by the subject were recorded. Three-dimensional motion capture equipment was used to track the position of visual markers mounted on the subject. Thus whole body response to base motion was captured in addition to the GRFs generated. The data presented herein supports the authors' previous findings that the self-excited force is a frequency sideband harmonic resulting from amplitude modulation of the lateral GRF. The gait behaviour responsible for this amplitude modulation is a periodic modulation of stride width in response to a sinusoidally varying inertia force induced by deck motion. In a separate analysis the validity of the passive inverted pendulum model, stabilised by active control of support placement was confirmed. This was established through comparison of simulated and observed frontal plane CoM motion. Despite the relative simplicity of this biomechanical model, remarkable agreement was observed.

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“…Note that Models 1 and 2 are effectively identical for small amplitude bridge motion. For Model 1, McRobie 47 derived an exact analytic expression for (shown as the green curve in the top panel of Fig. 4 a).…”

Section: Resultsmentioning

confidence: 99%

Emergence of the London Millennium Bridge instability without synchronisation

et al. 2021

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The pedestrian-induced instability of the London Millennium Bridge is a widely used example of Kuramoto synchronisation. Yet, reviewing observational, experimental, and modelling evidence, we argue that increased coherence of pedestrians’ foot placement is a consequence of, not a cause of the instability. Instead, uncorrelated pedestrians produce positive feedback, through negative damping on average, that can initiate significant lateral bridge vibration over a wide range of natural frequencies. We present a simple general formula that quantifies this effect, and illustrate it through simulation of three mathematical models, including one with strong propensity for synchronisation. Despite subtle effects of gait strategies in determining precise instability thresholds, our results show that average negative damping is always the trigger. More broadly, we describe an alternative to Kuramoto theory for emergence of coherent oscillations in nature; collective contributions from incoherent agents need not cancel, but can provide positive feedback on average, leading to global limit-cycle motion.

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Long-term solutions of Macdonald's model for pedestrian-induced lateral forces

Cited by 16 publications

References 17 publications

Experimental identification of the behaviour of and lateral forces from freely-walking pedestrians on laterally oscillating structures in a virtual reality environment

Experimental identification of the behaviour of and lateral forces from freely-walking pedestrians on laterally oscillating structures in a virtual reality environment

Experimental identification of the lateral human–structure interaction mechanism and assessment of the inverted-pendulum biomechanical model

Emergence of the London Millennium Bridge instability without synchronisation

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