Emergence of the London Millennium Bridge instability without synchronisation

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.

Computer Vision Technique for Blind Identification of Modal Frequency of Structures from Video Measurements

Operational modal analysis (OMA) is required for the maintenance of large-scale civil structures. This paper developed a novel methodology of non-contact-based blind identification of the modal frequency of a vibrating structure from its video measurement. There are two stages in the proposed methodology. The first stage is extracting the motion data of the vibrating structure from its video using a complex steerable pyramid. In the second stage, the principal component analysis combined with analytical mode decomposition is used for modal frequency separation from the motion data. Numerical validation of the methodology on a 10 DOF model is presented. The application of the proposed methodology on the London Millennium Bridge is also presented.

Nature of Financial Risk

Risk is endogenous. The brief opening and then the closing of the Millennium Bridge in London in 2000 illustrates how market prices play a dual role: they are simultaneously a reflection of market participants’ actions as well as an imperative for their actions.

VIBRATION RESPONSE OF A FOOTBRIDGE DUE TO PEDESTRIANS' MOVEMENTS

Failure of footbridges in England and France due to excessive vibrations from marching soldiers in the nineteenth century resulted in many fatalities and injuries. The unexpected lateral vibrations of the Millennium Bridge over the Thames River in London was a watershed event as large number of research studies were conducted on this subject following this incidence. However, there are still a number of issues related to vibration serviceability of footbridges that require further studies. Among these are: the amplification of structural response when a group of pedestrians cross a footbridge as compared to a single individual (group effects). This is important as footbridge vibrations are usually computed when subjected to one pedestrian’s crossing and are magnified to estimate those generated by a group of people. Therefore, it is important to conduct vibration testing of footbridges to better define the group effects. This paper presents an experimental study of a footbridge susceptible to vibrations due to human movements. With the help of a group of volunteers, the group effects were computed as a function of the group size. It was found that the results were not completely consistent with those in the literature. Conclusions are made based on the results of the data analysis.

Walking crowds on a shaky surface: stable walkers discover Millennium Bridge oscillations with and without pedestrian synchrony

Why did the London Millennium Bridge shake when there was a big enough crowd walking on it? What features of human walking dynamics when coupled to a shaky surface produce such shaking? Here, we use a simple biped model capable of walking stably in three dimensions to examine these questions. We simulate multiple such stable bipeds walking simultaneously on a bridge, showing that they naturally synchronize under certain conditions, but that synchronization is not required to shake the bridge. Under such shaking conditions, the simulated walkers increase their step widths and expend more metabolic energy than when the bridge does not shake. We also find that such bipeds can walk stably on externally shaken treadmills, synchronizing with the treadmill motion for a range of oscillation amplitudes and frequencies. Our simulations illustrate how interactions between (idealized) bipeds through the walking surface can produce emergent collective behaviour that may not be exhibited by just a single biped.

ARCHITECTURAL PLANNING PRINCIPLES OF URBAN BRIDGES RECONSTRUCTION

The bridges and overpasses of the city of Samara are considered, their main characteristics are identifi ed. A brief historical background of the appearance of the fi rst bridges as simple engineering structures is given, the main temporary periods are highlighted. Examples of implemented solutions that characterize the main stages of the history of bridge construction are given: the Hohenzollern Bridge in Cologne, the Millennium Bridge in Gateshead, the Ponte Vecchio Bridge in Florence, the Golden Gate Bridge in San Francisco, the Russian Bridge in Vladivostok, the String Bridge in Jerusalem. The analysis helps to understand how a modern bridge, located in the city building system, aff ects it, complements and enriches it, combines many functions and advanced technologies, and also has architectural expressiveness.