Wobbling of the Millennium Bridge
Prof. Edward Ott
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| Dr. Edward Ott |
To commemorate the start of the new Millennium, a strikingly beautiful foot bridge crossing the Thames River in London was opened in June, 2000. At the opening, as more walkers streamed onto the bridge, the bridge began to wobble violently. The bridge was subsequently closed, and modified, at substantial expense, so as to remove the wobble.
Research by Prof. Edward Ott and collaborators has quantitatively analyzed the mechanism of the wobble. This work, published in the journal Nature, has attracted much attention from the media, including numerous newspaper articles (e.g., a front page article on the NY Times weekly science section). In their Nature article, Prof. Ott and his collaborators describe a dynamical model for the self-consistent interaction of a large group of heterogeneous walkers with the dynamics of the bridge.
The key ingredient to their analysis is a description of how individual people, walking with different natural stepping frequencies, respond to the motion of the platform on which they are walking. By using techniques borrowed from mathematical biology, Prof. Ott and his collaborators showed that a self-synchronization instability results when the number of people on the bridge exceeds a critical value that depends in a precise manner on the natural frequency and damping of the wobble bridge mode, the stepping frequency probability distribution function, and response sensitivity of walkers. These results are of interest from several points of view: first, they provide a design criterion involving the dynamical response of a large group of humans (almost never included as a factor in the design of large structures); second, they are a verification of the efficacy of basic techniques often invoked in other scientific contexts, most notably, mathematical biology; and, finally, the result will be useful for the design of future such structures.
Researchers:
Steven H. Strogatz, Daniel M. Abrams, Allan McRobie, Bruno Eckhardt, and Edward Ott
Links:
Nature article: Theoretical Mechanics: Crowd Synchrony on the Millennium Bridge
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