Scientists from Russia solved a mathematical secret, «the dancing bridge»

© Flickr / Glen BowmanМост The Millennium. London, UKScientists from Russia solved a mathematical secret, «the dancing bridge»© Flickr / Glen Bowman

. Russian and American mathematicians have found a simple explanation for why the famous Millennium bridge in London began to dance and almost collapsed during its opening in 2000, said in an article published in the journal Science Advances.

«We tried to find the «magic» number of people who must at the same time to go over the bridge to the suddenly began to «dance». To achieve this level swing bridge will not be visible to the public, but after her swing sharply increase», — says Igor Belykh from Georgia state University in Atlanta (USA).

The so-called «dancing» bridges are well known to the public since the construction of the first metal structures of this kind in the late 19th and early 20th century and trying to pass by foot or on horse formation on their surface. Almost immediately, the naturalists and scientists of that time identified the reason why the bridges suddenly begin «to shake» and fall.

As it turned out, drill March, or any other synchronized movement of the feet of men and horses, as well as the wind gusts in some cases can cause a powerful resonant vibrations, similar to how the swing starts to swing harder, if you exert force on them at the right time. To get rid of these oscillations is quite simple – you can not just synchronize the movement of vehicles or pedestrians, or to install a special damper on the bridge.

Igor Belykh and his colleagues from the Volga state University of water transport, Nizhny Novgorod state University thought about the solution of the inverse problem – how many people need in order to make the bridge to «dance»?

To solve this mystery, scientists have turned to the most famous example of the «dancing» designs of this sort of debacle with the opening of the Millennium bridge in London in June 2000. His case, as the authors of the article, it is interesting that pedestrians, forcing the bridge to swing, not specifically synchronized her movement and walked across its surface is absolutely random.

However, the bridge still began to stagger, and the Russian and American mathematicians have tried to find out why it happened, creating a mathematical and computer model of how a large mass of people moving through a virtual bridge. Each person in this model had its own gait, the speed and manner of movement on the bridge that imitated the erratic movement of pedestrians on the surface of the «Millennium» on the day of its opening.

These calculations revealed some interesting properties of such «dancing» bridges. For example, it was found that there is a «magic number» of people on a similar design, at which the bridge starts to wobble dramatically. For example, for the London «Millennium» it is 165 pedestrians, and for other designs it can be less or more depending on the type and size of the bridge.

This computer model, as noted by the authors, can help bridge designers to avoid similar problems in the future, and prevent the development of situations such as the fiasco with the «Millennium» or the Russian «sister», the Volgograd bridge, open and immediately closed for reconstruction in 2010 due to powerful resonance of the vibrations generated by the winds.