Why does the Millennium Bridge shake?

Steve Strogatz is always interested in resonance. So when Cornell University's professor of applied mechanics and theory learned that thousands of pedestrians made the Millennium Bridge in London swing from side to side on the day of its inauguration. City, he noticed.

Before the bridge across the River Thames was inaugurated, designers praised it as " a basic model of construction structure ". Engineers call it " a perfect message of our ability at the threshold of the 21st century ".

Millennium Bridge in London.

But what happened on the opening day of the bridge was the subject of Strogatz's article.

The Millennium Bridge, a 320 meter long suspension bridge, connects London's financial district with Bankside, south of the River Thames, inaugurated on June 10, 2000. Thousands of pedestrians rushed to the new building.

First, the bridge stands still. But then it started to wobble, very light. Almost after that, pray to shake the team. And all of a sudden, everyone was walking like a skater trying to move, they were wide-legged, pushing their bodies to the side with each step. Left, right, left, right, almost evenly spaced.

The resonance is almost unconscious. But it was these unintentional steps, Strogatz said, that the $ 32 million worth of achievement became a silly performance. The bridge was closed almost immediately.

Strogatz said the problem lies in the mass effect as well as the bridge's architecture.

The Millennium Bridge exceeds the standard for heavy load and wind resistance. In addition, all non-human factors are examined. But instead of focusing on structure, Strogatz examines strange phenomena when people accidentally cooperate with each other, which is simply by walking.

It has been known for many years that the story of a team of soldiers marching on a bridge could create a vertical resonance force enough to destroy it. Therefore, the mandatory standard for soldiers is not to walk evenly when crossing any bridge.

But the problem with the Millennium Bridge is not exactly the same. Strogatz said in this case, oscillating horizontally, not vertically. More importantly, there are only pedestrians on the bridge. No one tried to walk evenly: they only did so to adapt to the strange vibrations of the bridge at their feet.

But what happens first, the vibration of the bridge or the rhythm of resonance? And what makes the system start first ?.

" That's the problem with eggs - chicken, what comes first ," Strogatz said. From the beginning, the bridge had two elements against it: It was designed to be a flexible structure, and its natural frequency coincided with human steps. From there, just a relatively small group of people would pass enough to activate the swaying phenomenon.

" If people initially go free and randomly, some of them happen to resonate in the footsteps, the bridge will become unstable, " he said. With a certain amount of critical walking, wobbling vibrations will become strong enough to force everyone to stride equally, adding to the seriousness of the problem.

Those critical pedestrians - tested later on the Millennium Bridge, by Strogatz and independently analyzed - are only 160. While the number of people crossing the bridge on the inauguration day is estimated at up to 80,000, and at any given time, up to 2,000 people passed through it.

" I'm not a construction engineer. I don't know anything about bridges, " Strogatz said - " what I know is the mass effect ."

The Millennium Bridge was reopened in 2002 after engineers attached it to 91 oscillators to absorb both horizontal and vertical vibrations. This repair cost about $ 8.9 million.

If Strogatz's analysis is correct - " and we hope someone will check ," he said - engineers can use it to prevent such costly and potentially dangerous failures right from head. " They can solve the problem before building it ." Strogatz said.

T. An ( according to Physorg )