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耦合共振现象

已有 8879 次阅读 2010-5-29 10:08 |个人分类:复杂系统|系统分类:科研笔记| 共振

塔科马海峡吊桥蛇形共振

起因为该桥梁设计成长带状,且未考虑其处于入海口处受到大风的影响,最终导致建成的桥梁在风荷载下产生耦合共振,最终坍塌

http://www.tudou.com/v/r2VCx3alZuU/v.swf

 

http://www.tudou.com/programs/view/r2VCx3alZuU/

 

实际上,历史上并不是只出现了在风荷载下桥梁共振引起坍塌的案例。在英国为迎接新世纪的到来而建立的千禧大桥也曾因大量行人在其上步行导致共振而关闭。

下面是转载自ScienceDaily上对于千禧大桥共振的分析文章:

Explaining Why The Millennium Bridge Wobbled

From: http://www.sciencedaily.com/releases/2005/11/051103080801.htm

ScienceDaily (Nov. 3, 2005) — Steve Strogatz has a penchant for things that happen in unison. So when the Cornell University professor of theoretical and applied mechanics (and author of the 2003 book "Sync: The Emerging Science of Spontaneous Order") heard that thousands of pedestrians had caused London's Millennium Bridge to rock from side to side on its opening day, he was intrigued.

 

Before the bridge across the River Thames opened, designers hailed it as "a pure expression of engineering structure." They compared its sleek look to a blade of light. Engineers called it "an absolute statement of our capabilities at the beginning of the 21st century."

But it's what happened on opening day that is the subject of Strogatz' Nov. 3 Nature paper.

The Millennium Bridge, a 320-meter-long lateral suspension bridge connecting London's financial district to Bankside, south of the river, opened June 10, 2000. Thousands of pedestrians streamed over it.

At first, the bridge was still. Then it began to sway, just slightly.

Then, almost from one moment to the next, the wobble intensified. And suddenly, people were walking like tentative ice skaters: planting their feet wide, pushing out to the side with each step. Left, right, left, right, in near-perfect unison.

The synchrony was utterly unintentional. But it was those unchoreographed footfalls, says Strogatz, that were responsible for turning a $32 million design triumph into a very embarrassing engineering quandary. The bridge was closed almost immediately.

Strogatz, who has studied the collective behavior of biological oscillators from neurons to fireflies, describes each of the factors that contributed to the bridge's swaying in his paper. Cornell graduate student Daniel Abrams is one of the paper's co-authors.

The problem, says Strogatz, was one of crowd dynamics as much as engineering. The bridge surpassed standards for withstanding weight and wind. Every nonhuman element had been tested.

Instead of focusing on the structure, Strogatz examines the strange phenomenon of people unknowingly working together, simply by walking.

The military has known for years that troops marching in step can create enough vertical force to destroy a bridge. It is standard practice for soldiers to break step at every bridge crossing.

But the Millennium Bridge problem is not quite the same, says Strogatz. In this case, the movement was lateral, not vertical. More importantly, the people were just pedestrians. No one was trying to walk in step; pedestrians did so only to accommodate the bridge's movement under their feet.

But which came first, the bridge's movement or the synchronous strides? And what set the whole thing off?

"It's a chicken-and-egg problem," says Strogatz. "That's what our paper explains." From the beginning, the bridge had two factors working against it: It was by design a flexible structure, and its natural frequency is close to that of human walking. From there, Strogatz says, all it needed was a relatively small crowd to spark the wobble.

"If the people are initially disorganized and random, if a few of them get into sync by accident, the bridge would become unstable," he says. With a certain critical number of pedestrians, the wobbling becomes marked enough to force everyone into stride -- thus compounding the problem.

And the critical number of pedestrians, tested subsequently on the Millennium Bridge and derived independently by Strogatz and co-authors, is as low as 160. An estimated 80,000 people crossed the bridge on opening day, with as many as 2,000 on it at any one time.

"I'm not a civil engineer. I know nothing about bridges," says Strogatz. "What I do know is group behavior. That was our contribution."

The Millennium Bridge reopened in 2002 after engineers fitted it with 91 dampers to absorb both lateral and vertical oscillations. The modifications cost about $8.9 million.

If Strogatz' analysis is correct -- "and we hope someone will test it," he says -- engineers will be able to use it to prevent such expensive, embarrassing and possibly dangerous fiascos in the first place.

"They could solve the problem before they build it," says Strogatz. "That's what this theory will do."

In addition to Abrams, the paper, "Crowd Synchrony on the Millennium Bridge," was authored by Allan McRobie of the University of Cambridge; Bruno Eckhardt of Fachbereich Physik, Philipps-Universität, Marburg, Germany; and Edward Ott of the University of Maryland. Eckhardt and Ott solved the problem independently for the same result.

与此相关的文章还有:

Why Did The London Millennium Bridge 'Wobble'?

From:http://www.sciencedaily.com/releases/2008/12/081216201406.htm

ScienceDaily (Dec. 18, 2008) — On its opening day, the London Millennium Bridge experienced unexpected swaying due to the large number of people crossing it. A new study finally explains the Millennium Bridge 'wobble' by looking at how humans stay balanced while walking.

The same pedestrian-structure interaction has also been identified on several other bridges, including Bristol's famous Clifton Suspension Bridge. The phenomenon is not related to the structural form of the bridge, but rather the behaviour of the pedestrians. The paper by civil engineers at the University of Bristol, published in the Royal Society journal Proceedings of the Royal Society A, examines the basic way humans maintain balance.

Balance is achieved by changing the position of foot placement for each step, based only on the final displacement and speed of the centre of mass from the previous step.

The same balance strategy as for normal walking on a stationary surface was applied to walking on a laterally swaying bridge.

Without altering their pacing frequency, averaged over a large number of cycles, the pedestrian can effectively act as a negative damper to the bridge motion, which may be at different frequency. Hence the pedestrian can inadvertently feed energy into bridge oscillations.

Dr John Macdonald, Senior Lecturer in Civil Engineering, said: "It is clear that the motion of the bridge affects the force from the pedestrian, rather than the pedestrian simply applying an external force."

It has generally been thought the Millennium Bridge 'wobble' was due to pedestrians synchronizing their footsteps with the bridge motion. However, this is not supported by measurements of the phenomenon on other bridges.

The researchers found, to their surprise, that pedestrians walking randomly, keeping balance as normal can cause large bridge sway. This finally seems to explain the initiation of the Millennium Bridge 'wobble' and gives new insight for designing bridges to avoid vibration problems.

这些分析表明了行人的微观运动特征是引起耦合共振的基本原因。



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