| MadSci Network: Engineering |
Boy, I wish I could see that video. I did a search for it, and did find some good sources on resonance in bridges: http://www.answers.com/topic/resonance?cat http://www.youtube.com/watch?v=j-zczJXSxnw Rest assured that a cat can walk across the George Washington bridge with impunity; she isn't going to cause it to resonate enough to cause failure. First, the resonance frequency of a large bridge is going to be fairly low. Like a pendulum, the frequency of oscillation will be longer the greater the span of the bridge is. So, while the idea that a small amount of energy applied at just the right time will cause a structure to vibrate with increasing amplitude, ie resonate, a cat trotting is going to be too fast. Second, a cat masses 10 pounds or so, while the bridge masses hundreds of tons. The weight of the cat is not going to affect the bridge at all. Third, there are lots of energy-damping systems in a bridge, so even if considerable energy is introduced (a mob of tigers walking in step was suggested by the madSci moderator) localized resonances might be started, but they would almost certainly be damped out before setting the entire bridge to vibrating. Of course, there have been instances of bridge resonance due to live loading. The story of the company of soldiers bringing down a bridge by walking over it in step is based on an actual incident: http://en.wikipedia.org/wiki/Angers_Bridge Ever since, soldiers have been ordered to break step while crossing a bridge; they most likely didn't have to, but it didn't hurt anything. More recently, the footbridge over the Thames in London had to be closed due to alarming vibration under foot traffic. After the design engineers looked at it and ran some computer analysies, it was determined that there was no danger. The interesting part of this was that groups of pedestrians, walking across the bridge, tended to fall into step because the mild vibrations of the bridge subtily encouraged them to. Soon total strangers were marching in step, at the resonance frequency of the bridge! The engineers installed energy absoprbing dampers, and the vibrations ceased. http://advance.uconn.edu/2001/011001/01100109.htm http://en.wikipedia.org/wiki/Millennium_Bridge_(London)
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