Vibration on a Bridge

​Had this very interesting discussion with Mark Parish yesterday when talking about variable pitch milling cutters. He told me this story of British soldiers breaking stride when crossing a bridge to prevent resonant vibrations that legend has it caused a massive bridge failure in 1831. I found this great article on the subject that explains how the rhythmic marching matched the vibrational frequency of the bridge. However this article leaves out a very important point. The vibration described was self excited and regenerative. It started when the first row of soldiers mounted the bridge. Each succeeding row increased the force applied to the bridge and amplified the vibration until enough rows of soldiers generated enough force that it reached its failure point. In milling, regenerative chatter (AKA regeneration of waviness) leads to tool failure. 

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