Mechanical Resonance: Can Soldiers' March Cause 16 Hz?

[opuktun]

Q: If a bridge has a natural frequency of 16 Hz and assuming that a battalion of soldiers marches across it, will mechanical resonance occur?

Personally, I was quite unclear about the physical implication of "16 Hz". In my interpretation, I feel that to cause a mechanical resonance on the bridge, at a particular spot of that bridge, 16 cycles of march per second is required. But to make a spot to experience these 16 cycles per second is not very possible. Henceforth, I would like to check with the experts out there to see if I have made some errors in understanding.

I would really appreciate some feedback. Thanks! :)

 

[Andy Resnick]

You are forgetting about harmonics: excitations at 2, 4, and 8 Hz will also excite a 16 Hz resonance.

 

[opuktun]

Actually, 16 Hz is the fundamental frequency. Sorry, I did not clarify properly.

 

[TVP45]

Bridge designers commonly check for 2 Hz resonances as that is about what you can expect from foot traffic, even in cadence. I think Henry Petroski has a good section on that in one of his books, though I can't remember which. American Scientist also ran a piece on this within the past twenty years though that might well have just been Petroski again.

 

[TVP45]

By the way, except for that nutty Millenium Footbridge, bridges don't have undamped natural resonances unless somebody screwed up big time.

 

[opuktun]

Bridge designers commonly check for 2 Hz resonances as that is about what you can expect from foot traffic, even in cadence. I think Henry Petroski has a good section on that in one of his books, though I can't remember which. American Scientist also ran a piece on this within the past twenty years though that might well have just been Petroski again.

By the way, except for that nutty Millenium Footbridge, bridges don't have undamped natural resonances unless somebody screwed up big time.

Hi TVP45, thanks for the reply. Well, it's a theoretical question given in my tutorial. But I have not been touching my physics materials for five years? heh :P

 

[TVP45]

And, BTW, designers do screw up. Here in Pittsburgh, a major new bridge span (less than 20 years old) fell off its rocker Thursday. Ouch!