Resonant Periods

[GalileoG]

Why is it that if a building possesses a resonant period similar to the the periodic motions of the ground, the building is more at risk? What if the resonant period is greater or smaller than the periodic motion of the ground, how does that effect the behavior of the structure? What type/size of buildings usually posses a periodic motion similar to that of the ground? Is there a journal/reference that you can refer me to that will aid me in understanding this?

Thanks!

 

[JKStruct]

These questions of structural dynamics are difficult to answer in a forum to give them due justice... but in short --

if the fundamental period (and thus, frequency) of the building is the same as the exciting frequency, resonance can occur. This causes amplification. Have you ever jumped on a trampoline? Have you (or someone else) excited the trampoline so that it vibrates (at it's natural frequency), then you jump at just the right time, and you vault higher in the air (in my child-hood days, we called it "double-bouncing")... that's analogous to resonance. For buildings, this is undesirable.

Period is proportional to mass and inversely proportional to stiffness. The "type or size" of the building that would cause this effect depend on these two things, along with geographical location imparting accelerations of a certain magnitude, along with many other factors.

As for a reference, start with any good structural dynamics book (I'll try to list a few when i get to the office in the morning), and go from there. Good luck!

 

[civeng80]

Probably easier to prove it mathematically, I think a good reference setting up the differential equations is in "Halliday and Resnick Physics".

 

[rtmote]

Matching frequencies give rise to amplifications, moderated by the amount of damping available. If there is no damping then maximum amplitudes and collapse will ensue. It is possible to match frequencies and see no response because there is so much damping. Proving the damping is difficult for buildings. The above ground structural arrangement and construction are key to the building response as the foundation belongs to the ground (unless you isolate these).

But in the foundation, two key terms to think of are low-tuned(typically ground-bearing) or high-tuned(piled) foundations. If a foundation is designed to be high-tuned then vibrations will never be felt above ground as the foundation frequency will be above the ground freqency. If the foundation is low-tuned then at the ground frequency there is minimal and acceptable vibration and even less knowing if damping plays a part. Frequency is a function of the square root of stiffness over the mass. The lateral stiffness of piles add to the frequency.

Frequency responses can be adjusted by fixing the stiffness (going higer)or adding mass (going lower) but don't do both!

A big subject with fantastic references out there.
I recommend Arya and Pincus as an intro to the basics of foundation dynamics before tackling building dynamics. The basic theory is solid, works and is key to everything.

Is your question related to seismic?



Robert Mote

http://www.motagg.com

 

[271828]

Like JKStruct typed, it's all about resonance, which allows unbelievably huge amplifications of motion. I have a great example. I once stood on the end of a very large cantilevered stadium balcony with a metronome and bounced fairly gently (just bend knees, straighten and repeat) at the natural frequency of the balcony. One of my pals was a solid 250' away on the tip and said that the vibrations were borderline scary. He and I were the only people on the balcony and I weigh orders of magnitude less than it weighs.

Chopra's structural dynamics book is a great place to research this stuff. He sticks with easy math. If you get a general vibe book, you'll be swimming (perhaps drowning, depending on your background and determination) in complex numbers in about 2 pages.