In many of the world's tallest skyscrapers
there's a secret device protecting not only the building,
but also the people inside from strong motion due to wind and earthquakes.
Did you know you can tune a skyscraper just like a guitar?
Hey I'm Grady
today on Practical Engineering we're comparing theory to the real world
for tuned mass dampers.
*dubstep music plays*
What do a marble in a bowl, a guitar string, and a skyscraper have in common?
Well you're on the wrong YouTube Channel if you think this is a joke. I'm talking about physics.
All three are examples of oscillators.
An oscillator is just a system, that when you displace it from its equilibrium position, it experiences a restoring force.
I move this marble from the center of the bowl. It experiences a force, gravity, pulling it back toward the equilibrium position.
I pull on the guitar string. The tension in the string increases, trying to pull it back to the center.
When the displacing force is released, the system oscillates around the equilibrium point.
What about the skyscraper?
Maybe this sweet montage will help answer that.
*Don't you love that dubstep Music?*
*oh this sweet dubstep *
* it's nearly over don't worry *
Sometimes to the detriment of the hedge fund managers and penthouse denizens on the top floors,
a skyscraper can act as an oscillator, just like the marble and the guitar string.
Wind can induce oscillation in a building just like a tie down strap in a vehicle.
A strong earthquake can also excite the buildings resonant frequency
just like plucking a guitar string.
In most cases the movement's not enough to threaten the safety of the building itself,
but that amount of movement can be profoundly uncomfortable to its occupants.
Most of us hold an intrinsic belief that buildings should not move.
We don't even think about it.
For our entire lives, Wednesdays come after Thursdays, the sun has risen in the East,
and our domiciles and dwellings have remained static beneath our feet.
So you can forgive your subconscious for feeling some amount of terror when such a fundamental belief is shaken,
especially when the shaking is literal.
It may not be enough to harm the building's structure, but it's certainly enough to cause a one-percenter on the top floor to lose his caviar.
And buildings aren't good for much if people don't want to be inside them.
So engineers have come up with some novel solutions for minimizing this unwelcome vacillation.
And I want to talk about one of those today, the tuned mass damper, or TMD.
A TMD reduces the amplitude of vibration by absorbing kinetic energy from the system.
In this case, the swaying motion of a tall building.
For a long time, TMDs were relegated to areas with the rest of the building's mechanical equipment, hidden from public view.
That changed in 2004 when the Taipei 101 tower finished construction in Taiwan.
Rather than hide the world's largest spherical tuned mass damper,
the building's designers chose to open it to the public.
Taipei 101's TMD has become a draw for tourists and
even has its own mascot: the damper baby
which...
looks like it came straight off the island of misfit mascots.
Anyway, the publicity associated with the Taipei 101
has sort of unveiled this really cool bit of engineering that is the tuned mass damper
and you can find tons of videos of it in action online.
So how does it work?
I constructed this model of a pendulum-style tuned mass damper in a skyscraper
I can pull the cart back and give the building a bump
which excites its resonant frequency just like an earthquake or a strong wind event
The benefit here is that I can do it in a somewhat repeatable
fashion so we can evaluate the effectiveness of the damper.
For the TMD, the damping comes from the tension of the screw which is acting as the hinge.
I can tighten the screw to increase the damping.
The tuning comes from moving this mass up or down on the pendulum shaft.
This changes the frequency of the pendulum just like a metronome
which can be tuned to the resonant frequency of the building.
Add an accelerometer on top of the building so we can measure its movements.
And this is hooked to an Arduino which is sending the data to my laptop.
There's more in the description below if you're curious about the data collection.
If I lock the pendulum and set the building swaying,
we can get a sense of how it would perform with only the building's own natural damping.
Plotting the acceleration response, we can see that the model experienced a maximum
amplitude of about four meters per squared second (13.12 ft/s²), or half a 'G'
with a period of 0.6 seconds.
Frequency is the inverse of period, so we can get the building's fundamental frequency:
1.7 hertz.
We can also see that the building has some natural damping just due to the internal friction in its movement.
Otherwise, it would just sway indefinitely.
We can estimate that model's natural damping ratio using the logarithmic decrement.
I get a damping ratio of 0.01.
The damping ratio, denoted by one of the tougher Greek letters to draw: zeta,
is a measure of how quickly the amplitude decays in an oscillating system.
Systems with a damping ratio greater than 1 are said to be over damped
because the system returns to equilibrium without oscillating.
Systems with a damping ratio less than 1 are said to be under damped
since they experience some oscillation.
If the damping ratio is exactly 1
the system is critically damped and returns to equilibrium
as quickly as possible.
And if the system is undamped, the oscillation continues indefinitely.
There are lesser known damping situations, but we wont' get into them in this video.
Now that we know an approximate natural frequency of the building
we can introduce the pendulum damper.
you may remember from you physics classes that a pendulum's frequency depends on its length
for a frequency of around 1.7 Hertz my pendulum needs to be approximately three and a half inches long.
Now let's try the exact same experiment with the pendulum able to swing freely.
The kinetic energy of the building does get transferred to the
pendulum at first but because there's no damping the pendulum transfers the
energy right back into the building so instead of reducing the amplitude,
instead the pendulum just continuously swaps the kinetic energy with the
building like a hot potato. You can only imagine that this erratic behavior would
be even more alarming to our topmost tenants than the steady but slowly
decaying motion of the previous example. Now let's tighten the screw to add some
damping to the pendulum and see what happens even without looking at the data
you can see a remarkable difference in performance. Looking at the plot of
acceleration response we can see that the peak acceleration was about three
and a half meters per square second (11.48 ft/s²) so a reduction of only about twelve percent.
But the big difference is how quickly the motion decays. At the beginning when
the pendulum is swinging, I calculated a damping ratio of over 0.6. That's about
six times more damping than without the TMD. Once the pendulum stops swinging, the
rest of the swing follows the approximate natural damping ratio of the
building itself as expected, but the majority of the kinetic energy has
already been dissipated by the damper,so the amplitude is much lower. Here's a
slow-speed side-by-side so you can really compare the two.
*more dubstep*
As silly as this little experiment looks, it's actually not that far off from what
engineers do in the real world. Usually without the googly eyes. The design phase
for just about every major building includes some physical scale model tests.
Of course a tune mass damper doesn't completely eliminate movement, but we
saw that it can certainly make a difference. In engineering you have
inexpensive, you have effective, and you have innovative, and usually you get to
pick one, sometimes two. For solving the problem of oscillation in tall buildings
though, the tune mass damper is truly all three a great example of elegance in
engineering. I hope you like the first practical engineering video and if you
did I would really appreciate it if you would push that like button and
subscribe to the channel. That helps motivate me to keep making cool stuff. If
you want more details have a question or suggestion for a topic, and especially if
you live or work at the top of a skyscraper, I would really love to hear
from you in the comments. You can also visit my website practical.engineering
to learn more. Thank you for watching and let me know what you think.
Grady Hillhouse 2016