Sometimes to the detriment of the hedge fund managers and penthouse denizens on on the top floors, a skyscraper can wobble and sway due to wind and earthquakes. In most cases, the movement is not enough to threaten the safety of the building itself, but it can be profoundly uncomfortable to its occupants. I built this model to demonstrate a popular solution to this unwelcome vacillation: the tuned mass damper. This is a great demo if you're doing a career day, science fair, or personal engineering project.
Rough Parts List:
- Small cart with smooth wheels (I built mine out of plywood and actobotics parts).
- Four 3/8" dowels about 36" long
- Small bungee cord
- For the pendulum damper, again I used actobotics.
- 1/8" steel shaft
- 1/8" clamping shaft collar
- 1/8" to 3/16" shaft coupler
- Small aluminum angle bracket
- #6 bolt with nylock nut
Step 1: Constructing the Model
A rough sketch of the model is shown above. You really just need something that wobbles, so use whatever scrap wood you have on hand. A couple of important points:
- I recommend adding braces between the front and back dowels. This will help constrain the wobbling to just the X-axis where you will be measuring. Otherwise you might get some swaying front to back which will muddy your results.
- I added a bungee cord and stopper to give a consistent "bump" to the structure. You may be able to save yourself the trouble of this whole part by just mounting the structure to a sturdy base and "plucking" it like a guitar string to get it started swaying. It would be much simpler, but I'm not sure if you could do it consistently.
Googly eyes are optional.
Step 2: Adding the Accelerometer
I used the ADXL345 triple-axis accelerometer breakout from Sparkfun. They have a great tutorial with everything you need to get this thing running on an Arduino, including code and wiring diagram. I used the Sparkfun "Basic Arduino Code," but just modified it to provide only the data from the X-axis of the accelerometer.
The ADXL345 is actually not supposed to run on the 5 volt logic that the Arduino uses. You should use a logic level converter between the arduino and the accelerometer. The tutorial doesn't mention this. I used current limiting resistors between the connections, which is not ideal, but is better than nothing for protection the board against damage from the 5v logic.
The code provided by Sparkfun just outputs the accelerometer values to serial. With the new Arduino software, you can use the "plot serial" and get a live graph of the output straight to your computer.
Step 3: Performing the Demonstration
The basic steps for the demonstration are as follows:
- Lock the pendulum from swinging and set the building swaying. The accelerometer data will show the peak amplitude and the slow decay of the motion.
- Calculate the building's natural period by measuring the time between two peaks on the graph.
- Calculate how long your pendulum needs to be to match the building's natural period.
- Loosen the screw on the pendulum so that it can swing but not freely. You want the pendulum to stop swinging after only one or two periods if you start it with your hand. This confirms that the pendulum is "damping."
- Set the building swaying again. Some of the kinetic energy should be transferred into the pendulum which dampens the motion. The motion should decay much quicker.
- If the pendulum is not damping enough, it will transfer the kinetic energy back into the building (see the last figure above). You don't want this, since it would make for a wild ride for our topmost tenants.
- You can use the logarithmic decrement equations to calculate the damping ratio for the two examples. I recommend using the amplitude from the first and second peaks, since this is where you will see the most damping from the pendulum.
If you have any questions, check out the YouTube video linked in the description, or visit my website Practical Engineering to learn more. Thanks for taking a look!