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Simulation of the Dynamics of a Folding Bridge

 2 years ago
source link: https://spieswl.github.io/projects/2017/folding-bridge-dynamics-simulation
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December 12, 2017

Simulation of the Dynamics of a Folding Bridge

This one is a cute little project.

Around the end of the Fall 2017 term at Northwestern, I put together a workbook in Wolfram Mathematica 11 with the intent to try and recreate the dynamics of the Hörn bridge in Kiel, Germany. This bridge is well-known for its elegant design and unique opening and closing behavior, so I opted to try and recreate how the bridge opens and closes as a project for my Machine Dynamics class with Todd Murphey. Thanks to its prestige as a unique example of bridge engineering, there was a higher-than-average amount of technical literature available on the Hörn bridge’s design. In turn, this gave me some much-needed insight into the physics of the bridge and how it unfolds. From there, it was all about coding and execution in Mathematica.

The Mathematica project notebook evolved through three different stages:

  • Initial problem setup & physical characterization
  • Finding the correct constraints on the bridge’s operation
  • Modeling the impact condition and attempting some form of control over the bridge’s action

The final form of the project is an animation of the bridge unfolding under the effects of gravity and experiencing an impact on the far side pylon. I implemented some basic controls, mostly so that the framework would exist should I choose to return later and install active controls law sufficient to safely deploy the bridge. At the time the project was submitted, it could only delay (or accelerate) the opening of the bridge under gravity, which then results in a hard collision on the farthest pylon. For the purposes of getting some meaningful data out of the simulation, I made sure to take a reading of the velocity experienced at the end of the final leaf at the moment of impact. After having taken that reading, it’s safe to conclude that the simulated bridge hits far too hard to be considered “safe” to just let gravity act on the bridge.

This project was an incredible amount of fun to work on. For those who would be interested in expanding on the foundations of the dynamic simulation already in place, or those curious to see an example of how I structured the evaluation and animation components, the source code for the project is available on GitHub!

BONUS: Here’s a GIF of the animation in action.


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