In this project you will study models for the structural failure of the Tacoma Narrows Bridge. Moderate winds caused this bridge to oscillate violently. In November of 1940, some four months after the bridge opened to traffic, the oscillations became so large that the bridge collapsed.

The project explores a sequence of differential equations that model the bridge oscillations. The first equation has an explicit solution. The second equation adds the bridge geometry into the model; numerical analysis is used to verify the large oscillations witnessed at Tacoma Narrows. Finally, more physical assumptions are made about the cables, following McKenna (1999), in order to give a concise explanation for the failure of the bridge.

The models described here appear in a paper by P. J. McKenna (1999). The dynamics of the Tacoma Narrows Bridge have been studied since it collapsed, and small scale oscillations have been understood for some time. However, McKenna and others are still working to understand how large scale oscillations arise and persist. In your project you will get a view of the newest research on this problem.

The details of this project are contained in the following links. Work your way through all the sections and then copy the template and work the six problems therein.

- Introduction
- Small oscillations and engineering analysis
- Large sustained torsional oscillations
- Transferring vertical oscillations into twisting oscillations
- McKenna reference and some WWW links
- Tacoma project, pdf (2250mapleL3a-F2004.pdf) Print this version if you did not get the printed copy in class.
- Maple worksheet (2250mapleL3a-F2004.mws) Shift-Mouse1 to copy this file to disk. Then open in xmaple.