The global structure of periodic solutions to a suspension bridge mechanical model

We study two systems of nonlinearly coupled ordinary di erential equations that govern the vertical and torsional motions of a cross section of a suspension bridge. We observe numerically that the structure of the set of periodic solutions changes considerably when we smooth the nonlinear terms. The smoothed nonlinearities describe the force that we wish to model more realistically and the resulting periodic solutions more accurately replicate the phenomena observed at the Tacoma Narrows Bridge on the day of its collapse. The main conclusion is that purely vertical periodic forcing can result in subharmonic primarily torsional motion.