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

We study two systems of nonlinearly coupled ordinary differentialequations that govern the vertical and torsional motions ofa cross-section of a suspension bridge. We observe numericallythat the structure of the set of periodic solutions changesconsiderably when we smooth the nonlinear terms. The smoothednonlinearities describe the force that we wish to model morerealistically and the resulting periodic solutions more accuratelyreplicate the phenomena observed at the Tacoma Narrows Bridgeon the day of its collapse. The main conclusion is that purelyvertical periodic forcing can result in subharmonic primarilytorsional motion.