Multiple periodic solutions to a suspension bridge O.D.E.

Abstract

We present an ordinary differential equation which models the torsional motion of a horizontal cross section of a suspension bridge. We use Leray-Schauder degree theory to prove that the undamped equation has multiple periodic weak solutions. We use a numerical continuation algorithm to demonstrate the existence of three periodic solutions (one of small amplitude and two of large amplitude) and to examine the bifurcation properties of the periodic solutions.

Keywords

• Torsional oscillations
• suspension bridge.