Existence of torsional solitons in a beam model of suspension bridge

Abstract

This paper studies the existence of solitons, namely stable solitary waves, in a suspension bridge. The bridge is modeled as a degenerate plate, that is, a central beam with cross sections, and displays two degrees of freedom: the vertical displacement of the beam and the torsional angles of the cross sections. Under fairy general assumptions, we prove the existence of solitons. Under the additional assumption of large tension in the sustaining cables, we prove that these solitons have a nontrivial torsional component. This appears relevant for the security since several suspension bridges collapsed due to torsional oscillations.