An instability result in the theory of suspension bridges. (July 2016)

• Record Type: Journal Article
• Authors: Marchionna, Clelia; Panizzi, Stefano
• Is Part Of: Nonlinear analysis. Volume 140(2016)
• Page Start: 12
• Page End: 28
• Publication Date: 2016-07
• Subjects: primary 37C75 -- secondary 35G31 34C15; Suspension bridges -- Torsional instability -- Poincaré map -- Hill equation; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2016.03.003
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We consider a second order system of two ODEs which arises as a single mode Galerkin projection of the so-called fish-bone (Berchio and Gazzola, 2015) model of suspension bridges. The two unknowns represent flexural and torsional modes of vibration of the deck of the bridge. The elastic response of the cables is supposed to be asymptotically linear under traction, and asymptotically constant when compressed (a generalization of the slackening regime). We establish a condition depending on a set of 3 parameters under which the flexural motions are unstable provided the energy is sufficiently large.