2015/02/20 by Elvise Berchio, E. Berchio, A. Ferrero +6 · 2 citations
Computer Science · Engineering · Mathematics · Physics and Astronomy · #35A15 #35C10 #35G31 #35L76 #74B20 #74K20 #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #Vibration and Dynamic Analysis #math.AP #msc:35A15 #msc:35C10 #msc:35G31 #msc:35L76 #msc:74B20 #msc:74K20
paper · pdf · doi:10.48550/arxiv.1502.05851
33 pages
arxiv created 2015/02/20 · openalex publication_date 2015/02/20 · arxiv updated 2015/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We model the roadway of a suspension bridge as a thin rectangular plate and we study in detail its oscillating modes. The plate is assumed to be hinged on its short edges and free on its long edges. Two different kinds of oscillating modes are found: longitudinal modes and torsional modes. Then we analyze a fourth order hyperbolic equation describing the dynamics of the bridge. In order to emphasize the structural behavior we consider an isolated equation with no forcing and damping. Due to the nonlinear behavior of the cables and hangers, a structural instability appears. With a finite dimensional approximation we prove that the system remains stable at low energies while numerical results show that for larger energies the system becomes unstable. We analyze the energy thresholds of instability and we show that the model allows to give answers to several questions left open by the Tacoma collapse in 1940.