An instability result in the theory of suspension bridges

DOI10.1016/j.na.2016.03.003zbMath1359.37056OpenAlexW2323420345MaRDI QIDQ276714

Clelia Marchionna, Stefano Panizzi

Publication date: 4 May 2016

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/11311/980246

zbMATH Keywords

suspension bridgesPoincaré mapHill equationtorsional instability

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Stability theory for smooth dynamical systems (37C75) Strings (74K05) Nonlinear resonances for nonlinear problems in mechanics (70K30) Initial-boundary value problems for systems of nonlinear higher-order PDEs (35G61) Initial-boundary value problems for nonlinear higher-order PDEs (35G31)

Related Items (5)

An Instability Result for Suspension Bridges ⋮ Existence of torsional solitons in a beam model of suspension bridge ⋮ Transfer of energy from flexural to torsional modes for the fish-bone suspension bridge model ⋮ Instability results for a Hill equation coupled with an asymmetrically nonlinear oscillator ⋮ On the instability tongues of the Hill equation coupled with a conservative nonlinear oscillator

Cites Work

• Nonlinear oscillations in a suspension bridge
• Existence and stability of large scale nonlinear oscillations in suspension bridges
• Coupled string-beam equations as a model of suspension bridges.
• Unstable simple modes for a class of Kirchhoff equations
• Mathematical models for suspension bridges. Nonlinear structural instability
• A new mathematical explanation of what triggered the catastrophic torsional mode of the tacoma narrows bridge
• A qualitative explanation of the origin of torsional instability in suspension bridges
• Continuous parameter dependence in linear systems of differential equations
• Large Torsional Oscillations in Suspension Bridges Visited Again: Vertical Forcing Creates Torsional Response
• Large Torsional Oscillations in a Suspension Bridge: Multiple Periodic Solutions to a Nonlinear Wave Equation
• Unstable simple modes of the nonlinear string
• Large-Amplitude Periodic Oscillations in Suspension Bridges: Some New Connections with Nonlinear Analysis
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