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Multistability, basin boundary structure, and chaotic behavior in a suspension bridge model. (English) Zbl 1129.74318

Summary: We consider the dynamics of the first vibrational mode of a suspension bridge, resulting from the coupling between its roadbed (elastic beam) and the hangers, supposed to be one-sided springs which respond only to stretching. The external forcing is due to time-periodic vortices produced by impinging wind on the bridge structure. We have studied some relevant dynamical phenomena in such a system, like periodic and quasiperiodic responses, chaotic motion, and boundary crises. In the weak dissipative limit the dynamics is mainly multistable, presenting a variety of coexisting attractors, both periodic and chaotic, with a highly involved basin of attraction structure.

MSC:

74H45 Vibrations in dynamical problems in solid mechanics
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37N15 Dynamical systems in solid mechanics
70K55 Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics
74H50 Random vibrations in dynamical problems in solid mechanics

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