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Large torsional oscillations in a suspension bridge: Multiple periodic solutions to a nonlinear wave equation. (English) Zbl 1018.35007
So far in the mathematical literature there are considered ODE models for the torsional motion of a horizontal cross section of the main span of a suspension bridge and proven the existence of multiple periodic solutions. In this paper the author proposes a PDE model (the forced sine-Gordon equation on a bounded domain) for the torsional motion along the length of the center span. The author proves (under suitable physical assumptions) existence of multiple periodic weak solutions, and then investigates these solutions numerically. Via numerical continuation algorithms the author discusses bifurcation properties of periodic solutions and shows that for small forcing occurs bifurcation from single to multiple solutions. The author shows that the qualitative properties such as amplitude, frequency, and nodal structure of computed solutions are consistent with the behaviour observed at Tacoma Narrows on the day of its collapse.

MSC:
35B10 Periodic solutions to PDEs
35B32 Bifurcations in context of PDEs
35L70 Second-order nonlinear hyperbolic equations
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