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Multiple periodic oscillations in a nonlinear suspension bridge system. (English) Zbl 1003.35089

Summary: We study periodic oscillations in a suspension bridge system governed by the coupled nonlinear wave and beam equations describing oscillations in the supporting cable and roadbed under periodic external forces. By applying a variational reduction method, it is proved that the suspension bridge system has at least three periodic oscillations.

MSC:

35L70 Second-order nonlinear hyperbolic equations
35B10 Periodic solutions to PDEs
74H45 Vibrations in dynamical problems in solid mechanics
35L20 Initial-boundary value problems for second-order hyperbolic equations
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
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