A mathematical model of suspension bridges.
The author considers a one-dimensional nonlinear string-beam system describing the vertical oscillations of a suspension bridge which is coupled with the main cable by the stays. The main cable is modelled as a vibrating string and the roadbed of the bridge is represented by a bending beam with simply supported ends. Using the Galerkin method together with the Leray-Schauder principle, the existence of a weak periodic solution is proved. Moreover, a regularity result is also given under some additional assumptions.
scientific article; zbMATH DE number 5074712