Static and aeroelastic limit states of the "Bridge of Sound" via a fully nonlinear continuum model

A parametric three-dimensional model of an arch bridge under fairly general static and dynamic loading conditions is proposed. The arch bridge geometry is parameterized in such a way that it also allows to account for generic inclinations of the arches with respect to the vertical configuration. By employing an exact kinematic formulation, the strain parameters are expressed as nonlinear functions of the displacement gradients and all deformation modes are considered, including shear, torsional and out-of-plane bending modes, both in the deck and supporting arches. The nonlinear equations of motion are obtained via a direct total Lagrangian formulation by adopting linearly hyperelastic constitutive equations for all structural members. The parametric nonlinear model, constructed for the specific case of Ponte della Musica in Rome, is employed to investigate the limit states appearing either as a limit point through path-following the response along the prescribed loading path or as the critical condition of a suitable eigenvalue problem associated with the equations of motion linearized about the in-service pre-stressed bridge configuration subject to the dead loads and wind forces. The proposed model takes into account the fully nonlinear extensionalflexural- torsional coupling and examines the aeroelastic effects induced by the wind forces with special attention to the calculation of the flutter speed and critical flutter mode shape.