A "deformable section" model for the dynamics of suspension bridges -Part II: Nonlinear analysis and large amplitude oscillations

The classical two-degree-of-freedom (2-d-o-f) "sectional model" is of common use to study the dynamics of suspension bridges. It takes into account the first pair of vertical and torsional modes of the bridge and describes well global oscillations caused by wind actions on the deck, yielding very useful information on the overall behaviour and the aerodynamic and aeroelastic response; however, it does not consider relative oscillations between main cables and deck. On the contrary, the 4-d-o-f model described in the two Parts of this paper includes longitudinal deformability of the hangers (assumed linear elastic in tension and unable to react in compression) and thus allows to take into account not only global oscillations, but also relative oscillations between main cables and deck. In particular, when the hangers go slack, large nonlinear oscillations are possible; if the hangers remain taut, the oscillations remain small and essentially linear: the latter behaviour has been the specific object of Part I (Sepe and Augusti 2001), while the present Part II investigates the nonlinear behaviour (coexisting large and/or small amplitude oscillations) under harmonic actions on the cables and/or on the deck, such as might be generated by vortex shedding. Because of the discontinuities and strong nonlinearity of the governing equations, the response has been investigated numerically. The results obtained for sample values of mechanical and forcing parameters seems to confirm that relative oscillations cannot a priori be excluded for very long span bridges under wind-induced loads, and they can stimulate a discussion on the actual possibility of such phenomena.