A deformable section model for the dynamics of suspension bridges. Part I:Model and linear response

The classical two-degree-of-freedom (2-d-o-f) "sectional model" is currentl y used to study the dynamics of suspension bridges. Taking into account the first pair of vertical and torsional modes of the bridge, it describes wel l global oscillations caused by wind actions on the deck and yields very us eful information on the overall behaviour and the aerodynamic and aeroelast ic response, but does not consider relative oscillation between main cables and deck. The possibility of taking into account these relative oscillatio ns, that can become significant for very long span bridges, is the main pur pose of the 4-d-o-f model, proposed by the Authors in previous papers and f ully developed here. Longitudinal deformability of the hangers (assumed lin ear elastic in tension and unable to react in compression) and external loa ding on the cables are taken into account: thus not only global oscillation s, but also relative oscillations between cables and deck can be described. When the hangers go slack, large nonlinear oscillations are possible; if t he hangers remain taut, the oscillations are small and essentially Linear. This paper describes the model proposed for small and large oscillations, a nd investigates in detail the limit condition for linear response under har monic actions on the cables (e.g., like those that could be generated by vo rtex shedding). These results are sufficient to state that, with geometric and mechanical parameters in a range corresponding to realistic cases of la rge span suspension bridges, large relative oscillations between main cable s and deck cannot be excluded, and therefore should not be neglected in the design. Forthcoming papers will investigate more general cases of loading and dynamic response of the model.