"Parametric interactions in the nonlinear sectional dynamics of suspended and cable-stayed bridges"

The paper presents a planar multi-body system which synthetically describes the geometrically nonlinear section dynamics of cable-supported bridges, characterized by strong quadratic interactions among the bridge deck and the suspender cables. The linear modal solution, based on a multiparameter perturbation method, defines the parameter combinations which realize remarkable 2:1:1 internal resonance conditions among a global deck mode and a pair of local cable modes. The nonlinear response of resonant systems shows that the global deck motion -- directly forced at primary resonance by an external harmonic load -- can parametrically excite the local cable motion, if the deck vibration amplitude overcomes the critical value at which a period-doubling bifurcation occurs. Both the internal resonance conditions and the critical vibration amplitudes are expressed as an explicit, though asymptotically approximated, function of the structural parameters.