Abstract
The nonlinear aeroelastic behavior of suspension bridges, undergoing dynamical in-plain instability (galloping), is analyzed. A nonlinear continuous model of bridge is formulated, made of a visco-elastic beam and a parabolic cable, connected each other by axially rigid suspenders, continuously distributed. The structure is loaded by a uniform wind flow which acts normally to the bridge plane. Both external and internal damping are accounted for the structure, according to the Kelvin-Voigt rheological model. The nonlinear aeroelastic effects are evaluated via the quasi-static theory, while structural nonlinearities are not taken into account. First, the free dynamics of the undamped bridge are addressed, and the natural modes determined. Then, the nonlinear equations ruling the dynamics of the aeroelastic system, close to the bifurcation point, are tackled by the Multiple Scale Method. This is directly applied to the partial differential equations, and provides the finite-dimensional bifurcation equations. From these latter, the limit-cycle amplitude and its stability are evaluated as function of the mean wind velocity. A case study of suspension bridge is analyzed.
Highlights
Suspension bridges are long, slender and flexible structures which are very sensitive to dynamic actions induced by wind, which potentially cause a variety of instability phenomena
Most of the studies about the aerodynamic instability of the bridge were devoted to flutter phenomena, according to which the aeroelastic instability involves two coalescent modes, one torsional, the other flexural. This is the case of bridges with low torsional stiffness, for which the natural torsional and flexural frequencies are close each other, prone to coalesce under aerodynamic excitation
An hysteresis can occur for wind velocity periodically changed. Such a behaviour is related to the opposite signs of the aerodynamic coefficients, b3 and b5, causing a change of the qualitative behaviour of the system, namely: (i) at small amplitudes the cubic terms in the motion Equation (8) prevails over the quintic term; (ii) at higher amplitudes, the opposite occurs
Summary
Suspension bridges are long, slender and flexible structures which are very sensitive to dynamic actions induced by wind, which potentially cause a variety of instability phenomena. In [25], a numerical method for full-bridge aeroelasticity is presented, based on unsteady cross-sectional wind loads and on the finite-element modeling of the structure. Most of the studies about the aerodynamic instability of the bridge were devoted to flutter phenomena, according to which the aeroelastic instability involves two coalescent modes, one torsional, the other flexural This is the case of bridges with low torsional stiffness, for which the natural torsional and flexural frequencies are close each other, prone to coalesce under aerodynamic excitation. A simple continuous model of suspension bridge, subjected to steady wind flow, is proposed to analyze the aeroelastic in-plain instability (galloping). An Appendix A, containing details about damping parameter identification, closes the paper
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