Experimental Analysis of the Bifurcation Behaviour of a Bridge Deck Undergoing Across-Wind Galloping

The phenomenon of aeroelastic galloping is a very important design consideration for bridges and other slender structures. It has been investigated by a number of researchers but, most frequently, the analysis is limited to quasi-steady aerodynamic and linearized aeroelastic considerations. Such treatment has been shown to be effective for simple cross-sectional shapes, such as rectangles. In this work, an aeroelastic model of a realistic bridge deck cross-section is tested in a low speed wind tunnel. Both static and dynamic tests are carried out and the resulting force and vibration measurements are presented. The static force results are used to set up a quasi-steady mathematical model. The dynamic responses are used to draw a complete bifurcation diagram within a chosen airspeed range and to discuss the stability of the system. It is shown that the experimental system undergoes a subcritical Hopf bifurcation, its phase space including both a stable and an unstable limit cycle. As consequence, throughout the chosen airspeed, the system can either remain stable or undergo limit cycle oscillations. The quasi-steady analysis fails completely in capturing this type of behaviour. The predicted galloping onset speed is too conservative and the predicted oscillation amplitudes too high. The reason for this failure is the fact that the quasi-steady mathematical model is incapable of modelling subcritical Hopf bifurcations.