Curve Veering of Eigenvalue Loci of Bridges with Aeroelastic Effects

The eigenvalues of bridges with aeroelastic effects are commonly portrayed in terms of a family of frequency and damping loci as a function of mean wind velocity. Depending on the structural dynamic and aerodynamic characteristics of the bridge, when two frequencies approach one another over a range of wind velocities, their loci tend to repel, thus avoiding an intersection, whereas the mode shapes associated with these two frequencies are exchanged in a rapid but continuous way as if the curves had intersected. This behavior is referred to as the curve veering phenomenon. In this paper, the curve veering of cable-stayed and suspension bridge frequency loci is studied. A perturbation series solution is utilized to estimate the variations of the complex eigenvalues due to small changes in the system parameters and establish the condition under which frequency loci veer, quantified in terms of the difference between adjacent eigenvalues and the level of mode interaction. Prior to the discussion of bridge frequency loci, the curve veering of a two-degree-of-freedom system comprised of a primary structure and tuned mass damper is discussed, which not only provides new insight into the dynamics of this system, but also helps in understanding the veering of bridge frequency loci. To study this more complicated dynamic system, a closed-form solution of a two-degree-of-freedom coupled flutter is obtained, and the underlying physics associated with the heaving branch flutter is discussed in light of the veering of frequency loci. It is demonstrated that the concept of curve veering in bridge frequency loci provides a correct explanation of multimode coupled flutter analysis results for long span bridges and helps to improve understanding of the underlying physics of their aeroelastic behavior.