Response types and general stability conditions of linear aero-elastic system with two degrees-of-freedom

The unified linear variant of the general mathematical description of stability conditions for a girder with a bluff cross-section under the influence of wind flow is presented. A double degree-of-freedom model for the heave and pitch self-excited motion is used. The properties of the response located at the stability limits and the tendencies of the response in their vicinity are analyzed by means of the Routh–Hurwitz theorem. The respective stability conditions are depicted in the frequency plane delimited by the frequencies of two principal aero-elastic modes. Conditions for flutter onset and divergence are identified as special cases of the general theory. The results can be used as an explanation of several experimentally observed effects. The application of this method to real bridges is presented and compared with existing results from other approaches.