Stability of two-degrees-of-freedom aero-elastic models with frequency and time variable parametric self-induced forces

• The paper combines neutral and flutter derivatives models on one common basis.
• It establishes linkage between these models to avoid the time–frequency duality.
• Stability is analysed by generalized Routh–Hurwitz approach and Liènard theorems.
• Examples of bridge stability analyses are compared with experiment and literature.

The lowest critical state of slender systems representing long suspension bridges can be investigated using two degree of freedom linear models. Initially, the neutral model with aero-elastic forces treated as constants can be used and such approach works well on the theoretical level. However, because time dependency is neglected, it is naturally limited to the very close neighbourhood of the bifurcation point. Thus, an approach using aero-elastic coefficients known as flutter derivatives was introduced in the past. The present paper combines these models together on one common basis and establishes linkage to avoid the time–frequency duality. The stability limits are analysed by means of the generalized Routh–Hurwitz approach and Liénard theorems. Some examples of bridge stability analyses are provided using experimentally ascertained or literature based data.