1:1 resonant Hopf bifurcations in slender space structures with tuned mass dampers

The effects of a tunable added mass on the aeroelastic stability of a SDOF bluff body exposed to a steady flow are investigated. The model captures the essential aspects of the behavior of flexible structures equipped with Tuned Mass Dampers orbiting at low position in the rare atmosphere. The system exhibits simple as well double Hopf bifurcations, of nonresonant and 1:1 resonant type. The occurrence of different types of bifurcations in the parameter space is discussed, and the Multiple Scale Method is employed to obtain a bifurcation equation in the complex amplitude of motion. Preliminary numerical results are drawn by numerically integrating this evolution equation. Steady solutions are compared with extract numerical results and asymptotic solutions previously obtained.