Simple and double Hopf bifurcations in aeroelastic oscillators with tuned mass dampers

The effects of an added mass on the oscillations of a SDOF bluff body, elastically supported, exposed to a steady flow and undergoing galloping oscillations, are investigated. The stability boundaries of the trivial equilibrium position of the 2DOF system are determined in a four parameters space. The occurrence of different types of bifurcation on these boundaries is highlighted, namely, simple Hopf, non-resonant double Hopf and 1 : 1 resonant double Hopf. The perturbation multiple scale method is employed to analyze the system postcritical behavior around the codimension-1 and codimension-2 critical manifolds. The analytical results are compared with numerical solutions obtained through direct integration of the equations of motion. Finally, the effects of the closeness of the critical frequencies on the non-resonant double Hopf manifold, are discussed by using a quasi-resonant asymptotic solutions.