Nonlinear interaction between galloping modes

A coupled, nonlinear, flexural two degree-of-freedom model, describing a perfectly flexible elastic suspended cable subject to galloping, is analyzed. By using a perturbative technique, two different critical conditions, corresponding to simple or double Hopf bifurcations, are found for different values of the aerodynamic coefficients. The nonlinear post-critical behavior of single taut strings in 1:1 primary internal resonance is studied through the multiple scale perturbation method. In the double Hopf bifurcation case the important role of the detuning between the critical eigenvalues on the post-critical behavior is highlighted. It is found that quasi-periodic motions, which are likely to occur in the linear field when the two critical frequencies are uncommensurable, are unstable in the nonlinear range. Therefore the postcritical behavior of the string is always characterized by stable periodic motions for any detuning values.