POSTCRITICAL BEHAVIOR OF CABLES UNDERGOING 2 SIMULTANEOUS GALLOPING MODES

A nonlinear two degree-of-freedom model, describing a flexible elastic suspended cable undergoing galloping oscillations, is analyzed. By us ing a perturbative approach, the critical conditions occuring for diff erent values of the aerodynamic coefficients are described. Two differ ent type of critical conditions, corresponding to simple or double Hop f bifurcations are found. The nonlinear postcritical behavior of singl e taut strings in 1:1 primary internal resonance is studied through th e multiple scale perturbation method. In the double Hopf bifurcation c ase the influence of the detuning between the critical eigenvalues on the postcritical behavior is illustrated. It is found that quasi-perio dic motions, which are likely to occur in the linear field when the tw o critical frequencies are incommensurable, are really unstable in the nonlinear range. Therefore, the postcritical behavior of the string c onsists of stable periodic motions for any detuning values.