22. Forced 3D Nonlinear Dynamics of a Hanging Cable Under Multiple Resonance Conditions

The forced, nonlinear, 3D dynamics of an elastic cable is analyzed by means of a reduced 4 d.o.f. model, already obtained several years ago by some of the Authors of this paper. The system is analyzed in the case of multiple internal resonance conditions and a 1:1 external primary resonance condition. The reduced model, because of a strong intrinsic symmetry due to the fact that anti-symmetric in-plane and out-of-plane modes have the same natural frequency (Irvine’s theory), is in principle not able to catch some interesting classes of motion, such as ballooning, which on the other hand have been observed in experimental tests. In the present paper, an imperfection between the equations ruling the in-plane and out-of-plane components is introduced through an internal detuning, which simulates the slight difference between the frequencies of the two involved modes, which is plausible as a consequence of the initial curvature of the cable as well as obtainable through more refined analytical models. A discussion on the similarity and differences with the solutions previously obtained is presented. Regions of non-regular response in the excitation control parameter plane are located and ballooning trajectories are analyzed.